Annuity Present Value Calculator

Formula

How this is calculated

An annuity is a series of equal payments made at regular intervals — mortgage repayments, pension payouts, lease payments, structured-settlement income. Its present value is the single lump sum that, invested today at the same periodic rate, would fund all those payments and be exactly exhausted at the final one. The core principle is time-value of money: a dollar received in the future is worth less than one received today, because the earlier dollar can earn interest in the meantime.

For an ordinary annuity (payments at the end of each period), the closed-form formula PV = PMT × [1 − (1+r)⁻ⁿ] ÷ r sums all the individual discounted payments at once. Here r is the periodic interest rate — the annual rate divided by the number of payments per year — and n is the total number of payments. An annuity due (payments at the beginning of each period) is worth exactly (1+r) times more, because every payment arrives one period earlier and therefore suffers one fewer period of discounting. When the interest rate is zero, time-value disappears and PV equals the simple sum of all payments.

The curve shows how the cumulative present value builds up as each successive payment is discounted and added: early payments contribute more than later ones of the same nominal amount because they are discounted less. The total interest embedded is the difference between the undiscounted sum of all payments and the present value — a measure of how much of the "free" returns the annuity buyer forgoes by receiving money in the future.