Case 1
- Future amount
- 1000
- Annual discount rate
- 10%
- In how many years?
- 3
- Regular future payment
- 0
- Periods per year
- 1
751.31
Open with these valuesPresent Value Calculator
751.31
Result: 751.31Money you get later is worth less than the same figure today, because today's money can be invested in the meantime. Present value undoes that: it discounts a future lump sum, a stream of regular payments, or both, back to what they are worth now. The higher the rate and the longer the wait, the smaller the answer.
Worked examples
Case 2
- Future amount
- 50000
- Annual discount rate
- 5%
- In how many years?
- 10
- Regular future payment
- 0
- Periods per year
- 1
30,695.66
Open with these valuesCase 3
- Future amount
- 0
- Annual discount rate
- 8%
- In how many years?
- 5
- Regular future payment
- 1000
- Periods per year
- 1
3,992.71
Open with these valuesHow it's calculated
PV = FV ÷ (1 + r)ⁿ + PMT × [1 − (1 + r)⁻ⁿ] ÷ r
- StepEnter the lump sum you expect, or zero if you are valuing only payments.
- StepEnter the discount rate — the return a comparable alternative would pay.
- StepSet the years and how many periods each year has.
- ResultRead today's value of everything that arrives later.
What this number means
Present value is this family's backward direction. Compound interest asks what today's money becomes; this page asks what tomorrow's money is worth now, which is the figure you need whenever a choice is between an amount today and a larger amount later. The defaults show the round trip: 1000 due in three years at 10 % is worth 751.31 today, and 751.31 compounded at 10 % for three years is 1000 again — the same equation, read from the other end. The second field pair extends it from one payment to many. Leave the future amount at zero, enter five yearly payments of 1000 at 8 %, and the answer is 3992.71: 5000 of nominal money loses over a thousand purely to the fact that four of the five payments have not arrived yet. Fill both parts at once, with coupons as the payment and the face value as the future amount, and you have the bond price calculator. The number contains no tax, no fees and no charges of any kind. Its real limit, though, is that discounting handles time and not doubt. The formula shrinks a payment because it is late, never because it might not come; a promise that could be broken is not made smaller here, and that risk has to be paid for somewhere else — in the rate you choose to discount with.
Discounting is compounding run backwards
Future value compounds today's money forward; present value discounts tomorrow's money back. Compound an amount and then discount it at the same rate over the same period, and you are back where you started.
Everything hangs on the discount rate
Use what a comparable, similarly risky alternative would return — your opportunity cost of capital. The answer is very sensitive to this choice, so it is worth testing a range.
Payments count as an ordinary annuity
Each payment falls at the end of its period and is discounted from its own future date, then the results are added up. Set the lump sum to zero to value the payments alone.
Commonly misread
A sum due far in the future is worth roughly its face amount.
1000 due in ten years at 5 % is worth 613.91 today. Double the rate to 10 % and it falls to 385.54.
The rate I enter applies to each payment period.
You enter the annual rate, and the calculator divides it by the periods per year. The number of periods is the years times the periods per year.
Reference table
| Future, rate, years, payment, periods | What it shows | Present value |
|---|---|---|
| 1000, 5, 1, 0, 1 | One year of waiting | 952.38 |
| 1000, 5, 5, 0, 1 | Five years | 783.53 |
| 1000, 5, 10, 0, 1 | Ten years | 613.91 |
| 1000, 10, 10, 0, 1 | Ten years, double the rate | 385.54 |
| 10000, 3, 20, 0, 1 | A long-dated lump sum | 5536.76 |
| 0, 8, 5, 1000, 1 | Five yearly payments, no lump sum | 3992.71 |
Questions
What is present value?
Present value is what a future sum of money is worth today, given a rate of return you could otherwise earn. It reflects the time value of money: cash in hand can be invested and grow, so money received years from now is worth less than the same figure today. Discounting a future amount tells you the most it is rationally worth paying now.
How do I calculate present value?
Divide the future lump sum by one plus the periodic rate raised to the number of periods, then add the payment stream discounted as an annuity. The periodic rate is the annual rate divided by the periods per year. For 50000 due in ten years at 5 % a year, the present value is 30695.66.
What is the difference between present and future value?
They are two sides of the same idea. Future value compounds today's money forward to see what it becomes; present value discounts tomorrow's money backward to see what it is worth now. Compound an amount and then discount it at the same rate over the same period, and you are back where you started.
What discount rate should I use?
A rate that reflects what a comparable, similarly risky alternative would return — your opportunity cost of capital. For safe cash flows that is close to government bond yields; for risky ones it should be higher to pay for the chance of loss. The answer is very sensitive to this choice, so it is worth testing a range.
How does it value a series of payments?
Enter the recurring amount in the payment field and it is treated as an ordinary annuity: each payment is discounted from its own future date and the results are added up. That is how pension streams, lease payments and bond coupons are valued. Set the lump sum to zero to value the payments alone.
Sources and last check
Information, not financial advice.