Finance Calculator
The classic 5-variable time-value-of-money solver, just like a BA II Plus or HP 12C. Pick which value you need — N, I/Y, PV, PMT, or FV — enter the other four, and get the solved value plus a full period-by-period schedule.
Balance over time
📈 Put idle cash to work
Compare investing optionsThe five variables behind every loan and investment calculator
Almost every financial calculator on this site — loans, mortgages, savings, annuities — is a special case of this same five-variable equation. N is how many periods you’re measuring, I/Y is the rate, PV and FV are the values at the start and end, and PMT is what moves between periods. Fix any four and the fifth is fully determined; this calculator lets you choose which one that is. Cash-flow sign convention keeps the books balanced: money leaving your pocket is negative, money arriving is positive, so a savings plan typically has a negative PV and PMT (money going in) producing a positive FV (money you’ll receive back).
How it’s calculated
With periodic rate i = (I/Y÷100)÷(C/Y÷P/Y) and n = N periods, the balance equation is PV(1+i)n + PMT(1+i·k)×[(1+i)n−1]÷i + FV = 0, where k = 1 for beginning-of-period payments and 0 for end-of-period. FV, PV, and PMT solve directly from this equation. N solves by isolating the exponential term and taking a logarithm. I/Y has no closed-form solution because the rate appears both inside and outside the exponent, so it is solved with bisection: the calculator repeatedly narrows a bracket around the rate until the equation balances to a near-zero residual.
Results update as you type and are estimates, not financial advice — verify any figure that matters with a professional or your product’s official statement.
Period-by-period schedule
Shows PV, PMT, interest, and FV for each of the first periods at your selected P/Y frequency, grouped by year once N is large.
Worked example
Solving for FV with N = 120 months, I/Y = 6%, PV = −$10,000, and PMT = −$200 a month (end of period, P/Y = C/Y = 12) gives FV = $50,969.84. Total payments equal $24,000.00, so the extra $16,969.84 came from compounding. Switching PMT to beginning-of-period raises FV to $51,133.72 — the one-extra-compounding-cycle effect in action.
Common mistakes
- Mixing up the sign convention — if PV and PMT are both entered as positive, the solved FV will look wrong (often negative) because the cash flows no longer represent a coherent transaction.
- Leaving P/Y and C/Y at different values by accident, which silently changes the effective periodic rate used in every calculation.
- Solving for I/Y with an FV that can never be reached from the given PV and PMT (for example, asking for growth with cash flows that only shrink the balance) — the bisection search will fail to converge in that case.
Where it is used
- Homework and exam prep for finance courses that use the BA II Plus or HP 12C five-key method.
- Backing out an implied interest rate from a known payment stream, such as a seller-financed deal.
- Checking any loan, lease, or savings calculator’s output against the underlying time-value-of-money math.
Frequently asked questions
What do N, I/Y, PV, PMT, and FV stand for?
N is the number of periods, I/Y is the interest rate per year, PV is present value, PMT is the periodic payment, and FV is future value. Together they describe any stream of equal payments at a fixed rate — this is the same five-variable model used by financial calculators like the BA II Plus or HP 12C.
Why are some of my numbers negative?
Financial calculators use cash-flow sign convention: money you pay out (an investment, a loan payment) is negative, and money you receive (a loan you take, a payout) is positive. If PV is negative and PMT is negative, the solved FV will be positive — that is money coming back to you.
How is I/Y solved when it can't be isolated algebraically?
The other four variables (N, PV, PMT, FV) rearrange cleanly, but the interest rate appears both inside a compounding exponent and as a plain divisor, so there is no closed-form solution. This calculator uses bisection — repeatedly narrowing a bracket around the rate until the cash-flow equation balances to a very small error — which converges to the correct I/Y in well under a second.
What's the difference between P/Y and C/Y?
P/Y is how many payments happen per year (12 for monthly payments) and C/Y is how many times interest compounds per year. They're usually equal, but a loan can compound daily while you pay monthly — set them separately if your product's terms specify different values.
Should payments be at the beginning or end of the period?
Most loans and mortgages pay at the end of the period (“ordinary annuity”); leases and some insurance products pay at the beginning (“annuity due”). Beginning-of-period payments compound for one extra period each, so they produce a slightly larger future value for the same PMT.