Choose which variable to solve for, fill in the other four, and this calculator solves the standard time value of money equation for it.
How to Use the Time Value of Money Calculator
Pick which variable to solve for from the dropdown — Present Value, Future Value, Payment, Number of Periods, or Interest Rate — then fill in the other four fields; the one you're solving for hides itself automatically.
Five numbers govern almost every lending, saving, and annuity problem in finance: present value, future value, payment, number of periods, and the rate that connects them. Know any four and the fifth is fully determined — this tool solves for whichever one you leave out.
The Relationship Behind All Five Modes
Every solve traces back to one identity, using the sign convention that present value and payment are amounts you contribute and future value is what you receive back — all entered as positive numbers:
FV = PV × (1 + r)ⁿ + PMT × ((1 + r)ⁿ − 1) ÷ r [r ≠ 0]
FV = PV + PMT × n [r = 0]Solving for present value, payment, or the number of periods just rearranges that same equation algebraically:
PV = (FV − PMT × ((1+r)ⁿ−1)/r) ÷ (1+r)ⁿ
PMT = (FV − PV×(1+r)ⁿ) × r ÷ ((1+r)ⁿ − 1)
N = ln((FV×r + PMT) ÷ (PV×r + PMT)) ÷ ln(1 + r)If those N inputs don't produce a positive number inside the logarithm — mismatched signs or magnitudes that can never reach the stated future value — the calculator says so rather than returning a meaningless result.
Why Rate Doesn't Get a Formula
There's no algebraic rearrangement that isolates r on one side of the equation — it's trapped inside an exponent alongside a separate linear term, and no amount of algebra untangles that combination into a closed form. So this mode works differently: it guesses a rate, checks how far off the resulting future value is, and narrows the guess by half each round (bisection) until the gap shrinks below a hair's width, searching between 0.001% and 100% per period. If the two ends of that range don't bracket a valid answer, it says so instead of guessing forever.
A Mortgage Is Just This, Renamed
A $10,000 loan repaid over 60 monthly periods at 1% per period, with no separate future value owed, is a payment-mode TVM problem wearing a mortgage's clothing. Retirement projections, loan payoffs, and bond math generally are all the same five-variable relationship with different labels stuck on the inputs — which is part of why this calculator exists as a general tool rather than five separate ones.
Solve for future value with $10,000 present value, no payment, 60 periods, and 1% per period and the answer is about $18,167 — pure compounding, nothing contributed along the way. Feed that same $18,167 back in as the future value, alongside the original present value and period count, and solve for rate instead: it bisects its way back to 1% per period, confirming the two modes are genuinely inverses of each other rather than independently-coded approximations that happen to agree most of the time.