How to Calculate Present Value
Present value equals the future amount divided by (1 + r) raised to the number of years: PV = FV ÷ (1 + r)ⁿ.
The Present Value formula
Calculator
Enter a future amount, a discount rate, and a number of years to get its value in today's dollars.
The dollar amount you will receive or pay at the later date.
Entered as a percent. The formula uses r = rate ÷ 100.
Periods between now and when the future amount is paid.
$1,000 received in 3 years is worth $793.83 today when the discount rate is 8%.
- Discount factor (1 + r)ⁿ
- 1.259712
- Cost of waiting (FV − PV)
- $206.17
What $1 today grows to over the whole waiting period. It compounds, so (1 + r)ⁿ, never 1 + rn.
The interest you give up by being paid later instead of now.
How to calculate Present Value, step by step
- 1Identify the future value (FV). Write down the dollar amount you will receive or pay at a later date.
- 2Convert the interest rate to a decimal (r). This is the discount rate; divide the percent by 100 (for example, 8% becomes 0.08).
- 3Count the number of years (n). Use the number of periods between now and when the future amount is paid.
- 4Compute the discount factor (1 + r)ⁿ. Add 1 to r, then raise that to the power n. This is how much $1 today grows to over n years.
- 5Divide FV by the discount factor. PV = FV ÷ (1 + r)ⁿ. The result is what that future amount is worth in today's dollars.
Worked example: Present Value
Find the present value of $1,000 received in 3 years at an interest rate of 8%. Convert the rate: r = 0.08. Compute the discount factor: (1 + 0.08)³ = 1.08 × 1.08 × 1.08 = 1.259712. Divide: PV = 1,000 ÷ 1.259712 = $793.83. So $1,000 three years from now is worth about $793.83 today.
Present Value questions
Why is a dollar today worth more than a dollar in the future?
A dollar today can be saved or invested to earn interest, so it grows over time. Because of this opportunity, receiving money later means giving up that interest, which is why future dollars are discounted to a smaller present value.
What does present value tell you?
Present value tells you what a future amount of money is worth in today's dollars. It lets you compare payments received at different times on equal footing, which is how you decide whether an investment or future payout is worth its cost today.
What happens to present value when the interest rate rises?
A higher interest rate lowers the present value. Because the discount factor (1 + r)ⁿ grows larger, dividing by it gives a smaller result, so future money is worth less today when rates are high.
How is present value different from future value?
Present value discounts a future amount back to today (PV = FV ÷ (1 + r)ⁿ), while future value grows a present amount forward (FV = PV × (1 + r)ⁿ). They are inverse operations built from the same variables.
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