🧮TVM Calculator

About this tool

Pick the value to solve for, fill in the other four, and choose the number of periods per year and whether payments fall at the start or end of each period. The calculator gives the answer, the total of the payments and the effective annual rate. It uses the same cash-flow sign convention as business calculators such as the BA II Plus and HP 12C.

How time value of money problems work

Money now is worth more than the same amount later, because it can earn interest. A single equation links five values: the number of periods (N), the interest rate (I/Y), the present value (PV), the regular payment (PMT) and the future value (FV). Know any four and the fifth follows. Signs show direction: money you pay out is negative and money you receive is positive. Investing 10,000 now (PV −10,000) and adding 200 a month (PMT −200) for 120 months at 6% a year grows to about 50,970 (FV +). A 300,000 loan at 6% over 360 months is the mirror image: you receive the PV (+300,000), and the payment works out at about −1,798.65 with FV 0. The rate is annual and divided by the periods per year, so 6% monthly is 0.5% a month, an effective 6.17% a year. Payments at the start of each period, an annuity due, suit rent and savings paid in advance. Not financial advice. The loan calculator, the mortgage calculator and the compound interest calculator are friendlier for single questions, and the NPV calculator handles uneven cash flows. How loan interest actually works explains the interest side.

Frequently asked questions