Time Value of Money Calculator: Solve for FV, PV, PMT, N or Rate
Enter four of the five time-value-of-money inputs and solve for the fifth — the monthly saving needed for a goal, the years it takes, the rate it needs, or what it grows to
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Time Value of Money Calculator: Solve for FV, PV, PMT, N or Rate
Printed 2026-10-27 from billorganizingapp.com/income/calculators/time-value-of-money/ — an estimate for planning, not financial or tax advice.
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Pick what to solve for, then fill in the others: the starting amount (PV), the deposit each period (PMT), the target (FV), the annual rate and the number of years. It works like the TVM keys on a financial calculator, but every amount is entered as a positive number because they all describe money you put in or want to reach. It models saving toward a goal; it isn't set up for loans.
The time value of money equation
A dollar today is worth more than a dollar later because it can earn interest in the meantime. The five values are tied together by one equation: PV × (1 + i)^N + PMT × ((1 + i)^N − 1) ÷ i = FV, where i is the rate per period and N the number of periods. FV, PV and PMT rearrange directly; N = ln((FV × i + PMT) ÷ (PV × i + PMT)) ÷ ln(1 + i). The rate can't be isolated, so the calculator finds it by trial (bisection), the way a financial calculator does.
Worked examples
Monthly compounding, deposits at the end of each month. To turn $2,000 into $50,000 in 10 years at 5%, you need about $300.78 a month. Saving $400 a month instead gets there in 8.0 years.
| Solve for | Given | Answer |
|---|---|---|
| Monthly deposit (PMT) | PV $2,000, FV $50,000, 5%, 10 years | $300.78 |
| Future value (FV) | PV $2,000, PMT $300, 5%, 10 years | $49,878.70 |
| Starting amount (PV) | PMT $300, FV $50,000, 5%, 10 years | $2,073.65 |
| Years (N) | PV $2,000, PMT $400, FV $50,000, 5% | 8.0 years |
| Rate (I/Y) | PV $2,000, PMT $300, FV $50,000, 10 years | 5.04% |
Picking a rate
The answer is only as good as the rate. For insured savings, use the APY the bank quotes today; the FDIC publishes national average rates each month. For investments, returns vary year to year and can be negative, so try a range rather than one number. The Federal Reserve's H.15 release lists current Treasury yields if you want a market benchmark. To see a result in today's dollars, use the inflation setting on the future value calculator.
Uneven cash flows
When the payments differ from period to period, solve for the rate with IRR and NPV instead.
Lump sum vs annuity
The same present-value logic decides between a lottery's cash option and its annuity.
Official sources
Tax rules, limits and pay data change. Check the current figures with the primary source before acting on them.
Frequently Asked Questions
What is the time value of money?+
The idea that money available now is worth more than the same amount later, because it can earn interest in the meantime. The TVM equation links present value, payments, future value, the rate and time.
How much do I need to save each month to reach a goal?+
PMT = (FV − PV × (1 + i)^N) × i ÷ ((1 + i)^N − 1). To reach $50,000 from $2,000 in 10 years at 5% compounded monthly, about $300.78 a month.
How do you calculate present value?+
PV = (FV − PMT × ((1 + i)^N − 1) ÷ i) ÷ (1 + i)^N. With no deposits it is FV ÷ (1 + i)^N. To reach $50,000 with $300 a month at 5% over 10 years you'd need to start with $2,073.65.
How do I find the interest rate needed to reach a goal?+
Solve for the rate. $2,000 plus $300 a month reaches $50,000 in 10 years at about 5.04% a year compounded monthly. There's no closed-form formula; calculators find it by trial.
Why are all amounts positive here when my financial calculator uses negatives?+
Financial calculators enter money paid out as negative and money received as positive. This calculator only models saving toward a goal, so deposits and the target are all entered as positive amounts.
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