Present value formula
The present value formula is PV = FV ÷ (1 + i)N: divide the future amount by one plus the rate per period, raised to the number of periods. It is the future value formula run backwards.[1]
Example: $10,000 in 10 years at 5%: 10,000 ÷ 1.0510 = 10,000 ÷ 1.628895 = $6,139.13. The $3,860.87 difference is the discount: the interest you give up by waiting.
Discount factors
The discount factor 1 ÷ (1 + i)N is the present value of $1. Multiply any future amount by it:
| Rate | 1 year | 5 years | 10 years | 20 years |
|---|---|---|---|---|
| 3% | 0.9709 | 0.8626 | 0.7441 | 0.5537 |
| 5% | 0.9524 | 0.7835 | 0.6139 | 0.3769 |
| 7% | 0.9346 | 0.7130 | 0.5083 | 0.2584 |
Higher rates and longer waits both shrink present value. At 7%, a dollar 20 years away is worth about 26 cents today.
Present value of an annuity
The present value of a series of equal payments is PMT × [(1 − (1 + i)−N) ÷ i] for payments at the end of each period; multiply by (1 + i) for payments at the start.[2] Ten yearly payments of $1,000 at 5% are worth $7,721.73 today, less than the $10,000 paid out, because later payments are discounted more.
Choosing a discount rate
The discount rate is the return you could earn elsewhere at similar risk. For money that is certain, a Treasury rate for the same term is a common benchmark: the latest 52-week bill auction (October 27, 2026) gave an investment rate of 4.496%.[3] For riskier cash flows people use a higher rate. Because the answer swings with the rate, the calculator also shows the result at 2% to 10%.
Common mistakesUsing an annual rate with monthly periods, discounting payments that start today as if they started in a year (use "start of period"), and comparing present values computed at different rates.
Present value in a spreadsheet
Excel and Google Sheets: =PV(rate, nper, pmt, fv, type). The first example is =PV(5%, 10, 0, -10000) = $6,139.13. To grow money forward instead, use the future value calculator; to find the monthly saving that reaches a goal, the savings goal calculator; to see a Treasury bill's price as a discounted value, the T-bill calculator.
Related calculators
- Future value calculatorA lump sum and a series of payments, grown forward
- Savings goal calculatorMonthly deposit needed for a target, or time to reach it
- T-bill calculatorPrice, investment rate and the state-tax edge over a CD
Frequently asked questions
What is present value?
The amount you would need to invest today, at a given rate, to have a certain sum at a future date. It answers "what is that future money worth now?"
How do you calculate present value?
Divide the future amount by (1 + rate)years. $10,000 in 10 years at 5%: 10,000 ÷ 1.6289 = $6,139.13.
What discount rate should I use?
The return you could get on an alternative with similar risk. Treasury yields are a common benchmark for certain cash flows; riskier flows deserve a higher rate.
What is the present value of an annuity?
The sum of each payment's present value: PMT × [(1 − (1 + i)−N) ÷ i]. $1,000 a year for 10 years at 5% is worth $7,721.73 today.