Present Value Calculator
Discount a future sum back to what it is worth today, at any rate and term.
Total discount (FV − PV): $3,860.87 — what $10,000.00 in 10 years loses to time.
Present value discounts a future sum to its worth today with PV = FV ÷ (1 + r)^n. A payment of $10,000 due in 10 years, discounted at 5%, is worth $6,139.13 now — because $6,139.13 invested at 5% would itself grow back to $10,000. The $3,860.87 gap is the cost of waiting.
What present value is
Present value (PV) answers a single question: how much is a future amount of money worth right now? A dollar you receive in ten years is worth less than a dollar today, because today’s dollar can be invested and earn a return in the meantime. Discounting reverses compounding — instead of growing a sum forward, you shrink a future sum backward at a chosen rate to find its equivalent value today.
FV is the future amount, r the annual discount rate as a decimal, and n the number of years; the total discount is FV − PV
Worked example
Find the present value of $10,000 due in 10 years, discounted at an annual rate of 5%.
- 1 Write the discount rate as a decimal. r = 5% ÷ 100 = 0.05.
- 2 Add 1 and raise to the number of years. (1 + 0.05)^10 = 1.05^10 ≈ 1.62889 — the discount factor.
- 3 Divide the future amount by that factor. $10,000 ÷ 1.62889 ≈ $6,139.13 — the present value.
- 4 Subtract to see the total discount. $10,000 − $6,139.13 = $3,860.87, the value lost to time.
- 5 Sanity-check by compounding forward. $6,139.13 × 1.05^10 ≈ $10,000 — the PV grows back to the FV.
Discount factor 1 ÷ (1 + r)^n
Multiply any future amount by the factor to get its present value. The higher the rate or the longer the wait, the smaller the factor — and the less the future sum is worth today.
| Discount rate | 5 years | 10 years | 20 years |
|---|---|---|---|
| 3% | 0.8626 | 0.7441 | 0.5537 |
| 5% | 0.7835 | 0.6139 | 0.3769 |
| 7% | 0.7130 | 0.5083 | 0.2584 |
| 10% | 0.6209 | 0.3855 | 0.1486 |
Why money today is worth more
The discount rate is the whole story. It represents the return you could earn on money if you had it now — an interest rate, an investment return, or your required rate of return. A higher rate discounts harder, so a distant payment is worth far less today. At 5% the $10,000 above is worth $6,139; at 10% it drops to just $3,855.
Time compounds against you. Because the factor is raised to the power n, each extra year of waiting shrinks the present value a little more than the last. That is why long-dated bonds and far-off pension promises are heavily discounted, while a payment due next year is worth nearly its face value.
Present value makes options comparable. Discounting every future cash flow back to today puts amounts arriving at different times on the same footing — the foundation of net present value, bond pricing, and any decision that trades money now for money later.