present value

Present Value Calculator

This present value calculator can be used to calculate the present value of a certain amount of money in the future or periodical annuity payments.

Present Value of Future Money

Present Value: $558.39

Total Interest: $441.61

Present Value of Periodical Deposits

Present Value: $736.01

Related Investment Calculator | Future Value Calculator

Present Value

Present Value, or PV, is defined as the value in the present of a sum of money, in contrast to a different value it will have in the future due to it being invested and compound at a certain rate.

Net Present Value

A popular concept in finance is the idea of net present value, more commonly known as NPV. It is important to make the distinction between PV and NPV; while the former is usually associated with learning broad financial concepts and financial calculators, the latter generally has more practical uses in everyday life. NPV is a common metric used in financial analysis and accounting; examples include the calculation of capital expenditure or depreciation. The difference between the two is that while PV represents the present value of a sum of money or cash flow, NPV represents the net of all cash inflows and all cash outflows, similar to how the net income of a business after revenue and expenses, or how net benefit is found after evaluating the pros and cons to doing something. The inclusion of the word 'net' denotes the combination of positive and negative values for a figure.

The Time Value of Money

PV (along with FV, I/Y, N, and PMT) is an important element in the time value of money, which forms the backbone of finance. There can be no such things as mortgages , auto loans , or credit cards without PV.

To learn more about or do calculations on future value instead, feel free to pop on over to our Future Value Calculator . For a brief, educational introduction to finance and the time value of money, please visit our Finance Calculator .

• Present Value (PV)

Written by True Tamplin, BSc, CEPF®

Reviewed by subject matter experts.

Updated on July 12, 2023

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Table of contents, what is present value (pv).

Present Value is a financial concept that represents the current worth of a sum of money or a series of cash flows expected to be received in the future.

PV takes into account the time value of money , which assumes that a dollar received today is worth more than a dollar received in the future due to its potential earning capacity.

The time value of money is a fundamental concept in finance, which states that money available at the present time is worth more than the same amount in the future.

This is because of the potential earnings that could be generated if the money were invested or saved.

PV is a crucial concept in finance, as it allows investors and financial managers to compare the value of different investments , projects, or cash flows.

Understanding PV is essential for making informed decisions about the allocation of resources and the evaluation of investment opportunities.

Present Value Formula

Components of the formula.

The Present Value formula is calculated using the following components:

Future Cash Flow: The amount of money expected to be received in the future.

Discount Rate: The interest rate used to discount future cash flows back to their present value.

Time Period: The number of periods into the future when the cash flow is expected to occur.

The formula for calculating Present Value is as follows:

PV = CF / (1 + r)^n

Where PV is the Present Value, CF is the future cash flow, r is the discount rate, and n is the time period.

PV Calculation Examples

Suppose an investor expects to receive $10,000 in five years and uses a discount rate of 5%. Using the Present Value formula, the PV of this future cash flow can be calculated as:

PV = $10,000 / (1 + 0.05)^5 = $7,835.26

This means that the current value of the $10,000 expected in five years is $7,835.26, considering the time value of money and the 5% discount rate.

Applications of Present Value

Investment analysis.

PV is used to evaluate and compare different investment opportunities by calculating the present value of their expected future cash flows. This helps investors determine the most profitable investments.

Capital Budgeting

Companies use PV in capital budgeting decisions to evaluate the profitability of potential projects or investments. By calculating the present value of projected cash flows, firms can compare the value of different projects and allocate resources accordingly.

Bond Valuation

In bond valuation, PV is used to calculate the present value of future coupon payments and the bond's face value. This information is used to determine the bond's fair market price.

Loan Amortization

PV calculations are used in loan amortization schedules to determine the present value of future loan payments. This information helps borrowers understand the true cost of borrowing and assists lenders in evaluating loan applications.

Retirement Planning

Individuals use PV to estimate the present value of future retirement income, such as Social Security benefits or pension payments . This information helps individuals determine how much they need to save and invest to achieve their desired retirement income.

Factors Affecting Present Value

Interest rates.

Interest rates have a significant impact on PV calculations. Higher interest rates result in lower present values, as future cash flows are discounted more heavily. Conversely, lower interest rates lead to higher present values.

Inflation affects the purchasing power of money over time, which in turn influences the present value of future cash flows. Higher inflation rates reduce the present value of future cash flows, while lower inflation rates increase present value.

Risk and Uncertainty

The level of risk and uncertainty associated with future cash flows can impact the discount rate used in PV calculations. Higher levels of risk and uncertainty typically require higher discount rates, which result in lower present values.

Conversely, lower levels of risk and uncertainty lead to lower discount rates and higher present values.

Time Horizon

The time horizon , or the length of time until a future cash flow is expected to be received, also impacts the present value. The longer the time horizon, the lower the present value, as future cash flows are subject to a greater degree of discounting.

Present Value vs Net Present Value (NPV)

Definitions and distinctions.

While Present Value calculates the current value of a single future cash flow, Net Present Value (NPV) is used to evaluate the total value of a series of cash flows over time.

NPV is calculated by summing the present values of all future cash flows, including inflows and outflows, and represents the net benefit of an investment or project.

When to Use PV or NPV

PV is suitable for evaluating single cash flows or simple investments, while NPV is more appropriate for analyzing complex projects or investments with multiple cash flows occurring at different times.

Comparison of the Two Methods

Both PV and NPV are important financial tools that help investors and financial managers make informed decisions.

PV provides a snapshot of the value of a single future cash flow, while NPV offers a comprehensive assessment of the net value of an investment or project, considering all cash flows over time.

Limitations of Present Value

Dependence on accurate cash flow estimation.

PV calculations rely on accurate estimates of future cash flows, which can be difficult to predict. Inaccurate cash flow estimates can lead to incorrect present values, which may result in suboptimal investment decisions.

Sensitivity to Discount Rate Changes

PV calculations are sensitive to changes in the discount rate. Small changes in the discount rate can significantly impact the present value, making it challenging to accurately compare investments with varying levels of risk or uncertainty.

Challenges With Non-conventional Cash Flow Patterns

PV calculations can be complex when dealing with non-conventional cash flow patterns, such as irregular or inconsistent cash flows. In these cases, calculating an accurate present value may require advanced financial modeling techniques.

Present Value is a fundamental concept in finance that enables investors and financial managers to assess and compare different investments, projects, and cash flows based on their current worth.

By taking into account factors such as interest rates, inflation, risk, and time horizon, financial professionals can employ Present Value calculations to make informed decisions about resource allocation and investment opportunities.

Understanding the applications and limitations of Present Value, including its dependence on accurate cash flow estimation and sensitivity to discount rate changes, is essential for making sound financial decisions.

Moreover, it is vital to recognize the differences between Present Value and Net Present Value, as each method serves a unique purpose in financial analysis.

While Present Value calculates the current value of a single future cash flow, Net Present Value evaluates the total value of a series of cash flows over time, offering a comprehensive assessment of an investment or project's net value.

By utilizing these financial tools effectively, investors and financial managers can optimize their investment portfolios and maximize their returns on investment.

Present Value (PV) FAQs

What is present value (pv).

Present value is a financial concept that represents the current value of an expected future sum of money, after accounting for the time value of money and the risk associated with the investment.

How is present value calculated?

PV is calculated by taking the future sum of money and discounting it by a specific rate of return or interest rate. This discount rate takes into account the time value of money, which means that money today is worth more than the same amount of money in the future.

What is the significance of present value in finance?

PV is a significant concept in finance, as it helps individuals and businesses to make investment decisions by estimating the current value of future cash flows. By calculating the PV of potential investments, investors can determine if an investment is worth pursuing or if they would be better off pursuing alternative investment opportunities.

What factors affect present value?

The primary factors that affect PV include the interest rate or discount rate used in the calculation, the length of time until the expected future cash flow is received, and the risk associated with the investment. Generally, a higher interest rate will result in a lower PV, while a longer time horizon or higher risk will result in a lower PV.

What are some common applications of present value?

PV is commonly used in a variety of financial applications, including investment analysis, bond pricing, and annuity pricing. It is also used to evaluate the potential profitability of capital projects or to estimate the current value of future income streams, such as a pension or other retirement benefits.

About the Author

True Tamplin, BSc, CEPF®

True Tamplin is a published author, public speaker, CEO of UpDigital, and founder of Finance Strategists.

True is a Certified Educator in Personal Finance (CEPF®), author of The Handy Financial Ratios Guide , a member of the Society for Advancing Business Editing and Writing, contributes to his financial education site, Finance Strategists, and has spoken to various financial communities such as the CFA Institute, as well as university students like his Alma mater, Biola University , where he received a bachelor of science in business and data analytics.

To learn more about True, visit his personal website or view his author profiles on Amazon , Nasdaq and Forbes .

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What Is Present Value?

How to calculate the present value of an investment

Definitions and Examples of Present Value

Types of present value, how present value works, present value vs. future value.

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Present value is what a sum of money in the future is worth in today’s dollars at a rate of interest.

The basic principle behind the time value of money is simple: One dollar today is worth more than one dollar you will receive in the future. This is because you can invest the dollar you have today, and it can grow over time at a rate of return, or interest. The dollar you receive “tomorrow” can’t be invested today, and therefore doesn’t have the same potential to increase in value.

Present value is what cash flow received in the future is worth today at a rate of interest called the “discount” rate.

Here’s an easy way to look at present value. If you invest $1,000 in a savings account today at a 2% annual interest rate, it will be worth $1,020 at the end of one year ($1,000 x 1.02). Therefore, $1,000 is the present value of $1,020 one year from now at a 2% interest, or discount, rate.

The discount rate has a big impact on the present value. What if we changed the discount rate in our example from 2% to 5%? How much money do we need to invest at 5% to have $1,020 at the end of one year? The calculation would look like this: $971.43 X 1.05 = $1,020.

So instead of needing $1,000, we only need $971.43 to reach the same resulting amount. More on this calculation later.

Present Value of a Lump Sum

Think of the present value of a lump sum in the future as the money you would need to invest today at a rate of interest that would accumulate to the desired amount in the future. In the example above, the amount of money you need to invest today that will accumulate to $1,020 a year in the future at 2% is $1,000.

Present Value of an Annuity

An annuity is a series of equal payments received for a fixed period of time. For example, lottery winners often have the option to receive their prize money in equal payments over 20 years. 

The present value of an annuity is the value of all the payments received over a period of time in the future in today’s dollars, at a certain discount rate.

One way to think of the present value of an annuity is a car loan. The initial loan is the present value. The annuity is the principal and interest payments you make every month until the balance of the loan is zero.

Present Value of Unequal Cash Flows

When a business invests in new equipment or a project, it may take time to see results. The revenue or cash flow projected may be low at first but grow over time.

When making investment decisions, a business has to analyze the present value of unequal cash flows.

The easiest way to calculate present value is to use one of the many free calculators on the internet, or a financial calculator app like the HP12C Financial Calculator, available on Google Play and in the Apple App Store. Most spreadsheet programs have present-value functions as well.

Present Value Tables

Another easy way to calculate present value is to use a present value table. These tables have factors and interest rates for annuity payments and lump sums. They look like this:

If we want to know the present value of $100,000 two years in the future at 4%, for instance, the calculation is:

Future value = $100,000

Present value factor at 4% for two years = .925 (see first table above)

Present value = $100,000 X .925 = $92,500

Real-World Example of Present Value

Joseph and Josephine are planning for their retirement . They decide that they will need an income as of age 65 of $80,000 a year, and they project living to age 85. Joseph and Josephine need to know how much money they need at age 65 to produce $80,000 of income for 20 years, assuming they will earn 4% (the discount rate).

Annuity payment = $80,000

Years paid = 20

Discount rate = 4%

Annuity factor from a present value table = 13.9503

Present value = $80,000 X 13.9503 = $1,116,024

At age 65, Joseph and Josephine will need $1,116,024 to produce $80,000 of income for 20 years at 4%.

Unequal Cash Flows

No matter what method you use– spreadsheet , calculator, table, or formula–calculating the present value of unequal cash flows takes a bit of work. An Excel spreadsheet is the easiest way to use the NPV (net present value) function; however, here’s an example of how to use the tables.

We can also measure future value . Future value is what a sum of money invested today will be worth over time, at a specified rate of interest.

As discussed earlier, $1,000 deposited in a savings account at a 2% annual interest rate has a future value of $1,020 at the end of one year. Let's look at what happens at the end of two years:

That $1,000 deposit becomes $1,040.40. The extra change is the 2% return on the $20 earned at the end of Year 1. The process of interest earning interest is called “compounding,” and it has a powerful effect on the future value of an investment.

Future value is the mirror image of present value.

Key Takeaways

• Present value measures the effect of time on money.
• Present value is what a sum of money or a series of cash flows paid in the future is worth today at a rate of interest called the “discount” rate.
• Present value is used to plan for financial goals and to make investment decisions.

Texas A&M University Commerce Department. " Present Value Tables ." Accessed July 29, 2021.

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• An Overview

Present Value

Net present value, key differences, the bottom line.

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Present Value vs. Net Present Value: What's the Difference?

Present Value vs. Net Present Value: An Overview

Present value (PV) is the current value of a future sum of money or stream of cash flow given a specified rate of return. Meanwhile, net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

Present value tells you what you'd need in today's dollars to earn a specific amount in the future. Net present value is used to determine how profitable a project or investment may be. Both can be important to an individual's or company's decision-making concerning investments or capital budgeting.

While PV and NPV both use a form of discounted cash flows to estimate the current value of future income , these calculations differ in an important way. The NPV formula also accounts for the initial capital outlay required to fund a project, making it a net figure. That makes it a more comprehensive indicator of potential profitability.

Since the value of revenue earned today is higher than that of revenue earned down the road , businesses discount future income by the investment's expected rate of return. This rate, called the hurdle rate , is the minimum rate of return a project must generate for the business to consider investing in it.

Key Takeaways

• Present value is the current value of a future sum of money that's discounted by a rate of return.
• It tells you the amount you'd need to invest today in order to earn a specific amount in the future.
• Net present value is the difference between the present value of cash inflows and cash outflows over a period of time.
• Both present value and net present value use discounted cash flows to estimate the current value of income.
• However, net present value also accounts for the initial outlay required to fund a project.

The PV calculation takes a future amount of cash and discounts it back to the present day. The formula for this is:

Present Value = FV/(1 + r) n

where FV is the future value, r is the required rate of return, and n is the number of time periods.

The NPV calculation takes the current value of future cash inflows and subtracts from it the current value of cash outflows. The formula for this is:

Net Present Value = cash flow/(1+i) t − initial investment

Where "i" is the required rate of return and "t" is the number of time periods.

Say that you can either receive $3,200 today and invest it at a rate of 4% or take a lump sum of $3,500 in a year. Calculating the PV of $3,500 can help you make a choice.

Present value = FV/(1 + r) n

Present value = $3,500/(1 + .04) 1

Present value = $3,365.38

That means you'd need to invest $3,365.38 today at 4% to get $3,500 a year later. The $3,200 today will result in a smaller return. Based on that, you may feel that the lump sum in a year looks more attractive.

Say that a company is considering investing in a potential project. It requires an initial investment of $10,000 and offers a future cash flow of $14,000 in a year. The required rate of return is 6%. We'll calculate the NPV using a simplified version of the formula shown previously.

Net present value = today's value of expected cash flows - today's value of cash invested

Net present value = $13,208 (the present value) - $10,000

Net present value = $3,208

The NPV is $3,208 and indicates project profitability. Based on that and other metrics, the company may decide to pursue the project.

What Does Net Present Value Indicate?

Net present value indicates the potential profit that could be generated by a project or investment. A positive net present value means that a project is earning more than the discount rate and may be financially viable.

Is a Higher Net Present Value Better?

A project or investment with a higher net present value is typically considered more attractive than one with a lower NPV or a negative NPV. Bear in mind, though, that companies normally look at other metrics as well before a final decision on a go-ahead is made.

Is PV or NPV More Important for Capital Budgeting?

NPV is. That's because it accounts for the PV and the costs required to fund a project. So it can provide a more informed view of project feasibility. That, in turn, informs capital budgeting.

While the PV value is useful, the NPV calculation is invaluable to capital budgeting . A project with a high PV figure may actually have a much less impressive NPV if a large amount of capital is required to fund it. As a business expands, it looks to finance only those projects or investments that yield the greatest returns, which in turn enables additional growth. Given a number of potential options, the project or investment with the highest NPV is generally pursued.

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PV Calculator (Click Here or Scroll Down)

Present Value (PV) is a formula used in Finance that calculates the present day value of an amount that is received at a future date. The premise of the equation is that there is "time value of money".

Time value of money is the concept that receiving something today is worth more than receiving the same item at a future date. The presumption is that it is preferable to receive $100 today than it is to receive the same amount one year from today, but what if the choice is between $100 present day or $106 a year from today? A formula is needed to provide a quantifiable comparison between an amount today and an amount at a future time, in terms of its present day value.

Use of Present Value Formula

The Present Value formula has a broad range of uses and may be applied to various areas of finance including corporate finance, banking finance, and investment finance. Apart from the various areas of finance that present value analysis is used, the formula is also used as a component of other financial formulas.

Example of Present Value Formula

An individual wishes to determine how much money she would need to put into her money market account to have $100 one year today if she is earning 5% interest on her account, simple interest.

The $100 she would like one year from present day denotes the C 1 portion of the formula, 5% would be r , and the number of periods would simply be 1.

Putting this into the formula, we would have

When we solve for PV, she would need $95.24 today in order to reach $100 one year from now at a rate of 5% simple interest.

Alternative Formula

The Present Value formula may sometimes be shown as

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• Present Value Factor
• Net Present Value
• Annuity - Present Value
• PV - Continuous Compounding
• Solve for Number of Periods - PV&FV

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Present Value Calculator

Table of contents

Present value calculator is a tool that helps you estimate the current value of a stream of cash flows or a future payment if you know their rate of return. Present value, also called present discounted value , is one of the most important financial concepts and is used to price many things, including mortgages, loans, bonds, stocks, and many, many more.

Many of the world's economies are based on future value calculations. Money is worth more now than it is later due to the fact that it can be invested to earn a return. (You can learn more about this concept in our time value of money calculator ).

Present value is also useful when you need to estimate how much to invest now in order to meet a certain future goal, for example, when buying a car or a home. So, if you're wondering how much your future earnings are worth today, keep reading to find out how to calculate present value.

If you find this topic interesting, you may also be interested in our future value calculator , or if you would like to calculate the rate of return, you can apply our discount rate calculator . Keep reading to find out how to work out the present value and what's the equation for it.

Present value formula

To calculate the present value of future incomes, you should use this equation:

PV = FV / (1 + r)

• PV — Present value;
• FV — Future value; and
• r — Interest rate.

Thanks to this formula, you can estimate the present value of an income that will be received in one year. If you want to calculate the present value for more than one period of time, you need to raise the (1 + r) by the number of periods. This turns the equation into this:

PV = FV / (1 + r) n

• n — Number of periods.

This is the most commonly used present valuation model. It applies compound interest , which means that interest increases exponentially over subsequent periods.

How to calculate present value

If you read the previous section, you already know that to estimate the present value, you need to:

• Determine the future value. In our example, let's make it $100 .
• Determine a periodic rate of interest. Let's say 8% .
• Determine the number of periods, n . Let's make it 2 years .
• Divide the future value by (1 + rate of interest) n .

In our example, it will look like this:

$100 / (1 + 0.08) 2 = $85.73

Now you know how to estimate the present value of your future income on your own, or you can simply use our present value calculator.

Other important present value calculations

Present value calculations are tied closely to other formulas, such as the present value of annuity . Annuity denotes a series of equal payments or receipts, which we have to pay at even intervals, for example, rental payments or loans. This causes the equation to be slightly different. Click through to our present value of annuity calculator to learn more.

What is present value?

The present value of an investment is the value today of a cash flow that comes in the future with a specific rate of return.

That means if I want to receive $1000 in the 5th year of investment, that would require a certain amount of money in the present, which I have to invest with a specific rate of return ( r ).

For example, if r = 20% , the present value would be $401.88 .

How to use present value for investing?

There are two main ways you can use the Omni Calculator present value tool:

• To calculate how much you should invest now for a specific cash flow in the future, given the yearly return.
• Given the desired future cash flow, the rate of return, and its present value, you can use the tool to determine how much time you have to leave the money compounding (gaining interest).

What is the present value of a cash flow of $1000 in 5 years?

$620.92. Here is how this answer is calculated:

• We have to define the rate of return ( r ).
• Suppose we take r = 10% . Then, we divide $1000 by the result of (1 + r) to the power of 5, or 1000/(1.1)⁵.
• We obtain $620.92 , the present value of $1000 in 5 years, with a rate of return of 10% annually.

How to know if a present value of an investment is good or bad?

Here's what you need to do to answer this question:

Acknowledge all the future cash flows that will come in the future and their specific time.

Bring all those future cash flows to the present, meaning we have to calculate their present value. You could try the Omni Calculator present value tool for this step.

Sum all the present values, then subtract the initial investment from that sum. If the final result is positive , then it is a good investment .

Future value

Interest rate

Compound frequency

How often the interest is added.

Present value

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How to Calculate Present Value (Detailed Examples Included)

April 14, 2021 By Vash Leave a Comment

In this article, we’re going to explore how to calculate Present Value. It’s a pretty in-depth article, so you might want to grab a cup of tea. If you’re just looking for the Present Value formula, we’ve included it just below.

Okay, let’s get into it.

The Present Value is calculated as…

Now, if you want to understand how it  really works (and why it works), then keep reading.

If the equation above is freaking you out, calm down. We’ve got your back. Stay with us.

What is Present Value?

Firstly, what is Present Value?

So it’s the value of future expectations or future cash flow, expressed in today’s terms.

Thus, the Present Value ultimately just reflects how much something is worth right here, right now, in the present. Hence the term “Present” value.

The Present Value Function

The Present Value is ultimately a function of two things, including:

• future expectations, and

Uses of the Present Value

The Present Value is probably the most important concept in Finance. Approximately 70%-80% of concepts in Finance end up relying on the PV in one way or another.

Broadly speaking though, the PV can be used for:

Investment Appraisal / Capital Budgeting

• Valuation (using the Discounted Cash Flow (DCF) valuation method)

Let’s now briefly consider these two.

We have a separate post on what capital budgeting is if you’re interested in learning more. But one of the most popular investment appraisal tools is the Net Present Value (NPV) .

And the Net Present Value is heavily reliant on the PV. We can even see this in the name!

The Net Present Value is just the Present Value,  net of the  investment.

The value of a company, or a stock, a business, etc, is all fundamentally based on the Present Value of future expectations.

And while the specific cash flows vary depending on the valuation model, for instance:

• Free cash flow
• Free cash flow to Equity (aka Flow to Equity, FTE)

It’s still fundamentally about “discounting” those future cash flows back to the present. Much more on “discounting” further down, but we do also have a separate article on discounting future cash flows if you’re interested.

For now, let’s think about how to calculate Present Value.

How to Calculate Present Value

Calculating the Present Value is actually incredibly straightforward.

Present Value of a Single Cash flow

Let’s start with the simplest case, of estimating the Present Value of a single cash flow.

The formula for PV of a single cash flow is as follows…

Now, as with most things in math, stuff makes so much more sense when we look at examples.

So before we get into explaining the PV formula above, let’s consider an example.

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Present Value Calculation Example #1

Imagine that you want to have $12,500 in your bank account exactly 1 year from today. Assume that your bank pays 5% interest. Assuming that you don’t have anything in your bank account right now, how much would you need to deposit today in order to have $12,500 in your account next year?

To figure this out, as with most things, when you’re working with different timeframes, it’s a good idea to work with the timeline.

Setup a timeline

And we’re saying that we want to have exactly $12,500 in our bank account in precisely one year’s time.

We can think of all of this information like this…

The question is, how much do we need to deposit today?

To solve this, we can actually start with something that we already know.

Stick to the fundamentals

At this stage, you should know how to calculate future value . If you don’t, then don’t worry – just have a quick read of our sister article and then come back here.

We’re going to assume that you (at least roughly) know how to calculate the FV.

So we can actually start with something that looks like the future value.

In other words, we can take this timeline and transform it into an equation, and that would look something like this…

Why can we express it like this?

We know that we want the cash to be worth $12,500 in a year’s time. Thus we can say…

Solve for the Cash Flow

Rearranging the equation gives us…

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Solve this and you’ll find that the exact value we need to deposit is approximately equal to $11,904.76

And because this particular cash flow represents the cash in the present, we can essentially see this as the present value.

Thus, we can say…

Does that make sense? If any part of the example is not quite clear, please read it again before moving on any further.

We’re going to assume that you’re more or less alright, so let’s actually just think about that equation in a little more detail.

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Present Value Formula (for a single cash flow)

Here’s the generalised equation for the present value for single cash flow we saw earlier on…

Components of the PV Formula

• interest rate,
• hurdle rate
• cost of capital
• required rate
• the required rate of return
• the opportunity cost of capital
• we could go on, really…

And it’s called the discount rate because this is the rate that we’re using to discount the future cash flow .

The Discounting Process

“Discounting” is the process of taking a future cash flow expressing it in present terms by “bringing it back” to the present day.

Now, recall that earlier we said that the Present Value is ultimately a function of two things, including:

The discount rate is actually a proxy for risk, and therefore, it’s how we penalise future cash flows for their level of risk.

That’s how we incorporate the risk of not earning future expectations, into our estimate for the present value.

Hopefully, you kind of understand the intuition behind the present value formula.

If you haven’t quite understood it just yet, then please pause for a moment now. Take your time to think about the equation and think about how it is actually a function of two things — future expectations and risk.

And take your time to see how we’re discounting future cash flows to get to the present value. Because this really is very important.

Okay. We’re going to assume that you’re more or less alright. So let’s go ahead now and step things up just a little bit by considering the case with multiple cash flows.

Present Value of Multiple Cash flows

Calculating the Present Value of multiple cash flows is actually very similar to the single cash flow case.

In a sense, you can think of it as calculating the PV of a single cash flow,  multiple times .

This will make more sense when you see it work in an example, so let’s go ahead and do that now.

Present Value Calculation Example #2

Consider the following cash flow stream. You expect to earn $10,000; $15,000; and $18,000 in 1, 2, and 3 years’ times respectively.

Assume the discount rate is 10%.

What is the Present Value of these cash flows?

As always, because we’re working with timeframes over here, it’s a good idea to start with the timeline.

It’s just a different way of writing it. But the point is that we’ve got three different timeframes.

The approach to discount these 3 cash flows is actually identical to the case of the single cash flow we saw earlier.

We know that for a single cash flow, the present value is equal to…

Thus, if we think of these 3 cash flows as 3 separate and individual cash flows, then we can say that the first cash flow can be discounted as…

Put differently, we need to discount this cash flow over 2 years in order to express it in present terms.

Solve for the PV

Combining all 3 individual discounted cash flows we have…

Solving for each item gives us…

Finally, we just need to add the 3 numbers to get our answer!

And now that we know how to estimate the Present Value of multiple cash flows, we can think about what the Present Value formula actually looks like.

So we can say that the formula for the Present Value of multiple cash flows is…

And because the process of discounting the cash flows is identical across all cash flows, we can actually summarise this further as…

In a nutshell, then, we can say that the Present Value is nothing but the sum of the discounted future cash flows .

And with that, you now know how to calculate Present Value!

Wrapping Up

Hopefully, all of this makes sense.

So it’s the value of something expressed in today’s terms or in present terms .

Furthermore, you learned that the Present Value can be calculated by using this particular formula…

In a nutshell, it’s just sum of the discounted cash flows.

If any part of the article isn’t quite clear, please read it again.

The Present Value is an incredibly important concept – it’s what approximately 70-80% of Finance is based on in one way or another.

If the math in this article was a bit too advanced for you, then we  strongly  recommend  exploring and enrolling on our Financial Math Primer course (see below).

The course is designed for the  absolute beginner , and will really help you finally get the mathematical foundation you’ve always needed.

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Present Value (PV)

Money now is more valuable than money later on .

Why? Because you can use money to make more money!

You could run a business, or buy something now and sell it later for more, or simply put the money in the bank to earn interest.

Example: You can get 10% interest on your money.

So $1,000 now can earn $1,000 x 10% = $100 in a year.

Your $1,000 now can become $1,100 in a year's time .

Present Value

We say the Present Value of $1,100 next year is $1,000

Because we could turn $1,000 into $1,100 (if we could earn 10% interest).

Now let us extend this idea further into the future ...

How to Calculate Future Payments

Let us stay with 10% Interest . That means that money grows by 10% every year, like this:

• $1,100 next year is the same as $1,000 now .
• And $1,210 in 2 years is the same as $1,000 now .

In fact all those amounts are the same (considering when they occur and the 10% interest).

Easier Calculation

But instead of "adding 10%" to each year it is easier to multiply by 1.10 (explained at Compound Interest ):

So we get this (same result as above):

Future Back to Now

And to see what money in the future is worth now , go backwards (dividing by 1.10 each year instead of multiplying):

Example: Sam promises you $500 next year , what is the Present Value?

So $500 next year is $500 ÷ 1.10 = $454.55 now (to nearest cent).

The Present Value is $454.55

Example: Alex promises you $900 in 3 years , what is the Present Value?

So $900 in 3 years is:

Better With Exponents

But instead of $900 ÷ (1.10 × 1.10 × 1.10) it is better to use exponents (the exponent says how many times to use the number in a multiplication).

Example: (continued)

The Present Value of $900 in 3 years (in one go):

As a formula it is:

PV = FV / (1+r) n

• PV is Present Value
• FV is Future Value
• r is the interest rate (as a decimal, so 0.10, not 10%)
• n is the number of years

Use the formula to calculate Present Value of $900 in 3 years :

Let us use the formula a little more:

Example: What is $570 next year worth now, at an interest rate of 10% ?

But your choice of interest rate can change things!

Example: What is $570 next year worth now, at an interest rate of 15% ?

Or what if you don't get the money for 3 years

Example: What is $570 in 3 years worth now, at an interest rate of 10% ?

One last example:

Example: You are promised $800 in 10 years time. What is its Present Value at an interest rate of 6% ?

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Finance and capital markets

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• Introduction to present value
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Video transcript

Financial Mentor

Present value calculator – npv, what is the net present value (npv calculator) of a lump sum payment discounted for inflation.

Use this present value calculator to compute the value today of a lump sum payment in the ...show more instructions future – discounted for inflation and the time value of money.

The net present value calculates your preference for money today over money in the future because inflation decreases your purchasing power over time.

If you want to calculate the present value of a stream of payments instead of a one time, lump sum payment then try our present value of annuity calculator here.

And when you're done calculating present values then put that knowledge to use in this free 5-part video series showing you 5 Rookie Financial Planning Mistakes That Cost You Big-Time (and what to do instead!)

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What Is The Present Value Of A Future Lump Sum?

Are you expecting to receive a lump sum of money in the future?

What is the value of that money in today's dollars? What is it worth to you today?

You must always think about future money in present value terms so that you avoid unrealistic optimism and can make apples-to-apples comparisons between investment alternatives.

This Present Value Calculator makes the math easy by converting any future lump sum into today's dollars so that you have a realistic idea of the value received.

Below is more information about present value calculations so you understand the factors that affect your money and how to use this calculator properly.

Net Present Value

Net present value (NPV) is the value of your future money in today’s dollars. The concept is that a dollar today is not worth the same amount as a dollar tomorrow.

The purchasing power of your money decreases over time with inflation, and increases with deflation .

In addition, there is an implied interest value to the money over time that increases its value in the future and decreases (discounts) its value today relative to any future payment.

Since the value of money changes with time, all financial calculations must be brought to a constant date (usually today, thus the term “present” value) to make accurate comparisons between competing investment alternatives.

Net present value is considered a standard way of making these investment decisions.

Related: How to take back control of your portfolio

Businesses use present value calculations for capital expenditures and routine business planning. Similarly, smart wealth builders run their finances like a business so they also use net present value for better family financial planning.

Net Present Value Illustration

Imagine someone owes you $10,000 and that person promises to pay you back after five years. If we calculate the present value of that future $10,000 with an inflation rate of 7% using the net present value calculator above, the result will be $7,129.86.

What that means is the discounted present value of a $10,000 lump sum payment in 5 years is roughly equal to $7,129.86 today at a discount rate of 7%.

In other words, you would view $7,129.86 today as being equal in value to $10,000 in 5 years, based on the same assumptions.

That's because the impact to your net worth of $7,129.86 today is roughly equal to $10,000 in 5 years net of inflation and interest.

That is what this present value calculator is demonstrating.

Present Value Formula

It is important to understand that the three most important components of present value are time, expected rate of return, and the size of the future cash amount. All of this is shown below in the present value formula:

PV = FV/(1+r) n

PV = Present value, also known as present discounted value, is the value on a given date of a payment. FV = This is the projected amount of money in the future r = the periodic rate of return, interest or inflation rate , also known as the discounting rate. n = number of years

When Is The Present Value Used?

The present value formula has a broad range of uses.

It is used both independently in a various areas of finance to discount future values for business analysis, but it is also used as a component of other financial formulas.

For example, present value is used extensively when planning for an early retirement because you'll need to calculate future income and expenses.

Present value can also be used to give you a rough idea of the amount of money needed at the start of retirement to fund your spending needs. You'll then compare that to what you have saved now – or what you think you'll have saved by your retirement date – and that gives you a rough idea of whether your savings is on track or not.

Related: How to be a pro at growing your wealth

To get a full picture of the amount you need to retire, see our Ultimate Retirement Calculator here and how it applies net present value analysis for your retirement planning needs.

Pros And Cons Of The Present Value Method

The net present value calculator is easy to use and the results can be easily customized to fit your needs. You can adjust the discount rate to reflect risks and other factors affecting the value of your investments.

Another advantage of the net present value method is its ability to compare investments. As long as the NPV of each investment alternative is calculated back to the same point in time, the investor can accurately compare the relative value in today's terms of each investment.

However, there are few disadvantages of using the net present value method.

Always keep in mind that the results are not 100% accurate since it's based on assumptions about the future. The calculation can only be as accurate as the input assumptions – specifically the discount rate and future payment amount.

Since the future can never be known there is always an element of uncertainty to the calculation despite the the scientific accuracy of the calculation itself.

Another problem with using the net present value method is that it does not fully account for opportunity cost. However, you can adjust the discount rate used in the calculator to compensate for any missed opportunity cost or other perceived risks.

Final Thoughts

The Present Value Calculator is an excellent tool to help you make investment decisions.

It discounts any future lump sum payment to today's value so you can make apple-to-apples comparisons and make smart investment choice.

Simply knowing about future value and using it in your calculations will help you save money and make better investment decisions.

Present Value Calculator Terms & Definitions

• Future Value – The value of an asset at a specific date in the future.
• Inflation Rate – The rate at which the general level of prices for services and goods is rising, and, subsequently, purchasing power is falling.
• Compound Interval – How often inflation compounds.
• Present Value – The value today of a sum of money in the future, in contrast to some future value it will have when it has been invested at compound interest.

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Present Value Formula

The present value formula refers to the application of the time value of money that discounts the future cash flow to arrive at its present-day value. The present value formula consists of the present value and future value related to compound interest. The present value or PV is the initial amount (the amount invested, the amount lent, the amount borrowed, etc). The future value or FV is the final amount. i.e., FV = PV + interest.  Let us understand the present value formula in detail in the following section.

What is the Present Value Formula?

Present value (PV) formula finds application in finance to calculate the present day value of an amount that is received at a future date. The present value formula (PV formula) is derived from the compound interest formula. The compound interest formula is,

FV = PV (1 + r / n) nt

Dividing both sides by (1 + r / n) nt ,

PV = FV / (1 + r / n) nt

Thus, the present value formula is:

PV = FV / (1 + r / n) nt

• PV = Present value
• FV = Future value
• r = Rate of interest (percentage ÷ 100)
• n = Number of times the amount is compounding
• t = Time in years

The value of n varies depending on the number of times the amount is compounding.

• n = 1, if the amount is compounded yearly.
• n = 2, if the amount is compounded half-yearly.
• n = 4, if the amount is compounded quart-yearly.
• n = 12, if the amount is compounded monthly.
• n = 52, if the amount is compounded weekly.
• n = 365, if the amount is compounded daily.

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Examples Using Present Value Formula 

Example 1: Jonathan borrowed some amount from a bank at a rate of 7% per annum compounded annually. If he finished paying his loan by paying $6,500 at the end of 4 years, then what is the amount of loan that he had taken? Round your answer to the nearest thousands.

The future value is, FV = $6500.

The time is t = 4 years.

n = 1 (as the amount is compounded annually).

The rate of interest is, r = 7% =0.07.

Substitute all these values in the the present value formula:

PV = 6500 / (1 + 0.07/1) 1(4)  = 6500 / (1.07) 4  = 5,000 (The answer is rounded to the nearest thousands).

Therefore, the borrowed amount = $5,000

Example 2: Mia invested some amount in a bank where her amount gets compounded daily at 5% annual interest. What is the amount invested by Mia if the amount she got after 10 years is $1,650? Round your answer to the nearest thousands.

The future value is, FV = $1650.

The time, t = 10 years.

n = 365 (as the amount is compounded daily).

The rate of interest is, r = 5% =0.05.

Substitute all these values in the present value formula:

PV = FV / (1 + r / n) n t  

PV = 1650 / (1 + 0.05/365) 365(10)  = 1000 (The answer is rounded to the nearest thousands).

Therefore, the invested amount = $1,000

Example 3: Josie borrowed some amount from a bank at a rate of 5% per annum compounded annually. If she finished paying her loan by paying $4,500 at the end of 4 years, then what is the amount of loan that she had taken? Round your answer to the nearest thousands.

Solution:  

The future value is, FV = $4500.

PV = 4500 / (1 + 0.05/1) 1(4)  = 4500 / (1.05) 4  = 3,800 (The answer is rounded to the nearest thousands).

Therefore, the borrowed amount = $3,800

FAQs on Present Value Formula

What is the present value formula .

The term present value formula refers to the application of the time value of money that discounts the future cash flow to arrive at its present-day value. By using the present value formula, we can derive the value of money that can be used in the future. 

What is the Formula to Calculate the Present Value? 

The present value formula (PV formula) is derived from the compound interest formula. Hence the formula to calculate the present value is: 

What is the Present Value Formula in Excel? 

Calculating the present value in excel is extremely easy and quick and uses a different formula. Present value formula helps in calculating the money coming but not in the current situation but in the future. The present value formula in excel is: 

PV in excel is =PV(rate, nper, pmt, [fv], [type])

• Rate = Interest rate per period 
• nper = Number of payment periods
• pmt = Amount paid each period (if omitted—it’s assumed to be 0 and FV must be included)
• [fv] = Future value of the investment (if omitted—it’s assumed to be 0 and PMT must be included)
• [type] = When payments are made (0, or if omitted—assumed to be at the end of the period, or 1—assumed to be at the beginning of the period) 

What is the Future Value Formula that is Used in the Present Value? 

The future value formula is: 

How to calculate the present and future value of annuities

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In the world of finance, an annuity is a contract between you and a life insurance company in which you give the company a lump sum or series of payments, and in return, the insurer promises to provide you with a stream of income, either now or in the future.

But annuities can also be more of a general concept that describes anything that’s broken up into a series of payments. For example, a lottery winner may opt to receive a series of payments over time instead of a single lump sum distribution. This can also be called an annuity.

Two terms related to annuities are present value and future value.

Here’s what you need to know.

Present value of an annuity vs. future value of an annuity: What’s the difference?

While future value tells you how much a series of investments will be worth in the future, present value takes the opposite approach. It calculates the current amount of money you’d need to invest today to generate a stream of future payments, considering a specific interest rate.

The future value should be worth more than the present value since it’s earning interest and growing over time.

Ordinary annuity vs. annuity due: What’s the difference?

When using the general term “annuity,” there are two types of annuities: ordinary and period due.

• Ordinary annuity: Payments are due at the end of the period.
• Annuity due: Payments are due at the beginning of the period.

This seemingly minor difference in timing can impact the future value of an annuity because of the time value of money . Money received earlier allows it more time to earn interest, potentially leading to a higher future value compared to an ordinary annuity with the same payment amount.

You can use an online calculator to figure both the present and future value of an annuity, so long as you know the interest rate, payment amount and duration.

How to calculate future value of an ordinary annuity

The future value tells you how much a series of regular investments will be worth at a specific point in the future, considering the interest earned over time.

In simpler terms, it tells you how much money the annuity will be worth after all the payments are received and compounded with interest .

It’s a tool for planning how much you’ll accumulate by consistently contributing to a retirement plan or understanding the total repayment amount for a loan with regular installments.

Imagine you plan to invest a fixed amount, say $1,000, every year for the next five years at a 5 percent interest rate. The time value of money comes into play here. The first $1,000 you invest earns interest for a longer period compared to subsequent contributions. So, the earlier contributions have a greater impact on the final value.

To calculate the future value of these regular investments, we can use the following formula for ordinary annuities:

FV = C x [((1 + i)^n – 1) / i] where: FV = Future Value C = Cash flow per period (your regular investment amount – $1,000 in this example) i = Interest rate (expressed as a decimal) n = Number of compounding periods (number of years you invest)

This formula considers the impact of both regular contributions and interest earned over time. By using this formula, you can determine the total value your series of regular investments will reach in the future, considering the power of compound interest.

Using the example above:

FV = $1,000 x [((1 + 0.05)^5 – 1) / 0.05] Solving for FV: Calculate (1 + 0.05)^5: (1 + 0.05)^5 = 1.2762815625 Subtract 1 and divide by the interest rate (0.05): (1.2762815625 – 1) / 0.05 = 5.52563125 Multiply the result by the cash flow per period (C): $1,000 x 5.52563125 ≈ $5,525.63

Therefore, the future value of your regular $1,000 investments over five years at a 5 percent interest rate would be about $5,525.63.

Note: This calculation assumes equal annual contributions and compound interest applied at the end of each year. In reality, accumulated interest might be different depending on how often interest is compounded.

How to calculate the present value of an ordinary annuity

Present value of an annuity refers to how much money must be invested today in order to guarantee the payout you want in the future.

Essentially, it asks: How much money do you need to invest now to generate a specific amount of money down the road?

Using the same example of five $1,000 annual payments, the present value calculation would determine the single upfront investment required to generate this future income stream, assuming a certain interest rate, in this case, 5 percent.

The formula for calculating the present value of an ordinary annuity is:

PV = C x [(1 – (1 + i)^-n) / i] where: PV = Present Value C = Cash flow per period (amount of each annual payment – $1,000 in this example) i = Interest rate (expressed as a decimal) n = Number of compounding periods (number of years)

By plugging in the values and solving the formula, you can determine the amount you’d need to invest today to receive the future stream of payments. In this example, with a 5 percent interest rate, the present value might be around $4,329.48.

This concept helps you compare future income streams with current investment opportunities, allowing you to make informed financial decisions.

If you own an annuity, the present value represents the cash you’d get if you cashed out early, before any fees, penalties or taxes are taken out. You can usually find the current present value of your annuity on your policy statements or your online account.

How to calculate the future value of an annuity due

Now let’s explore annuity due, where payments happen at the beginning of each period.

This slight difference in timing impacts the future value because earlier payments have more time to earn interest. Imagine investing $1,000 on Oct. 1 instead of Oct. 31 — it gains an extra month of interest growth.

To account for this time advantage, the formula for the future value of an annuity due is:

FVAnnuity Due = C x [((1 + i)^n – 1) / i] x (1 + i) where: FVAnnuity Due = Future Value of the annuity due C = Cash flow per period (your regular investment amount) i = Interest rate (expressed as a decimal) n = Number of compounding periods (number of years)

This formula incorporates both the time value of money within the period and the additional interest earned due to earlier payments.

Using the same example:

C = $1,000 (regular investment) i = 0.05 (5 percent interest rate) n = 5 (number of years) [((1 + 0.05)^5 – 1) / 0.05] ≈ 5.53 Multiply this result by (1 + i): 5.53 x (1 + 0.05) ≈ 5.8019

Therefore, the future value of your annuity due with $1,000 annual payments at a 5 percent interest rate for five years would be about $5,801.91.

Remember: Annuity due results in a higher future value compared to an ordinary annuity because of earlier payments.

How to calculate the present value of an annuity due

Similar to the future value, the present value calculation for an annuity due also considers the earlier receipt of payments compared to ordinary annuities. This reduces the present value needed to generate the same future income stream.

Think about it this way: Having $1,000 today is more valuable than having $1,000 a year from now because you can invest it and earn interest. So for an annuity due where you receive payments at the beginning of each period, you’d need to invest less today to generate the same future cash flow compared to an ordinary annuity with payments at the end.

The formula for the present value of an annuity due is:

PVAnnuity Due = C x [(1 – (1 + i)^-n) / i] x (1 + i) where: PVAnnuity Due = Present Value of the annuity due C = Cash flow per period (your regular payment amount) i = Interest rate (expressed as a decimal) n = Number of compounding periods (number of periods) (1 + 0.05)^-5 ≈ 0.783526 Subtract the result from 1 and divide by the interest rate (0.05): [1 – (1 + 0.05)^-5] / 0.05 ≈ 4.33 Multiply this result by the cash flow per period (C) and then by (1 + i): $1,000 x 4.33 x (1 + 0.05) ≈ $4,545.95

So the present value you’d need to invest today to cover five $1,000 payments, assuming a 5 percent interest rate, would be about $4,545.95.

As a reminder, this calculation assumes equal monthly payments and compound interest applied at the beginning of each month. In reality, interest accumulation might differ slightly depending on how often interest is compounded.

By calculating the present value, you can understand the effective cost in today’s dollars, potentially helping you with budgeting or financial planning.

Bottom line

Understanding annuities, both in concept and through the calculations of present and future values, can help you make informed decisions about your money. There are tools available to simplify the calculations for both the present and future value of annuities, ordinary or due. These online calculators typically require the interest rate, payment amount and investment duration as inputs.

Related Articles

Income annuities: What are they and how do they work?

Best Fixed Annuity rates for June 2024

Retirement annuities: Pros and cons of annuity investing

What is a fixed annuity?

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Carlyle chief executive officer harvey schwartz to present at bernstein’s 40th annual strategic decisions conference.

New York, NY and Washington, DC  – Carlyle (NASDAQ: CG) today announced that its Chief Executive Officer, Harvey Schwartz, will present at Bernstein’s 40th Annual Strategic Decisions Conference in New York on Thursday, May 30, 2024 at approximately 9:00 AM EDT.

A live webcast of the presentation will be available on the Investor Relations section of Carlyle’s website at  ir.carlyle.com . A replay will be available on the same site following the event.

About Carlyle

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FHFA Statistics Homeowners’ Equity Remains High

​​​​​​Around 97 percent of outstanding first-lien, closed-end residential mortgages in the United States, and 98.5 percent of those the Enterprises acquired, have home equity above 10 percent. Only 0.2 percent of these mortgages have negative equity, the lowest level in the past 10 years.​

Introduction

On June 30, 2023, the Federal Housing Finance Agency (FHFA) released the quarterly National Mortgage Database (NMDB®) Aggregate Statistics, 1 ​which cover outstanding first-lien, closed-end residential mortgages from the first quarter of 2013 through the same period of 2023. In this blog, we use a subset of data to explore home equity at the national level.

Home equity refers to the market value of homeowners’ unencumbered interest in their real property, or the difference between the home's current market value and the outstanding balance of all liens on the property. Home equity is an important asset that homeowners can potentially tap into for purposes such as financing home improvements, paying off high-interest debts, funding education expenses, or investing in other properties. Building equity in a home typically occurs over time through repaying the mortgage principal. Homeowners can also build equity through an increase in the home's value either through home improvements or price appreciation.

One of several ways to calculate home equity is to subtract the outstanding mortgage balance from the home's current market value. For example, if a property is currently valued at $300,000, and the homeowner owes $200,000 on the mortgage, the home equity would be $100,000, or 33.3 percent of the property value. One of the fields available in the NMDB Aggregate Statistics is the current mark-to-market (MTM) loan-to-value (LTV) ratio, which reflects what a homeowner owes on their first-lien mortgage divided by the property value of the home. In our example above, the MTM LTV ratio would equal $200,000 divided by $300,000, or 66.7 percent. Thus, we can calculate home equity as 1 – MTM LTV ratio = 1 – 66.7 percent = 33.3 percent. 2

We calculate four categories of homeowner equity using data available in the NMDB Aggregate Statistics. 3 These four categories include home equity:

•  Greater than or equal to 30 percent,
•  From 10 to 29.9 percent,
•  From 0 to 9.9 percent, and
•  ​Less than 0 percent (negative) home equity.

Additionally, we present analyses for all market segments, combined and separately, for the following three market segments:

• Enterprise Acquisitions - mortgages acquired by either Fannie Mae or Freddie Mac,
• Government/Non-Conventional (“Government-backed”) - mortgages insured or guaranteed by the Federal Housing Administration (FHA), U.S. Department of Veterans Affairs (VA), or Rural Housing Service (RHS) in the U.S. Department of Agriculture (USDA), and
• Other Conventional - other conforming and jumbo mortgages.

​Table 1 presents the number and outstanding balance of active mortgages as of the end of Q1 2023 for each market segment. There were slightly more than 50 million first lien, closed-end mortgages in the United States, with $11.27 trillion in current balance (or outstanding principal balance). By loan count, Enterprise acquisitions accounted for nearly 59 percent, followed by Government-backed with 22 percent, and Other Conventional with 19 percent. The percentages in terms of outstanding principal balance are 56 percent, 19 percent, and 25 percent, respectively. The Other Conventional market contains jumbo mortgages, which largely drives the difference between its share in terms of count versus its share in terms of current balance.

Table 1: Number and Balance of Active Residential Mortgages as of Q1 2023

​Note: The NMDB is a 5 percent sample and not a census of all mortgages.

​Home Equity for the Total Market

Nationally, as depicted in Figure 1, the percentage of mortgages with equity of more than or equal to 30 percent (high equity) has increased steadily from 46.1 percent in Q1 2013 to a 10-year high of 83.3 percent by Q1 2023. However, the percentage of high equity mortgages has been relatively constant over the past year.​

​​This trend is largely consistent with house price appreciation through this period. Most homeowners who purchased or refinanced their properties prior to Q2 2022 have seen large home price appreciation, and consequently, large increases in home equity, causing only 0.2 percent of mortgages to have negative equity, the lowest value since 2013. Figure 2 presents the percentage of mortgages in the bottom two homeowner equity buckets.

While house price appreciation has helped increase home equity, if house prices were to decline 10 percent,​ 4 homeowners with current equity of 10 percent or less (low equity) would go “underwater” or have negative equity, owing their lender more than the property’s worth. Nationally, the percentage of low equity mortgages has started to increase, from 2.2 percent in Q2 2022 to 3.1 percent in Q1 2023. This implies that a nationwide house price decline of 10 percent would result in over 1.5 million homeowners with negative equity. The number of low equity mortgages, however, remains historically low.

​Homeowner Equity by Market Segments

The level of home equity varies significantly by market segment. Figure 3 shows that the percentage of low equity mortgages has generally been declining over time for each of the three market segments. However, the percentage of low equity mortgages has been much higher in the Government-backed segment (currently 8.3 percent) compared to 1.5 percent for Enterprise acquisitions and 2.0 percent for Other Conventional, respectively, as of Q1 2023.

These results are not surprising given that mortgages in the Government-backed market segment are popular among homebuyers with limited downpayment funds. FHA mortgages typically require a minimum down payment of 3.5 percent of the purchase price, and many VA loans do not require any down payments. A down payment indicates the initial level of home equity, with a low-down payment associated with low home equity for new mortgages. As the mortgage matures, the equity changes based on the homeowner’s payments towards principal, home improvements, and house price appreciation.

The NMDB Aggregate Statistics data suggest that the percentage of mortgages with low equity is at a low level (about 3 percent as of Q1 2023), with the figure significantly lower in the Enterprises Acquisition and Other Conventional market segments compared to the Government-backed market segment.

We encourage readers to explore the NMDB Aggregate Statistics on the FHFA website .

1  FHFA and the Consumer Financial Protection Bureau jointly fund and manage the NMDB program.

2 The NMDB includes only first-lien mortgages that are reported to one of the three major credit bureaus. Therefore, the estimates for homeowners’ equity in their homes based on NMDB Aggregate Statistics are likely to be an overestimate since the calculation does not account for second liens and other potential encumbered interests. However, the second liens and other potential encumbered interests account for less than 1 percent of the principal balance securitized by the Enterprises.

3 The published NMDB Aggregate Statistics report data for six categories of MTM LTV ratio, providing additional detail for users interested in creating additional home equity categories.

4 Economists expect the U.S. housing market to cool in 2023 but little consensus exists on the change in house prices. For example, Moody's (Source: Moody’s Data Buffet) is forecasting the quarterly FHFA Purchase-Only HPI to fall to -3.3% (Year-over-Year) in Q3 2024 and be at -2.9% in Q4 2024. Goldman Sachs revised its forecast in June 2023 for house price decline from above 6 percent by year-end to under 3 percent for 2023. The Mortgage Bankers Association (MBA) (Source: Bloomberg) and Fannie Mae forecast HPI to drop by less than one percent by Q1 2024, and MBA expects mild recovery by year-end 2024.

Tagged: FHFA Stats Blog; Home Equity; Aggregate Statistics; Data; Open Data; Source: FHFA

By: Anju Vajja

FHFA Research Officer Division of Research and Statistics