Annuity Present Value Calculator

How it is calculated

The tool values an ordinary annuity, meaning each payment falls at the end of its period. It first converts the inputs to per-period terms: i = annual_rate ÷ 100 ÷ payments_per_year and n = years × payments_per_year. Then PV = payment × (1 − (1 + i)−n) ÷ i. The annual rate is a nominal percentage (6 means 6%), divided evenly across the periods rather than compounded from an effective annual rate. At a rate of exactly 0 the present value is simply payment × n. Payments per year must be a whole number above zero, years must be above zero, the payment cannot be negative and the rate must stay above −100%; otherwise no result is shown. A rate between −100% and 0 is allowed. The undiscounted total of all payments is shown too. Payments due at the start of each period (annuity due) are not covered.

Common mistakes

• Typing the rate as a decimal. Enter 6 for 6%, not 0.06; 0.06 is treated as 0.06% and the present value jumps close to the undiscounted total.
• Mismatching the payment and the frequency, for example entering a yearly amount while payments per year is 12. The payment must be the amount of one instalment.
• Entering a fractional payment frequency such as 2.5 per year, or a negative payment. Both give no result; use a whole number of payments per year and a positive amount.
• Assuming the first payment is made today. Payments here are at the end of each period, so an annuity due would be worth somewhat more.
• Treating a lower present value as a loss. The gap between $120,000.00 and $90,073.45 is the time value of money, not a fee or tax.