Time Value of Money (TVM) Calculator
Solve for present value, future value, payment, interest rate or number of periods. Enter the four variables you know and the calculator returns the fifth, using the standard cash-flow sign convention: money you pay out is negative, money you receive is positive.
What each TVM variable means
- PV — Present Value
- The lump sum today: the price of an asset, the amount you deposit now, or the principal of a loan. Enter it as a negative number when the cash leaves your pocket.
- FV — Future Value
- The balance at the end of the last period, after every payment and all compounding has occurred. Savings goals and balloon payments are entered here.
- PMT — Payment
- The equal cash flow that repeats every period — a loan installment, a monthly contribution or a lease payment. It must stay constant for the standard TVM formula to apply.
- I/Y — Interest Rate
- The nominal annual rate. The calculator divides it by the compounding frequency to get the periodic rate r = I/Y ÷ m, which is what actually drives the math.
- N — Number of Periods
- The horizon in years, multiplied internally by the compounding frequency. Ten years compounded monthly is 120 periods.
The formula behind it
Every case above is a rearrangement of one balance equation, where the discounted value of all cash flows must sum to zero:
PV · (1 + r)^N + PMT · [((1 + r)^N − 1) / r] · (1 + r·due) + FV = 0
Interest rate is the one variable with no closed-form solution, so it is found numerically by bisection — the same approach financial calculators use.
Worked examples
- Retirement savings: PV = −10,000, PMT = −200 monthly, I/Y = 6%, N = 10 years → solve for FV to see what the account is worth.
- Car loan payment: PV = 25,000, FV = 0, I/Y = 7%, N = 5 years, monthly → solve for PMT.
- Implied return: PV = −5,000, FV = 8,000, PMT = 0, N = 7 years, annual → solve for I/Y.
Frequently asked questions
What is the time value of money?
The time value of money states that a dollar today is worth more than a dollar tomorrow, because money available now can be invested and earn a return. TVM math converts cash flows across time using an interest rate.
What do PV, FV, PMT, I/Y and N mean?
PV is the present value (today's lump sum), FV is the future value (the balance at the end), PMT is the recurring payment each period, I/Y is the interest rate per period as a percentage, and N is the number of compounding periods.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period (loans, most bonds). An annuity due pays at the beginning of each period (rent, leases, some savings plans) and is therefore worth one extra period of interest.