modern methods of solving financial problems

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Money Basics  - Financial Problem Solving Strategies

Money basics  -, financial problem solving strategies, money basics financial problem solving strategies.

Money Basics: Financial Problem Solving Strategies

Lesson 2: financial problem solving strategies.

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Financial problem-solving strategies

Have you ever experienced a financial problem? Do you feel like finances are holding you back from reaching your goals? This lesson will give a brief overview of the general problem-solving process and how to apply it to the most common financial problems.

The problem-solving process

First, let's take a look at a general problem-solving process that you can apply to any situation, not just a financial one.

• Identify the problem . The first step in solving a problem is to identify it. What exactly do you need to overcome?
• Make a plan. What are the steps you need to take in order to overcome the problem?
• Implement the plan . This step actually puts the plan you created in place. While it sounds fairly straightforward, this is usually the most difficult step.
• Evaluate the plan . Although this is listed last, this step might actually occur simultaneously with implementing the plan. Things happen and circumstances change, so you may need to re-evaluate your plan as it is happening.

Identifying the problem

The first step in the problem-solving process is to get to the root of the problem and understand what you need to overcome. Here is a list of the most common financial problems people may face:

• Lack of income/job loss
• Unexpected expenses
• Too much debt
• Need for financial independence
• Overspending or lack of budget
• Lack of savings

When thinking about these common problems, each one falls into one of three areas: You need more money, you need to reduce your debt, or you need to change how you spend.

Making a plan

After identifying the problem you need to overcome, it's time to make a plan. Not sure where to start? No worries! We have you covered with some tips and places to begin.

Problem 1: You need more money . Whether you've lost your job, met an unexpected expense, or are working on becoming more financially independent, a form of income is necessary.

If you are a looking for additional work or maybe just a better-paying job, take some time to update your resume and cover letter. Make sure they are neat, up to date with your most current information, and free of spelling and grammar errors.

Be wary of any advertisements or jobs that offer fast, easy money. A lot of quick-cash methods come with unintended consequences. More often than not, if something sounds too good to be true, it probably is.

Problem 2: You need to reduce your debt . With high interest rates or the need to live paycheck to paycheck, high debt can be debilitating. Sometimes it feels like climbing a neverending mountain with an invisible peak. However, by prioritizing and negotiating your debt, you can make it more manageable.

Try listing all of your debt and the interest rates associated with each. Focus on paying off the ones with the highest interest rates first. If you're having trouble making payments, call the loan company and see if it can offer any solutions for you. The company may be able to lower your interest rate or offer a temporary forbearance to help you get back on your feet. If you need more help tackling your debt, you may want to contact a professional debt counselor like Consolidated Credit.

Problem 3: You need to change how you spend . Going from financial problems to a healthy financial status often requires organization and a shift in thinking. Avoiding overspending, building your savings, and gaining financial independence can often be accomplished with good spending habits.

The first thing you may want to try is creating a budget. There are many templates and resources available to help you create one. Sticking to one can be challenging, but simply having a budget laid out can help you see where you need to start spending less.

In addition to your budget, create a savings plan. Start out small. Even stowing away an extra dollar or two here and there can make a big difference. Also, try placing your savings in a place you cannot easily access. For example, create a savings account at a bank you don't usually use. The more difficult it is to access your money, the less likely you are to spend it.

Implementing the plan

Although the explanation of this part is the simplest, this is often the most difficult part to actually execute. It requires self-discipline and perseverance. The most important part of this step is to know that if your plan doesn't work or if you have a difficult time sticking to it, all is not lost. If it happens, move on to the next step, evaluate your plan, then repeat the process.

Overcoming financial obstacles can require changing your lifestyle, and this does not happen overnight. However, just having a plan itself can help to give you confidence and reassurance that you can eventually overcome whatever is in your way.

Evaluating your plan

As you implement your plan, you'll need to continually evaluate it. Maybe something happens and your original plan needs to change. Perhaps you've learned more along the way and realize that your original plan was incomplete. Or maybe your first plan went as planned and was a success. No matter the circumstances, it is always a good idea to look back and re-evaluate. Try answering these questions:

• Was your problem solved? Did a new problem arise?
• What went right?
• What went wrong?
• What circumstances changed?
• Was there anything you didn't account for?
• What was easy about implementing your plan?
• What was difficult about implementing your plan?

Financial obstacles can often seem debilitating and impossible to overcome. They often create a significant source of financial anxiety . We hope this lesson will help give you the confidence to take on your problem one step at a time so you can conquer your anxiety and move forward.

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22 tips for 2022

Life Kit's here to help you start — and continue — this year feeling refreshed, motivated and well cared-for.

22 tips for 2022: Money problems don't just disappear. Here's how to face them

Andee Tagle

Whether you're worried about keeping the lights on or you're feeling the pressure of student debt, financial woes are a heavy mental burden, and it's only natural to try to turn away from them. But avoiding money issues is often at the expense of our longer-term financial — and mental — wellbeing.

To upend problematic money behavior, try doing an audit of your last few money interactions.

Ask yourself questions like, "What felt good or bad? When did you feel like running away? Did avoiding the money problem lead you to a solution?"

"It can be as simple as noticing, you know, "Oh, when I think about money... I go and clean my kitchen," explains Dr. Judson Brewer , psychiatrist and neuroscientist. "And then what's the result of that? Well, I'm not actually getting at whatever the issue is where I need to pay my bills."

Practicing some simple mindfulness by mapping out our money-avoidance patterns can help dispel that anxious energy and help you reset for the future.

Here's more on how to address issues with money.

22 tips for 2022 is edited and curated by Dalia Mortada, Arielle Retting, Janet W. Lee, Beck Harlan, Beth Donovan and Meghan Keane. This tip comes from an episode of Life Kit hosted by Andee Tagle and produced by Sylvie Douglis.

• personal finance
• Life Kit: Money

Modern Heuristics for Finance Problems: A Survey of Selected Methods and Applications

Cite this chapter.

• Frank Schlottmann 3 &
• Detlef Seese 4  

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The high computational complexity of many problems in financial decision-making has prevented the development of time-efficient deterministic solution algorithms so far. At least for some of these problems, e.g., constrained portfolio selection or non-linear time series prediction problems, the results from complexity theory indicate that there is no way to avoid this problem. Due to the practical importance of these problems, we require algorithms for finding optimal or near-optimal solutions within reasonable computing time. Hence, heuristic approaches are an interesting alternative to classical approximation algorithms for such problems. Over the last years many interesting ideas for heuristic approaches were developed and tested for financial decision-making. We present an overview of the relevant methodology, and, some applications that show interesting results for selected problems in finance.

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Schlottmann, F., Seese, D. (2004). Modern Heuristics for Finance Problems: A Survey of Selected Methods and Applications. In: Rachev, S.T. (eds) Handbook of Computational and Numerical Methods in Finance. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8180-7_9

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DOI : https://doi.org/10.1007/978-0-8176-8180-7_9

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Book description

Learn how quantitative models can help fight client problems head-on

Before financial problems can be solved, they need to be fully understood. Since in-depth quantitative modeling techniques are a powerful tool to understanding the drivers associated with financial problems, one would need a solid grasp of these techniques before being able to unlock their full potential of the methods used. In The Mathematics of Financial Models , the author presents real world solutions to the everyday problems facing financial professionals. With interactive tools such as spreadsheets for valuation, pricing, and modeling, this resource combines highly mathematical quantitative analysis with useful, practical methodologies to create an essential guide for investment and risk-management professionals facing modeling issues in insurance, derivatives valuation, and pension benefits, among others. In addition to this, this resource also provides the relevant tools like matrices, calculus, statistics and numerical analysis that are used to build the quantitative methods used.

Financial analysts, investment professionals, risk-management professionals, and graduate students will find applicable information throughout the book, and gain from the self-study exercises and the refresher course on key mathematical topics. Equipped with tips and information, The Mathematics of Financial Models

Provides practical methodologies based on mathematical quantitative analysis to help analysts, investment and risk-management professionals better navigate client issues

Contains interactive tools that demonstrate the power of analysis and modeling

Helps financial professionals become more familiar with the challenges across a range of industries

Includes a mathematics refresher course and plenty of exercises to get readers up to speed

The Mathematics of Financial Models is an in-depth guide that helps readers break through common client financial problems and emerge with clearer strategies for solving issues in the future.

Table of contents

• Acknowledgments
• Why Is This Book Different?
• Road Map of the Book
• Market Instruments
• Linear Interpolation
• Cubic Splining
• Appendix: Finding Swap Rates Using A Floating Coupon Bond Approach
• Black-Scholes Formulae
• Adaptations of the Black-Scholes Formulae
• Limitations of the Black-Scholes Formulae
• Application in Currency Risk Management
• Uniform Number Generation
• Non-Uniform Number Generation
• Applications of Simulations
• Variance Reduction Techniques
• Valuing Path-Independent, European-Style Options on a Single Variable
• Valuing Path-Dependent, European-Style Options on a Single Variable
• Valuing path-Independent, European-Style Options on Two Variables
• Valuing Path-Dependent, European-Style Options on Multiple Variables
• Calibration of Parameters in the Black-Scholes Model
• Using Implied Black-Scholes Volatility Surface and Zero Rate Term Structure to Value Options
• Using Volatility Surface
• Calibration of Interest Rate Option Model Parameters
• Statistical Estimation
• Delta Hedging
• Assumptions Underlying Delta Hedging
• Beyond Delta Hedging
• Testing Hedging Strategies
• Analysis Associated with the Hedging of a European-Style Vanilla Put Option
• Death Benefit Riders
• Other Details Associated with GMDB Products
• Improving Modeling Assumptions
• Living Benefit Riders
• Surrendering a GMAB Rider
• Adding Servers in a Queue
• CHAPTER 10 Parting Thoughts
• About the Author
• About the Website
• End User License Agreement

Product information

• Title: The Mathematics of Financial Models: Solving Real-World Problems with Quantitative Methods
• Author(s): Kannoo Ravindran
• Release date: September 2014
• Publisher(s): Wiley
• ISBN: 9781118004616

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7.4: Methods for Solving Time Value of Money Problems

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Learning Objectives

By the end of this section, you will be able to:

• Explain how future dollar amounts are calculated.
• Explain how present dollar amounts are calculated.
• Describe how discount rates are calculated.
• Describe how growth rates are calculated.
• Illustrate how periods of time for specified growth are calculated.
• Use a financial calculator and Excel to solve TVM problems.

We can determine future value by using any of four methods: (1) mathematical equations, (2) calculators with financial functions, (3) spreadsheets, and (4) FVIF tables. With the advent and wide acceptance and use of financial calculators and spreadsheet software, FVIF (and other such time value of money tables and factors) have become obsolete, and we will not discuss them in this text. Nevertheless, they are often still published in other finance textbooks and are also available on the internet to use if you so choose.

Using Timelines to Organize TVM Information

A useful tool for conceptualizing present value and future value problems is a timeline. A timeline is a visual, linear representation of periods and cash flows over a set amount of time. Each timeline shows today at the left and a desired ending, or future point (maturity date), at the right.

Now, let us take an example of a future value problem that has a time frame of five years. Before we begin to solve for any answers, it would be a good approach to lay out a timeline like that shown in Table 7.1:

The timeline provides a visual reference for us and puts the problem into perspective.

Now, let’s say that we are interested in knowing what today’s balance of $100 in our saving account, earning 5% annually, will be worth at the end of each of the next five years. Using the future value formula

that we covered earlier, we would arrive at the following values: $105 at the end of year one, $110.25 at the end of year two, $115.76 at the end of year three, $121.55 at the end of year four, and $127.63 at the end of year five.

With the numerical information, the timeline (at a 5% interest or growth rate) would look like Table 7.2:

Using timelines to lay out TVM problems becomes more and more valuable as problems become more complex. You should get into the habit of using a timeline to set up these problems prior to using the equation, a calculator, or a spreadsheet to help minimize input errors. Now we will move on to the different methods available that will help you solve specific TVM problems. These are the financial calculator and the Excel spreadsheet.

Using a Financial Calculator to Solve TVM Problems

An extremely popular method of solving TVM problems is through the use of a financial calculator. Financial calculators such as the Texas Instruments BAII Plus™ Professional will typically have five keys that represent the critical variables used in most common TVM problems: N , I/Y , PV , FV , and PMT . These represent the following:

These are the only keys on a financial calculator that are necessary to solve TVM problems involving a single payment or lump sum .

Example 1: Future Value of a Single Payment or Lump Sum

Let’s start with a simple example that will provide you with most of the skills needed to perform TVM functions involving a single lump sum payment with a financial calculator.

Suppose that you have $1,000 and that you deposit this in a savings account earning 3% annually for a period of four years. You will naturally be interested in knowing how much money you will have in your account at the end of this four-year time period (assuming you make no other deposits and withdraw no cash).

To answer this question, you will need to work with factors of $1,000, the present value ( PV ); four periods or years, represented by N ; and the 3% interest rate, or I/Y . Make sure that the calculator register information is cleared, or you may end up with numbers from previous uses that will interfere with the solution. The register-clearing process will depend on what type of calculator you are using, but for the TI BA II Plus™ Professional calculator, clearing can be accomplished by pressing the keys 2ND and FV [ CLR TVM ].

Once you have cleared any old data, you can enter the values in the appropriate key areas: 4 for N , 3 for I/Y , and 1000 for PV . Now you have entered enough information to calculate the future value. Continue by pressing the CPT (compute) key, followed by the FV key. The answer you end up with should be displayed as 1,125.51 (see Table 7.3).

Important Notes for Using a Calculator and the Cash Flow Sign Convention

Please note that the PV was entered as negative $1,000 (or -$1000). This is because most financial calculators (and spreadsheets) follow something called the cash flow sign convention, which is a way for calculators and spreadsheets to keep the relative direction of the cash flow straight. Positive numbers are used to represent cash inflows, and negative numbers should always be used for cash outflows.

In this example, the $1,000 is an investment that requires a cash outflow. For this reason, -1000 is entered as the present value, as you will be essentially handing this $1,000 to a bank or to someone else to initiate the transaction. Conversely, the future value represents a cash inflow in four years’ time. This is why the calculator generates a positive 1,125.51 as the end result of this calculation.

Had you entered the present value of $1,000 as a positive number, there would have been no real concern, but the ending future value answer would have been returned expressed as a negative number. This would be correct had you borrowed $1,000 today (cash inflow) and agreed to repay $1,125.51 (cash outflow) four years from now. Also, it is important that you do not change the sign of any input value by using the - (minus) key). For example, on the TI BA II Plus™ Professional, you must use the +|- key instead of the minus key. If you enter 1000 and then hit the +|- key, you will get a negative 1,000 amount showing in the calculator display.

An important feature of most financial calculators is that it is possible to change any of the variables in a problem without needing to reenter all of the other data. For example, suppose that we wanted to find out the future value in our bank account if we left the money from our previous example invested for 20 years instead of 4. Before clearing any of the data, simply enter 20 for N and then press the CPT key and then the FV key. After this is done, all other inputs will remain the same, and you will arrive at an answer of $1,806.11.

Think It Through

How to determine future value when other variables are known.

Here’s an example of using a financial calculator to solve a common time value of money problem. You have $2,000 invested in a money market account that is expected to earn 4% annually. What will be the total value in the account after five years?

Follow the recommended financial calculator steps in Table 7.4.

The result of this future value calculation of the invested money is $2,433.31.

Example 2: Present Value of Lump Sums

Solving for the present value (discounted value) of a lump sum is the exact opposite of solving for a future value. Once again, if we enter a negative value for the FV, then the calculated PV will be a positive amount.

Taking the reverse of what we did in our example of future value above, we can enter -1,125.51 for FV , 3 for I/Y , and 4 for N . Hit the CPT and PV keys in succession, and you should arrive at a displayed answer of 1,000.

An important constant within the time value of money framework is that the present value will always be less than the future value unless the interest rate is negative. It is important to keep this in mind because it can help you spot incorrect answers that may arise from errors with your input.

How to Determine Present Value When Other Variables Are Known

Here is another example of using a financial calculator to solve a common time value of money problem. You have just won a second-prize lottery jackpot that will pay a single total lump sum of $50,000 five years from now. How much value would this have in today’s dollars, assuming a 5% interest rate?

Follow the recommended financial calculator steps in Table 7.5.

The present value of the lottery jackpot is $39,176.31.

Example 3: Calculating the Number of Periods

There will be times when you will know both the value of the money you have now and how much money you will need to have at some unknown point in the future. If you also know the interest rate your money will be earning for the foreseeable future, then you can solve for N, or the exact amount of time periods that it will take for the present value of your money to grow into the future value that you will require for your eventual use.

Now, suppose that you have $100 today and you would like to know how long it will take for you to be able to purchase a product that costs $133.82.

After making sure your calculator is clear, you will enter 5 for I/Y , -100 for PV , and 133.82 for FV . Now press CPT N , and you will see that it will take 5.97 years for your money to grow to the desired amount of $133.82.

Again, an important thing to note when using a financial calculator to solve TVM problems is that you must enter your numbers according to the cash flow sign convention discussed above. If you do not make either the PV or the FV a negative number (with the other being a positive number), then you will end up getting an error message on the screen instead of the answer to the problem. The reason for this is that if both numbers you enter for the PV and FV are positive, the calculator will operate under the assumption that you are receiving a financial benefit without making any cash outlay as an initial investment. If you get such an error message in your calculations, you can simply press the CE/C key. This will clear the error, and you can reenter your data correctly by changing the sign of either PV or FV (but not both of these, of course).

Determining Periods of Time

Here is an additional example of using a financial calculator to solve a common time value of money problem. You want to be able to contribute $25,000 to your child’s first year of college tuition and related expenses. You currently have $15,000 in a tuition savings account that is earning 6% interest every year. How long will it take for this account grow into the targeted amount of $25,000, assuming no additional deposits or withdrawals will be made?

Table 7.6 shows the steps you will take.

The result of this calculation is a time period of 8.7667 years for the account to reach the targeted amount.

Example 4: Solving for the Interest Rate

Solving for an interest rate is a common TVM problem that can be easily addressed with a financial calculator. Let’s return to our earlier example, but in this case, we know that we have $1,000 at the present time and that we will need to have a total of $1,125.51 four years from now. Let’s also say that the only way we can add to the current value of our savings is through interest income. We will not be able to make any further deposits in addition to our initial $1,000 account balance.

What interest rate should we be sure to get on our savings account in order to have a total savings account value of $1,125.51 four years from now?

Once again, clear the calculator, and then enter 4 for N , -1,000 for PV , and 1,125.51 for FV . Then, press the CPT and I/Y keys and you will find that you need to earn an average 3% interest per year in order to grow your savings balance to the desired amount of $1,125.51. Again, if you end up with an error message, you probably failed to follow the sign convention relating to cash inflow and outflow that we discussed earlier. To correct this, you will need to clear the calculator and reenter the information correctly.

After you believe you are done and have arrived at a final answer, always make sure you give it a quick review. You can ask yourself questions such as “Does this make any sense?” “How does this compare to other answers I have arrived at?” or “Is this logical based on everything I know about the scenario?” Knowing how to go about such a review will require you to understand the concepts you are attempting to apply and what you are trying to make the calculator do. Further, it is critical to understand the relationships among the different inputs and variables of the problem. If you do not fully understand these relationships, you may end up with an incorrect answer. In the end, it is important to realize that any calculator is simply a tool. It will only do what you direct it to do and has no idea what your objective is or what it is that you really wish to accomplish.

Determining Interest or Growth Rate

Here is another example of using a financial calculator to solve a common time value of money problem. Let’s use a similar example to the one we used when calculating periods of time to determine an interest or growth rate. You still want to help your child with their first year of college tuition and related expenses. You also still have a starting amount of $15,000, but you have not yet decided on a savings plan to use.

Instead, the information you now have is that your child is just under 10 years old and will begin college at age 18. For simplicity’s sake, let’s say that you have eight and a half years before you will need to meet your total savings target of $25,000. What rate of interest will you need to grow your saved money from $15,000 to $25,000 in this time period, again with no other deposits or withdrawals?

Follow the steps shown in Table 7.7.

The result of this calculation is a necessary interest rate of 6.194%.

Using Excel to Solve TVM Problems

Excel spreadsheets can be excellent tools to use when solving time value of money problems. There are dozens of financial functions available in Excel, but a student who can use a few of these functions can solve almost any TVM problem. Special functions that relate to TVM calculations are as follows:

Excel also includes a function called Payment (PMT) that is used in calculations involving multiple payments or deposits (annuities). These will be covered in Time Value of Money II: Equal Multiple Payments.

Future Value (FV)

The Future Value function in Excel is also referred to as FV and can be used to calculate the value of a single lump sum amount carried to any point in the future. The FV function syntax is similar to that of the other four basic time-value functions and has the following inputs (referred to as arguments), similar to the functions listed above:

Lump sum problems do not involve payments, so the value of Pmt in such calculations is 0. Another argument, Type, refers to the timing of a payment and carries a default value of the end of the period, which is the most common timing (as opposed to the beginning of a period). This may be ignored in our current example, which means the default value of the end of the period will be used.

The spreadsheet in Figure 7.3 shows two examples of using the FV function in Excel to calculate the future value of $100 in five years at 5% interest.

In cell E1, the FV function references the values in cells B1 through B4 for each of the arguments. When a user begins to type a function into a spreadsheet, Excel provides helpful information in the form of on-screen tips showing the argument inputs that are required to complete the function. In our spreadsheet example, as the FV formula is being typed into cell E2, a banner showing the arguments necessary to complete the function appears directly below, hovering over cell E3.

Cells E1 and E2 show how the FV function appears in the spreadsheet as it is typed in with the required arguments. Cell E4 shows the calculated answer for cell E1 after hitting the enter key. Once the enter key is pressed, the hint banner hovering over cell E3 will disappear. The second example of the FV function in our example spreadsheet is in cell E6. Here, the actual numerical values are used in the FV function equation rather than cell references. The method in cell E8 is referred to as hard coding . In general, it is preferable to use the cell reference method, as this allows for copying formulas and provides the user with increased flexibility in accounting for changes to input data. This ability to accept cell references in formulas is one of the greatest strengths of Excel as a spreadsheet tool.

Download the spreadsheet file containing key Chapter 7 Excel exhibits.

Determining Future Value When Other Variables Are Known . You have $2,000 invested in a money market account that is expected to earn 4% annually. What will be the total value in the account in five years?

Note: Be sure to follow the sign conventions. In this case, the PV should be entered as a negative value.

Note: In Excel, interest and growth rates must be entered as percentages, not as whole integers. So, 4 percent must be entered as 4% or 0.04—not 4, as you would enter in a financial calculator.

Note: It is always assumed that if not specifically stated, the compounding period of any given interest rate is annual, or based on years.

Note: The Excel command used to calculate future value is as follows:

You may simply type the values for the arguments in the above formula. Another option is to use the Excel insert function option. If you decide on this second method, below are several screenshots of dialog boxes you will encounter and will be required to complete.

This dialog box allows you to either search for a function or select a function that has been used recently. In this example, you can search for FV by typing this in the search box and selecting Go, or you can simply choose FV from the list of most recently used functions (as shown here with the highlighted FV option).

Figure 7.6 shows the completed data input for the variables, referred to here as “function arguments.” Note that cell addresses are used in this example. This allows the spreadsheet to still be useful if you decide to change any of the variables. You may also type values directly into the Function Arguments dialog box, but if you do this and you have to change any of your inputs later, you will have to reenter the new information. Using cell addresses is always a preferable method of entering the function argument data.

Additional notes:

• The Pmt argument or variable can be ignored in this instance, or you can enter a placeholder value of zero. This example shows a blank or ignored entry, but either option may be used in problems such as this where the information is not relevant.
• The Type argument does not apply to this problem. Type refers to the timing of cash flows and is usually used in multiple payment or annuity problems to indicate whether payments or deposits are made at the beginning of periods or at the end. In single lump sum problems, this is not relevant information, and the Type argument box is left empty.
• When you use cell addresses as function argument inputs, the numerical values within the cells are displayed off to the right. This helps you ensure that you are identifying the correct cells in your function. The final answer generated by the function is also displayed for your preliminary review.

Once you are satisfied with the result, hit the OK button, and the dialog box will disappear, with only the final numerical result appearing in the cell where you have set up the function.

The FV of this present value has been calculated as approximately $2,433.31.

Present Value (PV)

We have covered the idea that present value is the opposite of future value. As an example, in the spreadsheet shown in Figure 7.3, we calculated that the future value of $100 five years from now at a 5% interest rate would be $127.63. By reversing this process, we can safely state that $127.63 received five years from now with a 5% interest (or discount) rate would have a value of just $100 today. Thus, $100 is its present value. In Excel, the PV function is used to determine present value (see Figure 7.7).

The formula in cell E1 uses cell references in a similar fashion to our FV example spreadsheet above. Also similar to our earlier example is the hard-coded formula for this calculation, which is shown in cell E6. In both cases, the answers we arrive at using the PV function are identical, but once again, using cell references is preferred over hard coding if possible.

Determining Present Value When Other Variables Are Known

You have just won a second-prize lottery jackpot that will pay a single total lump sum of $50,000 five years from now. You are interested in knowing how much value this would have in today’s dollars, assuming a 5% interest rate.

• If you wish for the present value amount to be positive, the future value you enter here should be a negative value.
• In Excel, interest and growth rates must be entered as percentages, not as whole integers. So, 5 percent must be entered as 5% or 0.05—not 5, as you would enter in a financial calculator.
• It is always assumed that if not specifically stated, the compounding period of any given interest rate is annual, or based on years.
• The Excel command used to calculate present value is as shown here:

As with the FV formula covered in the first tab of this workbook, you may simply type the values for the arguments in the above formula. Another option is to again use the Insert Function option in Excel. Figure 7.8, Figure 7.9, and Figure 7.10 provide several screenshots that demonstrate the steps you’ll need to follow if you decide to enter the PV function from the Insert Function menu.

As discussed in the FV function example above, this dialog box allows you to either search for a function or select a function that has been used recently. In this example, you can search for PV by typing this into the search box and selecting Go, or you can simply choose PV from the list of the most recently used functions.

Figure 7.10 shows the completed data input for the function arguments. Note that once again, cell addresses are used in this example. This allows the spreadsheet to still be useful if you decide to change any of the variables. As in the FV function example, you may also type values directly in the Function Arguments dialog box, but if you do this and you have to change any of your input later, you will have to reenter the new information. Remember that using cell addresses is always a preferable method of entering the function argument data.

Again, similar to our FV function example, the Function Arguments dialog box shows values off to the right of the data entry area, including our final answer. The Pmt and Type boxes are again not relevant to this single lump sum example, for reasons we covered in the FV example.

Review your answer. Once you are satisfied with the result, click the OK button, and the dialog box will disappear, with only the final numerical result appearing in the cell where you have set up the function. The PV of this future value has been calculated as approximately $39,176.31.

Periods of Time

The following discussion will show you how to use Excel to determine the amount of time a given present value will need to grow into a specified future value when the interest or growth rate is known.

You want to be able to contribute $25,000 to your child’s first year of college tuition and related expenses. You currently have $15,000 in a tuition savings account that is earning 6% interest every year. How long will it take for this account grow into the targeted amount of $25,000, assuming no additional deposits or withdrawals are made?

• As with our other examples, interest and growth rates must be entered as percentages, not as whole integers. So, 6 percent must be entered as 6% or 0.06—not 6, as you would enter in a financial calculator.
• The present value needs to be entered as a negative value in accordance with the sign convention covered earlier.
• The Excel command used to calculate the amount of time, or number of periods, is this:

As with our FV and PV examples, you may simply type the values of the arguments in the above formula, or we can again use the Insert Function option in Excel. If you do so, you will need to work with the various dialog boxes after you select Insert Function.

As discussed in our previous examples on FV and PV, this menu allows you to either search for a function or select a function that has been used recently. In this example, you can search for NPER by typing this into the search box and selecting Go, or you can simply choose NPER from the list of most recently used functions.

• Once you have highlighted NPER, click the OK button, and a new dialog box will appear for you to enter the necessary details. As in our previous examples, it will look like Figure 7.12.

Figure 7.13 shows the completed Function Arguments dialog box. Note that once again, we are using cell addresses in this example.

As in the previous function examples, values are shown off to the right of the data input area, and our final answer of approximately 8.77 is displayed at the bottom. Also, once again, the Pmt and Type boxes are not relevant to this single lump sum example.

Review your answer, and once you are satisfied with the result, click the OK button. The dialog box will disappear, with only the final numerical result appearing in the cell where you have set up the function.

The amount of time required for the desired growth to occur is calculated as approximately 8.77 years.

Interest or Growth Rate

You can also use Excel to determine the required growth rate when the present value, future value, and total number of required periods are known.

Let’s discuss a similar example to the one we used to calculate periods of time. You still want to help your child with their first year of college tuition and related expenses, and you still have a starting amount of $15,000, but you have not yet decided which savings plan to use.

Instead, the information you now have is that your child is just under 10 years old and will begin college at age 18. For simplicity’s sake, let’s say that you have eight and a half years until you will need to meet your total savings target of $25,000. What rate of interest will you need to grow your saved money from $15,000 to $25,000 in this time, again with no other deposits or withdrawals?

Note: The present value needs to be entered as a negative value.

Note: The Excel command used to calculate interest or growth rate is as follows:

As with our other TVM function examples, you may simply type the values for the arguments into the above formula. We also again have the same alternative to use the Insert Function option in Excel. If you choose this option, you will again see the Insert Function dialog box after you click the Insert Function button.

Once we complete the input, again using cell addresses for the required argument values, we will see what is shown in Figure 7.16.

As in our other examples, cell values are shown as numerical values off to the right, and our answer of approximately 0.0619, or 6.19%, is shown at the bottom of the dialog box.

This answer also can be checked from a logic point of view because of the similar example we worked through when calculating periods of time. Our present value and future value are the same as in that example, and our time period is now 8.5 years, which is just under the result we arrived at (8.77 years) in the periods example.

So, if we are now working with a slightly shorter time frame for the savings to grow from $15,000 into $25,000, then we would expect to have a slightly greater growth rate. That is exactly how the answer turns out, as the calculated required interest rate of approximately 6.19% is just slightly greater than the growth rate of 6% used in the previous example. So, based on this, it looks like our answer here passes a simple “sanity check” review.

• 1 The specific financial calculator in these examples is the Texas Instruments BA II Plus™ Professional model, but you can use other financial calculators for these types of calculations.

7.3 Methods for Solving Time Value of Money Problems

Learning outcomes.

By the end of this section, you will be able to:

• Explain how future dollar amounts are calculated.
• Explain how present dollar amounts are calculated.
• Describe how discount rates are calculated.
• Describe how growth rates are calculated.
• Illustrate how periods of time for specified growth are calculated.
• Use a financial calculator and Excel to solve TVM problems.

We can determine future value by using any of four methods: (1) mathematical equations, (2) calculators with financial functions, (3) spreadsheets, and (4) FVIF tables. With the advent and wide acceptance and use of financial calculators and spreadsheet software, FVIF (and other such time value of money tables and factors) have become obsolete, and we will not discuss them in this text. Nevertheless, they are often still published in other finance textbooks and are also available on the internet to use if you so choose.

Using Timelines to Organize TVM Information

A useful tool for conceptualizing present value and future value problems is a timeline. A timeline is a visual, linear representation of periods and cash flows over a set amount of time. Each timeline shows today at the left and a desired ending, or future point (maturity date), at the right.

Now, let us take an example of a future value problem that has a time frame of five years. Before we begin to solve for any answers, it would be a good approach to lay out a timeline like that shown in Table 7.1 :

The timeline provides a visual reference for us and puts the problem into perspective.

Now, let’s say that we are interested in knowing what today’s balance of $100 in our saving account, earning 5% annually, will be worth at the end of each of the next five years. Using the future value formula

that we covered earlier, we would arrive at the following values: $105 at the end of year one, $110.25 at the end of year two, $115.76 at the end of year three, $121.55 at the end of year four, and $127.63 at the end of year five.

With the numerical information, the timeline (at a 5% interest or growth rate) would look like Table 7.2 :

Using timelines to lay out TVM problems becomes more and more valuable as problems become more complex. You should get into the habit of using a timeline to set up these problems prior to using the equation, a calculator, or a spreadsheet to help minimize input errors. Now we will move on to the different methods available that will help you solve specific TVM problems. These are the financial calculator and the Excel spreadsheet.

Using a Financial Calculator to Solve TVM Problems

An extremely popular method of solving TVM problems is through the use of a financial calculator. Financial calculators such as the Texas Instruments BAII Plus™ Professional will typically have five keys that represent the critical variables used in most common TVM problems: N , I/Y , PV , FV , and PMT . These represent the following:

These are the only keys on a financial calculator that are necessary to solve TVM problems involving a single payment or lump sum .

Example 1: Future Value of a Single Payment or Lump Sum

Let’s start with a simple example that will provide you with most of the skills needed to perform TVM functions involving a single lump sum payment with a financial calculator.

Suppose that you have $1,000 and that you deposit this in a savings account earning 3% annually for a period of four years. You will naturally be interested in knowing how much money you will have in your account at the end of this four-year time period (assuming you make no other deposits and withdraw no cash).

To answer this question, you will need to work with factors of $1,000, the present value ( PV ); four periods or years, represented by N ; and the 3% interest rate, or I/Y . Make sure that the calculator register information is cleared, or you may end up with numbers from previous uses that will interfere with the solution. The register-clearing process will depend on what type of calculator you are using, but for the TI BA II Plus™ Professional calculator, clearing can be accomplished by pressing the keys 2ND and FV [ CLR TVM ].

Once you have cleared any old data, you can enter the values in the appropriate key areas: 4 for N , 3 for I/Y , and 1000 for PV . Now you have entered enough information to calculate the future value. Continue by pressing the CPT (compute) key, followed by the FV key. The answer you end up with should be displayed as 1,125.51 (see Table 7.3 ).

Important Notes for Using a Calculator and the Cash Flow Sign Convention

Please note that the PV was entered as negative $1,000 (or -$1000). This is because most financial calculators (and spreadsheets) follow something called the cash flow sign convention, which is a way for calculators and spreadsheets to keep the relative direction of the cash flow straight. Positive numbers are used to represent cash inflows, and negative numbers should always be used for cash outflows.

In this example, the $1,000 is an investment that requires a cash outflow. For this reason, -1000 is entered as the present value, as you will be essentially handing this $1,000 to a bank or to someone else to initiate the transaction. Conversely, the future value represents a cash inflow in four years’ time. This is why the calculator generates a positive 1,125.51 as the end result of this calculation.

Had you entered the present value of $1,000 as a positive number, there would have been no real concern, but the ending future value answer would have been returned expressed as a negative number. This would be correct had you borrowed $1,000 today (cash inflow) and agreed to repay $1,125.51 (cash outflow) four years from now. Also, it is important that you do not change the sign of any input value by using the - (minus) key). For example, on the TI BA II Plus™ Professional, you must use the +|- key instead of the minus key. If you enter 1000 and then hit the +|- key, you will get a negative 1,000 amount showing in the calculator display.

An important feature of most financial calculators is that it is possible to change any of the variables in a problem without needing to reenter all of the other data. For example, suppose that we wanted to find out the future value in our bank account if we left the money from our previous example invested for 20 years instead of 4. Before clearing any of the data, simply enter 20 for N and then press the CPT key and then the FV key. After this is done, all other inputs will remain the same, and you will arrive at an answer of $1,806.11.

Think It Through

How to determine future value when other variables are known.

Here’s an example of using a financial calculator to solve a common time value of money problem. You have $2,000 invested in a money market account that is expected to earn 4% annually. What will be the total value in the account after five years?

Follow the recommended financial calculator steps in Table 7.4 .

The result of this future value calculation of the invested money is $2,433.31.

Example 2: Present Value of Lump Sums

Solving for the present value (discounted value) of a lump sum is the exact opposite of solving for a future value. Once again, if we enter a negative value for the FV, then the calculated PV will be a positive amount.

Taking the reverse of what we did in our example of future value above, we can enter -1,125.51 for FV , 3 for I/Y , and 4 for N . Hit the CPT and PV keys in succession, and you should arrive at a displayed answer of 1,000.

An important constant within the time value of money framework is that the present value will always be less than the future value unless the interest rate is negative. It is important to keep this in mind because it can help you spot incorrect answers that may arise from errors with your input.

How to Determine Present Value When Other Variables Are Known

Here is another example of using a financial calculator to solve a common time value of money problem. You have just won a second-prize lottery jackpot that will pay a single total lump sum of $50,000 five years from now. How much value would this have in today’s dollars, assuming a 5% interest rate?

Follow the recommended financial calculator steps in Table 7.5 .

The present value of the lottery jackpot is $39,176.31.

Example 3: Calculating the Number of Periods

There will be times when you will know both the value of the money you have now and how much money you will need to have at some unknown point in the future. If you also know the interest rate your money will be earning for the foreseeable future, then you can solve for N, or the exact amount of time periods that it will take for the present value of your money to grow into the future value that you will require for your eventual use.

Now, suppose that you have $100 today and you would like to know how long it will take for you to be able to purchase a product that costs $133.82.

After making sure your calculator is clear, you will enter 5 for I/Y , -100 for PV , and 133.82 for FV . Now press CPT N , and you will see that it will take 5.97 years for your money to grow to the desired amount of $133.82.

Again, an important thing to note when using a financial calculator to solve TVM problems is that you must enter your numbers according to the cash flow sign convention discussed above. If you do not make either the PV or the FV a negative number (with the other being a positive number), then you will end up getting an error message on the screen instead of the answer to the problem. The reason for this is that if both numbers you enter for the PV and FV are positive, the calculator will operate under the assumption that you are receiving a financial benefit without making any cash outlay as an initial investment. If you get such an error message in your calculations, you can simply press the CE/C key. This will clear the error, and you can reenter your data correctly by changing the sign of either PV or FV (but not both of these, of course).

Determining Periods of Time

Here is an additional example of using a financial calculator to solve a common time value of money problem. You want to be able to contribute $25,000 to your child’s first year of college tuition and related expenses. You currently have $15,000 in a tuition savings account that is earning 6% interest every year. How long will it take for this account grow into the targeted amount of $25,000, assuming no additional deposits or withdrawals will be made?

Table 7.6 shows the steps you will take.

The result of this calculation is a time period of 8.7667 years for the account to reach the targeted amount.

Example 4: Solving for the Interest Rate

Solving for an interest rate is a common TVM problem that can be easily addressed with a financial calculator. Let’s return to our earlier example, but in this case, we know that we have $1,000 at the present time and that we will need to have a total of $1,125.51 four years from now. Let’s also say that the only way we can add to the current value of our savings is through interest income. We will not be able to make any further deposits in addition to our initial $1,000 account balance.

What interest rate should we be sure to get on our savings account in order to have a total savings account value of $1,125.51 four years from now?

Once again, clear the calculator, and then enter 4 for N , -1,000 for PV , and 1,125.51 for FV . Then, press the CPT and I/Y keys and you will find that you need to earn an average 3% interest per year in order to grow your savings balance to the desired amount of $1,125.51. Again, if you end up with an error message, you probably failed to follow the sign convention relating to cash inflow and outflow that we discussed earlier. To correct this, you will need to clear the calculator and reenter the information correctly.

After you believe you are done and have arrived at a final answer, always make sure you give it a quick review. You can ask yourself questions such as “Does this make any sense?” “How does this compare to other answers I have arrived at?” or “Is this logical based on everything I know about the scenario?” Knowing how to go about such a review will require you to understand the concepts you are attempting to apply and what you are trying to make the calculator do. Further, it is critical to understand the relationships among the different inputs and variables of the problem. If you do not fully understand these relationships, you may end up with an incorrect answer. In the end, it is important to realize that any calculator is simply a tool. It will only do what you direct it to do and has no idea what your objective is or what it is that you really wish to accomplish.

Determining Interest or Growth Rate

Here is another example of using a financial calculator to solve a common time value of money problem. Let’s use a similar example to the one we used when calculating periods of time to determine an interest or growth rate. You still want to help your child with their first year of college tuition and related expenses. You also still have a starting amount of $15,000, but you have not yet decided on a savings plan to use.

Instead, the information you now have is that your child is just under 10 years old and will begin college at age 18. For simplicity’s sake, let’s say that you have eight and a half years before you will need to meet your total savings target of $25,000. What rate of interest will you need to grow your saved money from $15,000 to $25,000 in this time period, again with no other deposits or withdrawals?

Follow the steps shown in Table 7.7 .

The result of this calculation is a necessary interest rate of 6.194%.

Using Excel to Solve TVM Problems

Excel spreadsheets can be excellent tools to use when solving time value of money problems. There are dozens of financial functions available in Excel, but a student who can use a few of these functions can solve almost any TVM problem. Special functions that relate to TVM calculations are as follows:

Excel also includes a function called Payment (PMT) that is used in calculations involving multiple payments or deposits (annuities). These will be covered in Time Value of Money II: Equal Multiple Payments .

Future Value (FV)

The Future Value function in Excel is also referred to as FV and can be used to calculate the value of a single lump sum amount carried to any point in the future. The FV function syntax is similar to that of the other four basic time-value functions and has the following inputs (referred to as arguments), similar to the functions listed above:

Lump sum problems do not involve payments, so the value of Pmt in such calculations is 0. Another argument, Type, refers to the timing of a payment and carries a default value of the end of the period, which is the most common timing (as opposed to the beginning of a period). This may be ignored in our current example, which means the default value of the end of the period will be used.

The spreadsheet in Figure 7.3 shows two examples of using the FV function in Excel to calculate the future value of $100 in five years at 5% interest.

In cell E1, the FV function references the values in cells B1 through B4 for each of the arguments. When a user begins to type a function into a spreadsheet, Excel provides helpful information in the form of on-screen tips showing the argument inputs that are required to complete the function. In our spreadsheet example, as the FV formula is being typed into cell E2, a banner showing the arguments necessary to complete the function appears directly below, hovering over cell E3.

Cells E1 and E2 show how the FV function appears in the spreadsheet as it is typed in with the required arguments. Cell E4 shows the calculated answer for cell E1 after hitting the enter key. Once the enter key is pressed, the hint banner hovering over cell E3 will disappear. The second example of the FV function in our example spreadsheet is in cell E6. Here, the actual numerical values are used in the FV function equation rather than cell references. The method in cell E8 is referred to as hard coding . In general, it is preferable to use the cell reference method, as this allows for copying formulas and provides the user with increased flexibility in accounting for changes to input data. This ability to accept cell references in formulas is one of the greatest strengths of Excel as a spreadsheet tool.

Download the spreadsheet file containing key Chapter 7 Excel exhibits.

Determining Future Value When Other Variables Are Known . You have $2,000 invested in a money market account that is expected to earn 4% annually. What will be the total value in the account in five years?

Note: Be sure to follow the sign conventions. In this case, the PV should be entered as a negative value.

Note: In Excel, interest and growth rates must be entered as percentages, not as whole integers. So, 4 percent must be entered as 4% or 0.04—not 4, as you would enter in a financial calculator.

Note: It is always assumed that if not specifically stated, the compounding period of any given interest rate is annual, or based on years.

Note: The Excel command used to calculate future value is as follows:

You may simply type the values for the arguments in the above formula. Another option is to use the Excel insert function option. If you decide on this second method, below are several screenshots of dialog boxes you will encounter and will be required to complete.

This dialog box allows you to either search for a function or select a function that has been used recently. In this example, you can search for FV by typing this in the search box and selecting Go, or you can simply choose FV from the list of most recently used functions (as shown here with the highlighted FV option).

Figure 7.6 shows the completed data input for the variables, referred to here as “function arguments.” Note that cell addresses are used in this example. This allows the spreadsheet to still be useful if you decide to change any of the variables. You may also type values directly into the Function Arguments dialog box, but if you do this and you have to change any of your inputs later, you will have to reenter the new information. Using cell addresses is always a preferable method of entering the function argument data.

Additional notes:

• The Pmt argument or variable can be ignored in this instance, or you can enter a placeholder value of zero. This example shows a blank or ignored entry, but either option may be used in problems such as this where the information is not relevant.
• The Type argument does not apply to this problem. Type refers to the timing of cash flows and is usually used in multiple payment or annuity problems to indicate whether payments or deposits are made at the beginning of periods or at the end. In single lump sum problems, this is not relevant information, and the Type argument box is left empty.
• When you use cell addresses as function argument inputs, the numerical values within the cells are displayed off to the right. This helps you ensure that you are identifying the correct cells in your function. The final answer generated by the function is also displayed for your preliminary review.

Once you are satisfied with the result, hit the OK button, and the dialog box will disappear, with only the final numerical result appearing in the cell where you have set up the function.

The FV of this present value has been calculated as approximately $2,433.31.

Present Value (PV)

We have covered the idea that present value is the opposite of future value. As an example, in the spreadsheet shown in Figure 7.3 , we calculated that the future value of $100 five years from now at a 5% interest rate would be $127.63. By reversing this process, we can safely state that $127.63 received five years from now with a 5% interest (or discount) rate would have a value of just $100 today. Thus, $100 is its present value. In Excel, the PV function is used to determine present value (see Figure 7.7 ).

The formula in cell E1 uses cell references in a similar fashion to our FV example spreadsheet above. Also similar to our earlier example is the hard-coded formula for this calculation, which is shown in cell E6. In both cases, the answers we arrive at using the PV function are identical, but once again, using cell references is preferred over hard coding if possible.

Determining Present Value When Other Variables Are Known

You have just won a second-prize lottery jackpot that will pay a single total lump sum of $50,000 five years from now. You are interested in knowing how much value this would have in today’s dollars, assuming a 5% interest rate.

• If you wish for the present value amount to be positive, the future value you enter here should be a negative value.
• In Excel, interest and growth rates must be entered as percentages, not as whole integers. So, 5 percent must be entered as 5% or 0.05—not 5, as you would enter in a financial calculator.
• It is always assumed that if not specifically stated, the compounding period of any given interest rate is annual, or based on years.
• The Excel command used to calculate present value is as shown here:

As with the FV formula covered in the first tab of this workbook, you may simply type the values for the arguments in the above formula. Another option is to again use the Insert Function option in Excel. Figure 7.8 , Figure 7.9 , and Figure 7.10 provide several screenshots that demonstrate the steps you’ll need to follow if you decide to enter the PV function from the Insert Function menu.

As discussed in the FV function example above, this dialog box allows you to either search for a function or select a function that has been used recently. In this example, you can search for PV by typing this into the search box and selecting Go, or you can simply choose PV from the list of the most recently used functions.

Figure 7.10 shows the completed data input for the function arguments. Note that once again, cell addresses are used in this example. This allows the spreadsheet to still be useful if you decide to change any of the variables. As in the FV function example, you may also type values directly in the Function Arguments dialog box, but if you do this and you have to change any of your input later, you will have to reenter the new information. Remember that using cell addresses is always a preferable method of entering the function argument data.

Again, similar to our FV function example, the Function Arguments dialog box shows values off to the right of the data entry area, including our final answer. The Pmt and Type boxes are again not relevant to this single lump sum example, for reasons we covered in the FV example.

Review your answer. Once you are satisfied with the result, click the OK button, and the dialog box will disappear, with only the final numerical result appearing in the cell where you have set up the function. The PV of this future value has been calculated as approximately $39,176.31.

Periods of Time

The following discussion will show you how to use Excel to determine the amount of time a given present value will need to grow into a specified future value when the interest or growth rate is known.

You want to be able to contribute $25,000 to your child’s first year of college tuition and related expenses. You currently have $15,000 in a tuition savings account that is earning 6% interest every year. How long will it take for this account grow into the targeted amount of $25,000, assuming no additional deposits or withdrawals are made?

• As with our other examples, interest and growth rates must be entered as percentages, not as whole integers. So, 6 percent must be entered as 6% or 0.06—not 6, as you would enter in a financial calculator.
• The present value needs to be entered as a negative value in accordance with the sign convention covered earlier.
• The Excel command used to calculate the amount of time, or number of periods, is this:

As with our FV and PV examples, you may simply type the values of the arguments in the above formula, or we can again use the Insert Function option in Excel. If you do so, you will need to work with the various dialog boxes after you select Insert Function.

As discussed in our previous examples on FV and PV, this menu allows you to either search for a function or select a function that has been used recently. In this example, you can search for NPER by typing this into the search box and selecting Go, or you can simply choose NPER from the list of most recently used functions.

• Once you have highlighted NPER, click the OK button, and a new dialog box will appear for you to enter the necessary details. As in our previous examples, it will look like Figure 7.12 .

Figure 7.13 shows the completed Function Arguments dialog box. Note that once again, we are using cell addresses in this example.

As in the previous function examples, values are shown off to the right of the data input area, and our final answer of approximately 8.77 is displayed at the bottom. Also, once again, the Pmt and Type boxes are not relevant to this single lump sum example.

Review your answer, and once you are satisfied with the result, click the OK button. The dialog box will disappear, with only the final numerical result appearing in the cell where you have set up the function.

The amount of time required for the desired growth to occur is calculated as approximately 8.77 years.

Interest or Growth Rate

You can also use Excel to determine the required growth rate when the present value, future value, and total number of required periods are known.

Let’s discuss a similar example to the one we used to calculate periods of time. You still want to help your child with their first year of college tuition and related expenses, and you still have a starting amount of $15,000, but you have not yet decided which savings plan to use.

Instead, the information you now have is that your child is just under 10 years old and will begin college at age 18. For simplicity’s sake, let’s say that you have eight and a half years until you will need to meet your total savings target of $25,000. What rate of interest will you need to grow your saved money from $15,000 to $25,000 in this time, again with no other deposits or withdrawals?

Note: The present value needs to be entered as a negative value.

Note: The Excel command used to calculate interest or growth rate is as follows:

As with our other TVM function examples, you may simply type the values for the arguments into the above formula. We also again have the same alternative to use the Insert Function option in Excel. If you choose this option, you will again see the Insert Function dialog box after you click the Insert Function button.

Once we complete the input, again using cell addresses for the required argument values, we will see what is shown in Figure 7.16 .

As in our other examples, cell values are shown as numerical values off to the right, and our answer of approximately 0.0619, or 6.19%, is shown at the bottom of the dialog box.

This answer also can be checked from a logic point of view because of the similar example we worked through when calculating periods of time. Our present value and future value are the same as in that example, and our time period is now 8.5 years, which is just under the result we arrived at (8.77 years) in the periods example.

So, if we are now working with a slightly shorter time frame for the savings to grow from $15,000 into $25,000, then we would expect to have a slightly greater growth rate. That is exactly how the answer turns out, as the calculated required interest rate of approximately 6.19% is just slightly greater than the growth rate of 6% used in the previous example. So, based on this, it looks like our answer here passes a simple “sanity check” review.

• 1 The specific financial calculator in these examples is the Texas Instruments BA II Plus™ Professional model, but you can use other financial calculators for these types of calculations.

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• Authors: Julie Dahlquist, Rainford Knight
• Publisher/website: OpenStax
• Book title: Principles of Finance
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How to overcome 8 sources of financial problems & difficulties.

Financial problems and challenges happen to everyone at some point, and the stress and worry can get to you. However, realizing that there is almost always a way out can help you not feel so depressed. You may be able to find the way out yourself, or you may need someone else's perspective to help you find a solution. Below we’ll show you  how to overcome financial problems and difficulties  and ease your stress. But, one size does not fit all. If your situation is beyond the general help provided here, we’ll also let you know who you can go to for more in-depth help.

1. Identify the Underlying Problem That's Causing the Difficulties

The first step to overcoming financial problems is to identify the underlying issue that’s causing the financial difficulties. Financial problems are usually a symptom of a bigger issue. To come up with solutions that work in the long run, take the time to identify the real source of your financial troubles. Here are some common things to think about: 

Your problem may not be listed above or it may be more complex. However, the concept of identifying a specific problem is important because it is more likely to result in a lasting solution. Just like with a leaky faucet; placing a bucket below is temporary. Fix the tap and the leak will stop. Focus on solving the problem that’s causing your money troubles, rather than dwelling on your stress.

2. Create a Budget - Spend Money in a Way That Helps Solve the Problem 

One of the best weapons for combating financial problems is a budget. A budget is a monthly spending plan for your money. Creating a budget is like turning the lights on to find your way around a dark room. You no longer need to wander in the dark; banging your shins, tripping over the furniture, and stepping on the dog. Instead, with the lights on, you can see what’s going on and prevent problems before they happen. A budget works much the same way; it guides your spending decisions so that you're spending money on what's really important to you. In this case, you'll  spend your money in a way that helps solve your financial problem .

Click here to learn more about creating a budget , or try out our  budget calculator that guides you through the budgeting process , points out common problems, and offers suggestions to improve your budget.

Track Your Expenses to Build a Budget That Works

As you create your budget, it’s important that your expenses aren’t just guesses – they need to reflect reality. You may want to ​ track your expenses  for at least a couple of weeks (a month is best) to objectively see where you are spending your money and how much you’re spending. Although you may think you know where your money is going, when most people tally up all their purchases for a month, they are usually quite surprised to notice that their spending doesn’t always match up with what they thought their priorities were.

3. Determine Financial Priorities to Guide Your Spending Choices

4. Identify Small Steps You Can Take to Address the Problem & Achieve Your Goals

Look here to get ideas of where find some extra money each month , get the card paid off, and then permanently have $50 extra to use in your budget every month. However, if by the time you reach this goal you’ve learned to get by without this $50, then use it to accelerate the payment of another debt each month, and get all of your debts paid off more quickly. 

Look for Things You Can Do, Even Temporarily, to Improve Your Situation

Here are more ideas or steps you can consider taking to improve your financial situation and alleviate difficulties:

• As you look through your budget, ask yourself: Do I want this or do I need it? Will spending this money get me closer to my financial goals or further away? Can I live without it?  Learn more about separating needs from wants .
• Do you use credit cards for impulse purchases? This can contribute to a cycle of ongoing financial difficulty and  add as much as 50% to everything you purchase .  Learn how to reduce or change impulsive spending habits .
• Ask yourself if you can downsize anything in your budget or switch to a less expensive option. If vehicle costs are straining your budget, can you downsize your vehicle, get rid of one vehicle (the average person spends over $9,000 per year to own and operate a vehicle), take transit (80% cheaper than owning a vehicle), or car pool? If your rent, mortgage, or home upkeep is bleeding you dry, can you downsize to something more affordable, rent out your basement, rent a room in your house, rent out the storage space in your garage, or can you take in a student for some extra income?
• If debt is causing you financial problems, here are a lot of ways to reduce your debt or here are a dozen of the most effective ways to get out of debt .

• Can you take on a side job or create another source of income with something you know how to do well?
• Look outside the box, ask yourself tough questions, invite a trusted friend to have a look at your budget and make suggestions, or  sit down with a Credit Counsellor and get their suggestions .
• Research viable options that will move you towards your goals. A  consolidation loan ,  speaking with a Credit Counsellor , a  Debt Management Program , or some other option may be a possibility.

While doing any of these can be an unappealing thought, don’t just dismiss them because they’ll move you out of your comfort zone. Keep thinking about them and give them some consideration. Come back to these ideas from time to time to see if you can come up with a new angle on decreasing your expenses or increasing your income that might just work for you. Remember, you’re trying to get through a tough a time; you don’t need to do this forever, just to get back on track. If you’re really struggling, an  experienced Credit Counsellor can be a great, free source of suggestions .

5. Develop Your Plan to Overcome Financial Problems for Good

Once you’ve come up with some ideas for how to begin tackling your financial problems and difficulties, you can  put together a realistic plan to accomplish your goals . Some goals will have a timeline of a few months; others will need a longer timeline, like 24 - 36 months. Write your goals down, but also write down where you’re at now in relation to each goal. For example, if one of your goals is to pay off a $4,000 debt, make sure to write down the current debt balance and your future goal of paying this down to $0. You’ll want to include in your plan the amount of money you’re going to pay on this debt every month so that you can pay it off within your desired time frame. For more  help on setting goals, have a look at this . Here are also some  tips on setting financial goals with your spouse .

If you’re really feeling overwhelmed and stressed by your situation, you can also  reach out to a non-profit credit counselling agency for help . They have professionally trained Credit & Debt Counsellors who can review your situation with you, help you put together a realistic budget, and help you come up with a plan to solve your current challenges and get your finances back on track. Their help is usually free and is always confidential.

6. Review How Things are Going

The last step takes place once you are a few months into working on your plan. Every once-in-a-while, take a few minutes to review how things are going. Is your plan working? Are you making progress toward your goals? If not, you’ll need to take a closer look to figure out why not and adjust your plan. Your plan needs to be realistic, or it’s not going to work. It should also contain some things you weren’t doing before you put the plan in place.

If you keep doing what you were doing before, then you’ll continue to get the same result  as before – problems.  You’ve got to do something different to get a different outcome.

As you follow your plan and see improvements in your situation, be open to the possibility of fine-tuning the plan. Once you start making some progress, you may find you’re doing better than you thought, or you may come up with some new insights. Improving your plan so that you accomplish your goals more quickly is good as long as your budget can afford the changes and everyone who relies on your budget is okay with the more aggressive approach.

Preventing Future Financial Challenges

Unexpected financial challenges are bound to arise in the future - in fact, research shows that  6 in 10 Canadians will experience major life events that will challenge their prior financial plans . The key to tackling these challenges is to be flexible. Review your budget occasionally and make necessary changes.  Build up savings so that you can handle unanticipated expenses  without going into debt and putting yourself in a difficult situation.

Overcoming financial problems and difficulties isn’t easy, but by setting some clear priorities for yourself, identifying ways to achieve these goals, and persevering with your plan, you can overcome the challenges and at the same time, put an end to the financial stress.

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• Add new comment

vivienne replied on Mon, 12/10/2018 - 4:59pm Permalink

how to overcome 8 types of financial problems

sagar pal replied on Tue, 05/28/2019 - 11:43pm Permalink

MyMoneyCoach Team replied on Wed, 05/29/2019 - 8:51am Permalink

Where to get help

Bandela Pratap replied on Thu, 03/05/2020 - 7:10am Permalink

Financial problems

MyMoneyCoach Team replied on Thu, 03/05/2020 - 8:40am Permalink

Finding help

Pushkaraj Sawant replied on Fri, 09/04/2020 - 7:21am Permalink

More More Money Problem

MyMoneyCoach Team replied on Fri, 09/25/2020 - 9:40am Permalink

You should speak with a credit counsellor

Diganta Gohain replied on Sat, 09/05/2020 - 8:43am Permalink

Drastic financial problems

MyMoneyCoach Team replied on Fri, 09/25/2020 - 9:43am Permalink

Two places to look for help

Lanie Won replied on Wed, 05/04/2022 - 7:35am Permalink

Nina replied on Sat, 07/08/2023 - 10:42am Permalink

68 years old with little money for the golden years

MyMoneyCoach Team replied on Mon, 07/10/2023 - 2:58pm Permalink

You should speak with a financial planner

5 Simple Steps to Resolve Money Problems

Money problems can take many forms..

Posted April 23, 2019

Money problems can take many forms. You might be swamped with debt, struggling to save or pay for college for your kids or worried about outliving your resources in retirement . (Retirement? What retirement?)

Maybe you’re confused by a bewildering array of options and so you do nothing, which just adds to your stress and deepens the hole you find yourself in.

But money problems are just itching for solutions, if you have the foundation, courage and focus to make changes.

By foundation, I mean the basic knowledge you need to understand how to make financial decisions that move you toward the life you value.

If your first reaction is, "Whoa—I don’t know much about the fine points of money," you’re not alone. Here’s a quiz to give you a quick idea of how firm your financial foundation is right now.

Answer each with either TRUE or FALSE:

• Spending more than I can afford (adding to debt) reduces my financial well-being. ___
• The more debt I carry, the more difficult it is to save. _____
• Spending on things I do not truly value is likely to lead me into trouble. ___
• Having a liquid emergency fund is prudent for unexpected expenses or situations, like a major home repair or losing my job. _____
• Investing in risky assets is a dangerous strategy for money I’ll need in the short-term. ___
• Protecting my most valuable assets (health, family, property) is important. ____
• I should have a Will and Powers of Attorney in case I die or become incapacitated. ____
• Filing my taxes on time is important. _____
• My portfolio should support my situation and future plans as well as my risk tolerance and time horizon. ____

If you answered TRUE to these questions, your foundation is on its way. If you answered FALSE to any of these questions, send me an email with your thoughts.

You can hire someone to help you with the foundation ( here’s a list of fee only financial planners), or you can educate yourself on the fundamentals. But once you have that firm foundation, you can follow these five steps to work your way out of money problems.

Define the problem—you can’t solve what you don’t acknowledge. What’s happening that’s causing you financial difficulties, stress and worry? Writing it down will help bring clarity (and stop that endless loop going on in your head).

Know what you don’t know. Identify and sort through what you know from what you don’t. For example, you might know that you’ve got $10,000 in credit card debt, but you’re not sure the best way to dig yourself out.

Explore resources. Whether you hire a professional to help you or commit to learning from books, courses and articles from trusted sources, find the answers and/or solutions to what you don’t know.

Create an action plan. Write it down and put it where you can’t avoid seeing it every day. If you don’t act on your goals and plan, nothing changes.

Track your progress. Measure your headway, celebrate your wins, and make adjustments or course corrections, as you need them.

These steps aren’t complicated, but they require your personal resolve, courage, to keep on track. Missteps and challenges are not fatal. They test your desire to reach your goals—the best thing you can do with a mistake is learn from it.

Your resilience and support from your personal and professional team will get you through those moments of doubt or mistakes.

Given how complicated life is, keeping your focus on a simple, direct and clear action plan is your best ally to success.

Michael F. Kay is a Certified Financial Planner, practitioner and CPA. He is the president of the firm Financial Life Focus.

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6.6: Classification of Finance Problems

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• Page ID 37880

• Rupinder Sekhon and Roberta Bloom
• De Anza College

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Learning Objectives

In this section, you will review the concepts of chapter 6 to:

• Re-examine the types of financial problems and classify them.
• Re-examine the vocabulary words used in describing financial calculations

We'd like to remind the reader that the hardest part of solving a finance problem is determining the category it falls into. So in this section, we will emphasize the classification of problems rather than finding the actual solution.

We suggest that the student read each problem carefully and look for the word or words that may give clues to the kind of problem that is presented. For instance, students often fail to distinguish a lump-sum problem from an annuity. Since the payments are made each period, an annuity problem contains words such as each, every, per etc.. One should also be aware that in the case of a lump-sum, only a single deposit is made, while in an annuity numerous deposits are made at equal spaced time intervals. To help interpret the vocabulary used in the problems, we include a glossary at the end of this section.

Students often confuse the present value with the future value. For example, if a car costs $15,000, then this is its present value. Surely, you cannot convince the dealer to accept $15,000 in some future time, say, in five years. Recall how we found the installment payment for that car. We assumed that two people, Mr. Cash and Mr. Credit, were buying two identical cars both costing $15, 000 each. To settle the argument that both people should pay exactly the same amount, we put Mr. Cash's cash of $15,000 in the bank as a lump-sum and Mr. Credit's monthly payments of x dollars each as an annuity. Then we make sure that the future values of these two accounts are equal. As you remember, at an interest rate of 9%

the future value of Mr. Cash's lump-sum was \(\$ 15,000(1+.09 / 12)^{60}\), and

the future value of Mr. Credit's annuity was \(\frac{x\left[(1+.09 / 12)^{60}-1\right]}{.09 / 12}\).

To solve the problem, we set the two expressions equal and solve for \(m\).

The present value of an annuity is found in exactly the same way. For example, suppose Mr. Credit is told that he can buy a particular car for $311.38 a month for five years, and Mr. Cash wants to know how much he needs to pay. We are finding the present value of the annuity of $311.38 per month, which is the same as finding the price of the car. This time our unknown quantity is the price of the car. Now suppose the price of the car is \(\mathrm{P}\), then

the future value of Mr. Cash's lump-sum is \(\mathrm{P}(1+.09 / 12)^{60}\), and

the future value of Mr. Credit's annuity is \(\frac{\$ 311.38\left[(1+.09 / 12)^{60}-1\right]}{.09 / 12}\).

Setting them equal we get,

\[\begin{array}{l} P(1+.09 / 12)^{60}=\frac{\$ 311.38\left[(1+.09 / 12)^{60}-1\right]}{.09 / 12} \\ P(1.5657)=(\$ 311.38)(75.4241) \\ P(1.5657)=\$ 23,485.57 \\ P=\$ 15,000.04 \end{array} \nonumber \]

CLASSIFICATION OF PROBLEMS AND EQUATIONS FOR SolutionS

We now list six problems that form a basis for all finance problems. Further, we classify these problems and give an equation for the solution.

Example \(\PageIndex{1}\)

If $2,000 is invested at 7% compounded quarterly, what will the final amount be in 5 years?

Classification: Future (accumulated) Value of a Lump-sum or FV of a lump-sum.

Equation: \[\mathrm{FV}=\mathrm{A}=\$ 2000(1+.07 / 4)^{20} \nonumber \]

Example \(\PageIndex{2}\)

How much should be invested at 8% compounded yearly, for the final amount to be $5,000 in five years?

Classification: Present Value of a Lump-sum or PV of a lump-sum.

Equation: \[\mathrm{PV}(1+.08)^{5}=\$ 5,000 \nonumber \]

Example \(\PageIndex{3}\)

If $200 is invested each month at 8.5% compounded monthly, what will the final amount be in 4 years?

Classification: Future (accumulated) Value of an Annuity or FV of an annuity.

Equation: \[\mathrm{FV}=\mathrm{A}=\frac{\$ 200\left[(1+.085 / 12)^{48}-1\right]}{.085 / 12} \nonumber \]

Example \(\PageIndex{4}\)

How much should be invested each month at 9% for it to accumulate to $8,000 in three years?

Classification: Sinking Fund Payment

Equation: \[\frac{m\left[(1+.09 / 12)^{36}-1\right]}{.09 / 12}=\$ 8,000 \nonumber \]

Example \(\PageIndex{5}\)

Keith has won a lottery paying him $2,000 per month for the next 10 years. He'd rather have the entire sum now. If the interest rate is 7.6%, how much should he receive?

Classification: Present Value of an Annuity or PV of an annuity.

Equation: \[\mathrm{PV}(1+.076 / 12)^{120}=\frac{\$ 2000\left[(1+.076 / 12)^{120}-1\right]}{.076 / 12} \nonumber \]

Example \(\PageIndex{6}\)

Mr. A has just donated $25,000 to his alma mater. Mr. B would like to donate an equivalent amount, but would like to pay by monthly payments over a five year period. If the interest rate is 8.2%, determine the size of the monthly payment?

Classification: Installment Payment .

Equation: \[\frac{m\left[(1+.082 / 12)^{60}-1\right]}{.082 / 12}=\$ 25,000(1+.082 / 12)^{60} \nonumber \]

GLOSSARY: VOCABULARY AND SYMBOLS USED IN FINANCIAL CALCULATIONS

As we’ve seen in these examples, it’s important to read the problems carefully to correctly identify the situation. It is essential to understand to vocabulary for financial problems. Many of the vocabulary words used are listed in the glossary below for easy reference.

• The Biggest Accounting Problems and...

The Biggest Accounting Problems and How to Overcome Them

Table of Content

Key takeaways.

• Accounting problems and challenges involve difficulties in managing financial transactions, records, and reporting due to factors like outdated systems, regulations, and human error.
• Streamline multi-currency management with advanced accounting software and international finance expertise to overcome complexities and ensure accurate financial processes.
• Modernize accounting operations by embracing technology and automation to eliminate inefficiencies caused by outdated systems and manual processes, ensuring accurate financial management and improved productivity.

Introduction 

In today’s dynamic business landscape, accounting professionals encounter a multitude of financial challenges and complexities. From outdated systems to regulatory compliance issues, these obstacles can impede financial progress and hinder business growth.

Navigating the intricacies of accounting is crucial for running a successful business, but overcoming these challenges can be daunting. That’s why we’ve compiled a list of the top 10 accounting problems and challenges, along with simple solutions to eliminate them. By addressing these issues head-on, your business can stay on track for success.

What Are Accounting Problems and Challenges?

Accounting problems and challenges refer to difficulties or obstacles encountered in the process of managing financial transactions, records, and reporting within an organization. These challenges can arise due to various factors, such as outdated systems, complex regulations, human error, or inadequate internal controls.

For example, a company may face challenges in accurately recording transactions, reconciling accounts, or complying with changing accounting standards and regulations. These problems can impact the reliability and accuracy of financial information, potentially leading to errors in financial statements and reports.

Addressing accounting problems and challenges requires proactive measures, including implementing efficient systems and processes, staying updated on regulatory changes, enhancing internal controls, and providing adequate training to accounting staff.

The Most Common Accounting Problems and Challenges

There’s a famous quote that you must have read somewhere, and it is relevant to this topic:

“Only a fool learns from his own mistakes. The wise man learns from the mistakes of others.”

Mistakes are valuable lessons that we must cherish and learn from. However, it is even more important to identify the mistakes made by businesses or individuals like us, in order to gain insights on how to avoid them.

Keeping this in mind, we have compiled a comprehensive list of the top 7 accounting challenges that you are likely to encounter, along with effective solutions to overcome them.

Top 7 Accounting Problems and Solutions

1. difficulty in managing multiple currencies.

Accounting across borders presents a formidable challenge for businesses. Managing multiple currencies introduces complexities due to fluctuating exchange rates and intricate currency conversion calculations. These factors can complicate financial reporting and analysis, leading to potential errors and inefficiencies in accounting processes.

Solution:  To address this accounting challenge effectively, businesses can leverage advanced accounting software equipped to handle multi-currency transactions seamlessly. These tools automate currency conversions and provide real-time updates on exchange rates, ensuring accurate and efficient accounting processes. Additionally, seeking expertise in international finance and implementing hedging strategies can help mitigate currency risks and optimize financial management across borders.

2. Payroll errors

With the rapid evolution of the employment landscape, businesses are facing new challenges in managing payroll efficiently. The shift towards remote work and diverse geographical locations has introduced complexities in navigating tax laws and employment regulations, adding to the payroll management burden.

Research indicates that 54% of companies acknowledge the need for enhancements in their current payroll policies and practices, reflecting the widespread recognition of existing payroll challenges.

Payroll errors can have significant repercussions for businesses, ranging from financial losses to legal penalties, not to mention the adverse impact on employee morale and productivity. Despite the critical importance of accurate payroll processing, statistics show that 54% of Americans have encountered pay-related issues.

Solution:  To mitigate payroll errors, it’s essential to prioritize regular payroll reconciliation after each payroll cycle and promptly address any discrepancies with the assistance of an accountant. Moreover, leveraging automated payroll solutions can streamline processes, minimize errors, and ensure adherence to pertinent laws and regulations.

3. Cash flow management

Maintaining a healthy cash flow is crucial for the survival and growth of any business. Did you know that  82%  of all businesses fail due to poor cash flow management? Despite its importance, many businesses struggle with cash flow, leading to liquidity issues and potential insolvency.

Solution:  Investing in automation is the most effective way to manage cash flow and monitor your business’s financial performance. By leveraging automated  cash flow management tools , you can streamline treasury operations and reduce the need for manual tasks. This enables financial professionals to focus on liquidity and risk management, ultimately enhancing team efficiency.

4. Delayed accounts receivable collection

Delayed accounts receivable collection poses a significant accounting problem for businesses, impacting  cash flow  and operational efficiency. Late payments from customers disrupt financial stability and hinder the ability to meet obligations, leading to increased financial strain.

Solution:  To address this  problem of accounting, businesses must implement strategic accounts receivable management practices. This includes establishing clear payment terms and communicating them upfront to set expectations with customers. Additionally, prompt follow-up on overdue payments and incentives for early settlement can expedite collections and improve cash flow. By adopting a proactive approach to accounts receivable management, businesses can enhance financial stability and operational effectiveness.

5. Lack of internal controls

Internal controls are policies and procedures designed to safeguard assets, prevent fraud, and ensure accurate financial reporting. However, many businesses lack robust internal controls, leaving them vulnerable to errors and fraudulent activities.

Solution:  Develop and implement a comprehensive system of internal controls tailored to your business’s specific needs. This may include segregation of duties, regular audits, and implementing checks and balances throughout the organization.

6. Regulatory compliance and reporting burdens

Navigating the ever-evolving landscape of regulatory compliance and reporting requirements can be a daunting task for accounting professionals. With complex regulations such as GAAP and IFRS constantly evolving, staying compliant can feel like an uphill battle.

Solution:  To address these challenges effectively, businesses can implement solutions such as investing in advanced accounting software, providing regular training for financial professionals on regulatory changes, ensuring compliance with GAAP standards, and maintaining transparency in operations. By proactively addressing regulatory compliance issues and reporting burdens, businesses can enhance their financial reporting accuracy, compliance, and overall operational efficiency.

7. Outdated systems and manual processes

Technological advancements have transformed the accounting landscape, rendering outdated systems and manual processes inefficient. Despite this, finance teams, often considered the lifeblood of any successful business, still rely on obsolete systems and manual methods, struggling with technological obsolescence. Many of these teams continue to manually process and send payments, collect checks, reconcile financial data from a multitude of sources, and match a large volume of transactions.

This reliance on outdated methods hampers their ability to deliver accurate results and leads to hours of lost time. Without streamlined automation and digital integration, tasks such as data entry, reconciliation, and reporting become laborious and error-prone.

Solution:  To overcome this  issue in accounting, it’s imperative to embrace technology and automation. Regularly assess and upgrade accounting systems and software to stay current with technological advancements. Explore cloud-based solutions that offer scalability, automation, and real-time data access. Additionally, provide training and support to employees to ensure smooth adoption of new technologies.

By harnessing the power of innovative  accounting solutions  like HighRadius, accounting heads and managers can streamline processes and eliminate manual errors. HighRadius offers cutting-edge automation tools that seamlessly integrate with existing systems, revolutionizing the way businesses manage their finances.

1. How do you resolve accounting issues?

Resolving accounting issues requires a systematic approach, starting with identifying the root cause through audits and reviewing financial records. Implementing corrective measures in line with accounting standards, such as adjusting entries or implementing internal controls, is crucial. Also, effective communication with stakeholders is essential to ensure transparency and alignment.

2. What constitutes the most challenging aspect of an accountant’s role?

The role of an accountant comes with various challenges, but one of the most significant is striking the right balance between accuracy and efficiency while also meeting tight deadlines and managing a high volume of transactions.

3. How can we solve accounting problems?

Solving accounting problems demands a multifaceted approach. It starts with a thorough analysis followed by the implementation of appropriate solutions. Additionally, leveraging technology can streamline processes and help prevent future issues.

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