The time-value-of-money relationship
Every input here is tied together by one equation: a present value grows with interest over time, a stream of equal payments adds to or subtracts from the balance, and the result is a future value. Fix any four of the five quantities — present value, payment, rate, term, and future value — and the fifth is determined.
Sign matters. Money flowing in one direction is positive and money flowing the other way is negative. For everything except a straight future-value projection, the solver looks for the unknown that drives the ending balance to zero, so a deposit is entered as a negative payment and a withdrawal as a positive one. If a result comes back with an unexpected sign, it usually means an input needs its sign flipped.
What each "solve for" mode does
Pick the variable you do not know and supply the rest:
- Future value — grows the present balance and the monthly payments forward to the end of the term.
- Present value — the lump sum today that, with the given payments, lands at a zero balance.
- Payment — the level monthly amount needed to move the present balance to zero over the term.
- Rate — the annual rate implied by the other figures, found numerically by bisection.
- Periods — the number of years required, returned with fractional precision.
Reading the results
The headline value is shown in the units that fit the mode: currency for value and payment, a percentage for rate, and years for term. The rate and term solvers return extra decimal places because small differences there compound into large dollar effects.
If the math has no valid answer — for example, inputs whose signs never let the balance reach zero — the calculator reports an error instead of a misleading number. That is a prompt to re-check your figures rather than a bug.
Assumptions and caveats
This solver assumes an ordinary annuity with monthly compounding: payments land at the end of each month and interest is credited monthly. Tools that assume annual compounding or beginning-of-period payments will give slightly different numbers.
The rate is solved by bisection over a wide range and will not converge if no rate in that range balances the equation. Results ignore taxes, fees, and inflation, and are for educational use — not personalized financial advice.
Formula
FV = PV·(1+r)ⁿ + PMT·(((1+r)ⁿ − 1)/r), r = rate/100/12, n = years×12Frequently asked questions
- When are payments assumed to occur?
- At the end of each month (an ordinary annuity), compounded monthly.