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
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.
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.
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% |
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.
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.
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.
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.
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.
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.
Tax rules, limits and pay data change. Check the current figures with the primary source before acting on them.