TVM Calculator

The time value of money (TVM) is the principle that money available today is worth more than the same amount in the future because it can earn interest. TVM calculations let you compare cash flows at different points in time by converting between present value and future value using an interest rate.

This calculator implements the same five-variable TVM model (N, I/YR, PV, PMT, FV) used by HP financial calculators. You can solve for any one variable given the other four, just like pressing CPT on an HP 10BII or solving on an HP 12C. It also supports compounding and payment frequency settings, and beginning/end of period payment timing.

Financial calculators follow a sign convention: money you pay out (invest, deposit, or pay on a loan) is negative, and money you receive (withdrawals, loan proceeds) is positive. For a savings scenario, you enter PV as negative (you invest it) and FV as positive (you receive it). For a loan, PV is positive (you receive the loan) and PMT is negative (you pay it back).

End-of-period (ordinary annuity) means the payment happens after interest accrues for that period — this is the default for most loans and mortgages. Beginning-of-period (annuity due) means the payment happens first, before interest — common for rent payments and some lease structures. Beginning-of-period payments earn one extra period of interest compared to end-of-period.

P/Y (payments per year) is how many times you make a payment each year — 12 for monthly, 4 for quarterly. C/Y (compounding periods per year) is how many times interest compounds per year. They are often the same, but can differ — for example, some Canadian mortgages have monthly payments (P/Y=12) but semi-annual compounding (C/Y=2).

Yes. Unlike simple formulas, solving for the interest rate requires numerical methods because the TVM equation cannot be rearranged algebraically for i. This calculator uses a bisection method to find the rate — the same approach used internally by HP financial calculators.

Yes. All calculations happen entirely in your browser using JavaScript. No data is sent to any server. We do not track, store, or collect any of your financial inputs or results. There are no accounts, no cookies set by us, and no sign-up required.

The core TVM equation is: PV(1+i)^N + PMT × [((1+i)^N - 1)/i] × (1+i×BEG) + FV = 0, where i is the interest rate per period, N is the number of periods, and BEG is 1 for annuity due or 0 for ordinary annuity. Solving for i requires numerical root-finding. Solving for N uses logarithms when PMT=0, or numerical methods otherwise.

Solving for interest rate can fail if the inputs are contradictory — for example, if PV and FV have the same sign and PMT is zero, there is no interest rate that connects them. Make sure your sign convention is correct: cash out is negative, cash in is positive. Also verify that at least one cash flow has a different sign from the others.

Yes. For a mortgage, enter the loan amount as a positive PV (you receive the money), the monthly payment as a negative PMT (you pay it), set FV to 0 (or the balloon amount), enter the annual interest rate, set P/Y=12 and C/Y=12 for monthly payments, and solve for the variable you need.