Present Value Calculator
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Results
$10,000.00 received in 10 years is worth $6,139.13 today at a 5% discount rate
| Year | Value | Interest that year |
|---|---|---|
| 0 | $6,139.13 | – |
| 1 | $6,446.09 | $306.96 |
| 2 | $6,768.39 | $322.30 |
| 3 | $7,106.81 | $338.42 |
| 4 | $7,462.15 | $355.34 |
| 5 | $7,835.26 | $373.11 |
| 6 | $8,227.02 | $391.76 |
| 7 | $8,638.38 | $411.35 |
| 8 | $9,070.29 | $431.92 |
| 9 | $9,523.81 | $453.51 |
| 10 | $10,000.00 | $476.19 |
The discount rate is an assumption. A common choice is the return you could otherwise earn on the money with similar risk.
How to use the present value calculator
- Choose a lump sum (one amount at a future date) or regular payments (the same amount every period).
- Enter the amount and the time. For payments, also choose how often they come and whether each arrives at the start or end of its period.
- Enter a discount rate and how often it compounds. The rate is your assumption about what the money could earn elsewhere.
- Read the present value, the discount and the table showing how each year contributes.
Present value formulas
Payments (ordinary annuity): PV = PMT × [1 − (1 + i)−n] ÷ i
Payments at the start (annuity due): PV = PMT × [1 − (1 + i)−n] ÷ i × (1 + i)
FV is the future amount, PMT each payment, i the discount rate per period and n the number of periods. With annual compounding, i is the yearly rate and n the years. With other compounding, i is converted to match the payment period, so the effective yearly discount stays the same.
Present value is compound interest run backwards. If $6,139 invested today at 5% grows to $10,000 in 10 years, then $10,000 in 10 years is worth $6,139 now: you would be indifferent between the two. The annuity formula adds up the present value of every payment, each discounted for its own waiting time. Payments at the start of each period arrive one period sooner, so they are worth more.
Worked examples
- Lump sum: $10,000 in 10 years at 5% is worth $10,000 ÷ 1.0510 = $6,139.13 today.
- Annuity: $1,000 at the end of each year for 10 years at 5% is worth $7,721.73 today, even though you receive $10,000 in total. If each payment came at the start of the year, it would be worth $8,107.82.
- Prize choice: a prize of $50,000 a year for 20 years, the first paid now, is worth $706,697 today at an assumed 4%. A cash option above that amount would be worth more at that rate, before tax.
Present value of $10,000 by rate and time
| Discount rate | In 5 years | In 10 years | In 20 years | In 30 years |
|---|---|---|---|---|
| 3% | $8,626 | $7,441 | $5,537 | $4,120 |
| 4% | $8,219 | $6,756 | $4,564 | $3,083 |
| 5% | $7,835 | $6,139 | $3,769 | $2,314 |
| 6% | $7,473 | $5,584 | $3,118 | $1,741 |
| 8% | $6,806 | $4,632 | $2,145 | $994 |
| 10% | $6,209 | $3,855 | $1,486 | $573 |
Annual compounding. Higher rates and longer waits both shrink the present value, and they compound together: at 10%, money 30 years away is worth less than 6 cents on the dollar today.
Choosing a discount rate
- Opportunity cost. Use the return you could reasonably earn on the money with a similar level of risk. A safe payment deserves a lower rate than an uncertain one.
- Inflation only. Discounting at the inflation rate tells you what a future sum is worth in today's prices; see the inflation calculator.
- Debt. If the alternative is paying down a loan, the loan's interest rate is a natural discount rate.
- Try a few rates: the answer can change a lot, and no single rate is "correct".
To go the other way, from money today to its value later, use the future value calculator. For problems mixing a lump sum, payments and a target, the finance calculator solves for any one value.
Frequently asked questions
What is present value?
Present value is what a future amount is worth today, given a rate of return you could earn in the meantime. At 5% a year, $10,000 received in 10 years has a present value of $6,139.13, because $6,139.13 invested at 5% grows to $10,000 in 10 years.
How do you calculate the present value of an annuity?
Use PV = PMT × [1 − (1 + i)^−n] ÷ i. For $1,000 at the end of each year for 10 years at 5%, PV = 1,000 × 7.7217 = $7,721.73. If the payments come at the start of each year, multiply by 1.05 to get $8,107.82.
What discount rate should I use?
Use the return you could realistically earn on the money elsewhere with similar risk, or a loan rate you would otherwise pay. It is always an assumption, so try a few rates and see how much the answer changes.
Why is the present value lower than the total I will receive?
Because money received later could have been earning interest in the meantime. Ten yearly payments of $1,000 total $10,000, but at 5% they are worth $7,721.73 today; the $2,278.27 difference is the discount.
Should I take a lump sum or annual payments?
Compare the lump sum with the present value of the payments at a realistic rate. $50,000 a year for 20 years, the first paid now, is worth about $706,697 at 4%. A larger lump sum is worth more at that rate, before tax and other factors.