About the Present Value Calculator
A present value calculator discounts a future sum or stream of payments back to what it is worth today. It is the core tool of financial valuation — every bond price, project appraisal, and lottery lump-sum decision is a present value calculation.
The formula
PV = FV / (1 + r)ᵗ (lump sum)FV is the future amount, r the discount rate, and t the number of periods. For a stream of equal payments, the annuity formula PV = PMT · [(1 − (1+r)⁻ᵗ) / r] applies.
How to use this calculator
- 1Enter your Future Value ($). The field starts at
20000, which you can overwrite. - 2Enter your Discount Rate (%). The field starts at
6, which you can overwrite. - 3Enter your Number of Years. The field starts at
5, which you can overwrite. - 4Enter your Annual Payment ($, 0 = lump sum). The field starts at
0, which you can overwrite. - 5Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Future Value ($) | 20000 |
| Discount Rate (%) | 6 |
| Number of Years | 5 |
| Annual Payment ($, 0 = lump sum) | 0 |
Result
Present Value (Lump Sum): $14945.16
Present Value (Annuity): $0.00
Total Present Value: $14945.16
Discount: $5054.84
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Discounting reflects that money arriving later is worth less, because you forgo the chance to invest it in the meantime. At an 8 percent discount rate, 20,000 dollars in five years is worth about 13,600 today — which is why a lottery lump sum is so much smaller than the advertised annuity total.
The discount rate encodes both opportunity cost and risk, and choosing it is where judgement enters. A higher rate suits riskier or more distant cash flows and produces a lower present value. Small changes matter enormously over long horizons: at 5 percent, a payment 30 years out retains 23 percent of its value; at 10 percent, only 6 percent.
Things worth knowing
- Net present value subtracts the initial cost. A positive NPV means the project adds value at your chosen discount rate.
- The discount rate should reflect risk. Certain cash flows warrant a low rate, speculative ones a high one.
- Distant cash flows contribute very little, which is why long-dated projections rarely change a decision.
- When comparing a lump sum against an annuity, discount the annuity at a rate you could realistically achieve.
- Use consistent periods. An annual rate requires annual cash flows, or convert both to monthly.
Frequently asked questions
What is present value?+
The value today of money to be received in the future, discounted at a rate reflecting opportunity cost and risk. It lets you compare amounts arriving at different times on a common basis.
What discount rate should I use?+
Your cost of capital or the return you could earn on a comparable-risk alternative. Higher risk justifies a higher rate, which lowers present value. There is no single correct figure.
Should I take the lottery lump sum or the annuity?+
Compare the lump sum against the present value of the annuity payments at a return you could realistically achieve. The lump sum usually wins mathematically if you invest it, but the annuity protects against overspending.
What is net present value?+
The present value of all future cash inflows minus the initial investment. A positive NPV means the project is expected to create value at your chosen discount rate.