Pick which variable to solve for — N, I/Y, PV, PMT, or FV — then fill in the remaining four. This uses the standard ordinary-annuity TVM equation behind every financial calculator's TVM keys.
Some financial calculators (the TI BA II Plus and HP 12C among them) require opposite signs for money moving in different directions — a positive PV and a negative PMT, say, to represent "received then paid out." This tool does not use that convention: PV and PMT are simply added as contributions to the same growing balance, both positive by default. If a result is being cross-checked against a calculator that uses the opposite-sign convention and the numbers do not match, this is almost always why — flip the sign on one input on the other calculator to compare like with like.
This solver assumes every PMT lands at the end of its period — an "ordinary annuity," the same assumption a standard loan payment schedule uses. Rent and some insurance premiums are typically paid at the start of a period instead (an "annuity due"), which compounds for one extra period and so grows to a slightly larger future value: multiply the annuity portion of the result by (1 + I/Y) to convert from one convention to the other.
FV, PV, and PMT all come from one algebraic rearrangement of the same equation — plug in numbers and get an answer directly. N does too, using a logarithm. I/Y is different: there is no way to isolate it algebraically once it is raised to a variable power, so this tool instead searches for it, narrowing a range between -99% and 1000% per period roughly in half, up to 100 times, until the two sides of the equation match. It is slower in principle than the others but converges to more decimal places than this page displays, long before the 100th step.
Two more places this same five-variable equation shows up directly: the Present Value Calculator solves only for PV, and the Future Value Calculator only for FV — both friendlier single-purpose layouts built on the identical formula this page solves in every direction at once. For a stream of payments considered on its own, without a separate lump sum, see the Annuity Calculator.
The Time Value of Money (TVM) is the principle that a dollar today is worth more than a dollar in the future, because today's dollar can be invested and earn a return in the meantime. Every loan payment, investment projection, and savings-goal calculation on this site rests on this same idea — this tool exposes the underlying equation directly so you can solve for any one of its five variables instead of just one fixed output.
PV is present value — a lump sum you have today. FV is future value — what that lump sum (plus any payments) grows to. PMT is a recurring payment or contribution made each period. N is the number of periods. I/Y is the interest rate earned per period, entered as a percentage. Together, these five describe any stream made up of a starting lump sum plus equal periodic contributions growing at a fixed rate per period.
Solve for FV to project how a lump sum plus regular contributions will grow by a target date. Solve for PV to find what a future goal is worth in today's dollars. Solve for PMT to find the contribution needed each period to hit a target. Solve for N to find how many periods it takes to reach a goal. Solve for I/Y to back out what rate of return a known investment history actually implies.
This is a general-purpose TVM solver that computes any one of the five variables from the other four, the same way the TVM keys on a financial calculator work. For a purpose-built tool focused on lump-sum growth over time, see the Compound Interest Calculator; for a friendlier layout built specifically around regular contributions, see the Investment Calculator.
Worked example — solving for FV: N = 10 periods, I/Y = 6% per period, PV = $1,000, PMT = $100 per period. FV = 1,000 × (1.06)10 + 100 × ((1.06)10 − 1) ÷ 0.06 = 1,790.85 + 1,318.08 = $3,108.93. Feeding that same $3,108.93 back in as FV and solving for I/Y instead returns 6.00%, confirming the equation is being solved consistently in both directions.
Solving specifically for PV, with a lump-sum or annuity toggle, is quicker on the dedicated present value calculator.