Present Value Calculator

What Is a Present Value Calculator?

A Present Value Calculator is an online financial tool that helps you find how much future money is worth today using a discount rate and time period.

Present value (PV) is based on the time value of money, which means money available today is generally worth more than the same amount received in the future when it can earn a positive return.

Our free PV Calculator supports two calculation methods:

• Present Value of Future Money: Calculate today's value of a single amount you expect to receive in the future.

• Present Value of Periodical Deposits: Find the present value of a series of equal payments made at the beginning or end of each period.

You can use it to compare future payments, evaluate investment opportunities, and plan long-term financial decisions.

How to Use the Present Value Calculator

Our online calculator provides two options depending on the type of present value calculation you need.

Option 1: Present Value of Future Money

Use this option to calculate the present value of a single future payment.

1. Future Value: Enter the amount you expect to receive in the future.

2. Discount Rate: Enter the annual discount rate as a percentage.

3. Number of Years: Enter how many years until you receive the money.

4. Click Calculate: View the present value and other results.

The calculator displays:

• Present Value Today

• Future Value

• Discount Rate

• Discount Amount

• Present Value Over Time chart

Option 2: Present Value of Periodical Deposits

Use this option to calculate present value for a series of equal payments or deposits.

1. Number of Periods (N): Enter the total number of payment periods.

2. Interest Rate: Enter the interest or discount rate per period.

3. Periodic Deposit (PMT): Enter the amount deposited or paid each period.

4. PMT made at the: Choose Beginning or End, depending on when each payment occurs.

5. Click Calculate: View the present value and payment breakdown.

The calculator displays:

• Present Value Today

• Future Value

• Total Principal

• Total Interest

• Cumulative PV of Deposits chart

• PV Calculation History chart

Important: The interest rate must match the payment period. For example, if payments occur monthly, use a monthly rate and enter the number of months as the number of periods.

Present Value Formula – How to Calculate Present Value

The present value formula discounts future money to its equivalent value today. The appropriate PV formula depends on whether you are calculating a single future amount or a series of payments.

1. Present Value Formula for Future Money

The standard PV formula is:

$PV=\frac{FV}{(1+r)^n}$

Where:

• PV = Present Value

• FV = Future Value

• r = Discount rate per period (in decimal form)

• n = Number of periods

For annual calculations, use the annual discount rate and the number of years.

A higher discount rate or longer waiting period generally reduces the present value of a future payment.

2. Present Value Formula for Periodic Deposits

For equal payments made at the end of each period, use the ordinary annuity formula:

$PV=PMT\times\frac{1-(1+r)^{-n}}{r}$

Where:

• PMT = Payment or deposit made each period

• r = Discount rate per period

• n = Total number of payments

This formula assumes payments are equal, the discount rate remains constant, and payments occur at regular intervals.

3. Payments Made at the Beginning of Each Period

When payments are made at the beginning of each period, the calculation uses the annuity due formula:

$PV_{\text{beginning}}=PV_{\text{end}}\times(1+r)$

Beginning-of-period payments have a higher present value than end-of-period payments when the discount rate is positive because each payment is discounted for one fewer period.

You can also explore related payment calculations using our Annuity Calculator.

4. Present Value Calculation at a 0% Discount Rate

When the discount rate is zero, no discounting occurs.

For a single future payment:

$PV=FV$

For periodic payments:

$PV=PMT\times n$

For example, 10 payments of $100 at a 0% discount rate have a present value of $1,000, regardless of whether payments are made at the beginning or end of each period.

Present Value Calculation Examples

The following examples use the same values and results displayed by our calculator.

Example 1: Present Value of Future Money

Suppose you expect to receive $10,000 after 10 years, and the annual discount rate is 5%.

Using the present value formula:

$PV=\frac{10000}{(1+0.05)^{10}}$

$PV = \$6{,}139.13$

Calculation Results

What does this result mean?

Receiving $10,000 in 10 years is equivalent to receiving approximately $6,139.13 today when discounted at 5% annually.

The discount amount of $3,860.87 represents the difference between the future payment and its present value.

Example 2: Present Value of Periodic Deposits

Suppose you make 10 equal deposits of $100, with an interest rate of 5% per period.

The present value depends on when the deposits are made.

Payments Made at the End of Each Period

$PV=100\times\frac{1-(1+0.05)^{-10}}{0.05}$

$PV = \$772.17$

Payments Made at the Beginning of Each Period

$PV_{\text{beginning}}=772.17\times1.05$

$PV_{\text{beginning}} \approx \$810.78$

Results Comparison

Deposits made at the beginning of each period have a higher present value and future value because the money is invested earlier.

The Total Interest values shown here represent projected growth above the total deposits, assuming the stated interest rate.

Understanding Your Present Value Calculator Results

After you calculate present value, the tool displays a summary based on your selected calculation mode.

Present Value Today: The current equivalent value of future money or a series of future payments.

Future Value: The amount expected at a future date. In the periodic deposits mode, this is the projected accumulated value of the deposits.

Discount Rate: The percentage used to discount future money to today's value.

Discount Amount: The difference between the future value and present value of a single future payment.

Total Principal: The combined amount of all periodic deposits before investment growth.

Total Interest: The projected growth above the total deposits in the periodic deposits calculation.

The calculator also provides charts to help you understand the results.

The Present Value Over Time chart illustrates how the present value of a future amount changes with the discounting period.

The Cumulative PV of Deposits chart shows the accumulated present value of periodic payments.

The PV Calculation History chart displays results from previous calculations, helping you compare different scenarios.

Present Value vs. Future Value

Present value and future value are related financial concepts, but they answer different questions.

For example, $10,000 received in 10 years has a present value of approximately $6,139.13 at a 5% annual discount rate.

Similarly, $6,139.13 invested today at 5% annually would grow to approximately $10,000 after 10 years.

You can estimate how today's money may grow using our Future Value Calculator.

For additional background on discounting and the time value of money, see the Investor.gov introduction to compound interest.

When Should You Use a Present Value Calculator?

A present value calculation is useful when comparing amounts of money received or paid at different times.

Common uses include:

• Investment planning: Estimate today's value of future investment proceeds.

• Retirement planning: Evaluate future retirement payments or regular income streams.

• Loan analysis: Compare future payment obligations using an appropriate discount rate.

• Business decisions: Estimate the current value of expected future receipts.

• Financial planning: Compare receiving money today with receiving it later.

The discount rate is an important assumption. A rate that is too high or too low can significantly change the estimated present value.

For financial planning, consider factors such as inflation, investment risk, and the opportunity cost of money.

You can explore additional financial education through Investor.gov, a resource provided by the U.S. Securities and Exchange Commission.