This calculator solves the basic time value of money problem. Money changes in value over time because it can earn interest, so a payment today and a payment later are not the same. Use the first box to choose what you want to find: the future value, the present value, the payment, the time or the interest rate.
Fill in the other boxes. The tool only shows the boxes that matter for your choice. Enter amounts you receive or hold as positive numbers. For a loan, enter the loan amount as the present value, zero as the future value, and the payment will come out as a negative number, which simply means money paid out.
You can also set how many payments are made each year, and whether they happen at the start or the end of each period. Payments at the start earn a little more interest, so the timing changes the result slightly.
After you press Calculate, the answer appears first, then the other values for reference, the number of payments, the total of all payments and the growth or interest in the plan.
Future value = present value x (1 + i) raised to n, plus payment x (1 + i x timing) x ((1 + i) raised to n – 1) / i. Here i is the rate per period and n is the total number of payments. Timing is 1 for payments at the start and 0 for payments at the end.
The present value and the payment are found by rearranging this equation. The number of periods comes from the natural log of a ratio, divided by the natural log of (1 + i). The interest rate cannot be rearranged neatly, so the calculator searches for the rate that makes the equation true and narrows it down until the answer is exact.