How to use the present value calculator
- Enter the future value, a single amount received or paid at the end. Use 0 if there are only regular payments.
- Enter the annual discount rate: the return you could earn elsewhere, or the interest rate that applies.
- Enter the number of periods and choose whether they are years, half-years, quarters or months. The annual rate is divided by the number of periods in a year.
- Optionally, enter a payment each period for an annuity, and choose whether payments come at the end or the start of each period.
The results show the present value of the lump sum and of the payments, the total, the discount, and a table of each cash flow with its discount factor.
The present value formula
i is the rate per period (annual rate ÷ periods per year) and n is the number of periods. Each future dollar is divided by (1 + i) once for every period you have to wait for it. Payments at the start of each period (an annuity due) are each received one period sooner, so they are worth (1 + i) times more than payments at the end (an ordinary annuity).
Worked example
The calculator's defaults ask what $10,000 received 10 years from now is worth today at a 6% discount rate.
- Rate per period: 6% ÷ 1 = 6% a year.
- Discount factor: 1 ÷ 1.06^10 = 1 ÷ 1.790848 = 0.558395.
- Present value: $10,000 × 0.558395 = $5,583.95.
So $5,583.95 invested today at 6% a year would grow to $10,000 in ten years. The discount, $4,416.05, is the interest you give up by waiting.
Add $1,000 a year at the end of each year as well, and the payments are worth $1,000 × (1 − 1.06^−10) ÷ 0.06 = $1,000 × 7.360087 = $7,360.09, for a total present value of $12,944.03 (unrounded, $5,583.948 + $7,360.087). If the payments came at the start of each year instead, they would be worth $7,360.09 × 1.06 = $7,801.69, for a total of $13,385.64.
Present value of $10,000 at different rates
| Discount rate | In 10 years | In 20 years | In 30 years |
|---|---|---|---|
| 3% | $7,440.94 | $5,536.76 | $4,119.87 |
| 5% | $6,139.13 | $3,768.89 | $2,313.77 |
| 6% | $5,583.95 | $3,118.05 | $1,741.10 |
| 8% | $4,631.93 | $2,145.48 | $993.77 |
| 10% | $3,855.43 | $1,486.44 | $573.09 |
Higher rates and longer waits both shrink present value, and they compound each other: at 10%, money 30 years away is worth less than 6 cents on the dollar today.
Choosing a discount rate
The discount rate is the most important input, and it depends on the question. To compare a future payment with investing the money yourself, use the return you would realistically earn. To value a pension or legal settlement, an interest rate on safe bonds of a similar term is common. To compare against inflation only, use the expected inflation rate; that gives the future amount in today's buying power, like the inflation calculator does.
Frequently asked questions
What is the difference between present value and future value?
They are the same calculation in opposite directions. Future value grows today's money forward at a rate; present value pulls future money back to today. $5,583.95 today has a future value of $10,000 in ten years at 6%, and $10,000 in ten years has a present value of $5,583.95. The future value calculator works the other way.
Should I use monthly or yearly periods?
Match how the money actually arrives. For a single sum, yearly periods are standard. For monthly payments, such as rent or an annuity, choose months, enter the number of months and enter the monthly amount. $10,000 in 120 months at 6% compounded monthly has a present value of $5,496.33, a little less than with yearly discounting.
How do I compare a lump sum with payments over time?
Find the present value of the payment stream at your discount rate and compare it with the lump sum offered. If a lottery or pension offers $100,000 now or a series of payments, the payments are worth more only if their present value exceeds $100,000. The annuity calculator covers payouts in more detail.
Can the discount rate be negative?
Yes, though it is rare. With a negative rate, future money is worth more than today's, so the present value comes out above the future amount. The calculator accepts rates above −100%.
Related calculators
- Future Value Calculator — What a sum today plus regular payments grows to, with any compounding and payments at the start or end.
- Finance Calculator — Time value of money: solve for N, I/Y, PV, PMT or FV, like a financial calculator, with simple sign rules.
- IRR Calculator — Internal rate of return, NPV and payback period for an investment and a series of yearly or monthly cash flows.
- Annuity Calculator — What an annuity or savings plan grows to from a starting principal plus yearly or monthly additions.
Results are estimates for educational purposes and are not financial, tax or legal advice. See our disclaimer.