Time Value of Money Calculator
Solve for future value, present value, periodic payment, nominal annual rate or time using equal periods and a constant rate. Payments can occur at the end or beginning of each period.
Planning model: results assume a constant rate and perfectly regular cash flows. Taxes, fees, inflation, market volatility, payment failures and product rules are not inferred.
TVM formulas
For periodic rate i, number of periods n, present value PV and equal payment PMT:
FV = PV × (1 + i)n + PMT × [((1 + i)n − 1) ÷ i] × timing factor
The timing factor is 1 for end-of-period payments and 1 + i for beginning-of-period payments. At a zero rate, the annuity factor becomes n. Present value and payment are rearranged algebraically; rate and time are solved numerically inside disclosed bounds.
Six checked examples
| Unknown | Inputs | Checked result |
|---|---|---|
| Future value | PV 10,000; PMT 500 monthly; 6%; 10 years; end | 100,133.64 |
| Present value | FV 100,000; PMT 500 monthly; 6%; 10 years; end | 9,926.55 |
| Payment | PV 10,000; FV 100,000; 6%; 10 years; end | 499.18 per month |
| Annual rate | PV 10,000; PMT 500 monthly; FV 100,000; 10 years | About 5.98% nominal |
| Time | PV 10,000; PMT 500 monthly; FV 100,000; 6% | About 9.99 years |
| Future value, payment at beginning | Same first example; beginning of month | 100,543.34 |
How to interpret the result
- Nominal annual rate is divided by the selected number of periods. The effective annual rate includes within-year compounding.
- Payment timing matters: an annuity-due contribution earns one additional period compared with an ordinary-annuity contribution.
- Solving for rate is limited to −99.9% through 1,000% nominal annually. Solving for time is limited to 120 years.
- The rate and time solvers require nonnegative starting value and payments so the solution is monotonic and unambiguous.
- Estimated growth equals future value minus present value minus the algebraic total of periodic cash flows.
Related calculators: Compound Interest Calculator, Retirement Calculator, APY Calculator and ROI Calculator.
Questions
What is different from a compound interest calculator?
A compound-interest projection normally calculates an ending balance. This tool can instead solve backward for the starting amount, regular payment, rate or time needed for a specified ending value.
Is the nominal rate the same as APY?
No. The nominal rate is divided by the selected periods. The displayed effective annual rate is the compounded one-year equivalent under the same periodic rate.
Can I enter withdrawals?
For direct future-value, present-value or payment calculations, negative periodic cash flow represents withdrawals. Rate and time solvers intentionally require nonnegative payments.
Does the result guarantee an investment outcome?
No. It is deterministic arithmetic based on the entered rate and timing, not a forecast or investment recommendation.