Present Value Calculator

How to use the calculator

1. Future value: the single amount received at the end, for example a bond's face value or a savings goal. Enter 0 if there is none.
2. Discount rate per period: the return you require each period. Use an annual rate with periods in years, or a monthly rate with periods in months.
3. Number of periods: years or months until the future amount is paid. Fractions such as 2.5 are allowed.
4. Payment per period: an equal amount received every period; 0 for a lump sum only.
5. Advanced options: whether payments arrive at the end of each period (the usual case) or at the start, as with rent or an annuity due.

Formula

Discounting is compound interest run backward. With rate i per period and n periods:

PV = FV ÷ (1 + i)^n + PMT × (1 − (1 + i)^−n) ÷ i

The first term is the present value of the lump sum, the second the present value of the payments. When payments come at the start of each period, the second term is multiplied by (1 + i), because each payment arrives one period sooner. The discount factor 1 ÷ (1 + i)^n is what one dollar paid in n periods is worth today. With a 0% rate, present value equals the simple sum. The total discount shown is the sum of all amounts minus their present value.

If you only have an annual rate and need monthly periods, a nominal rate compounded monthly becomes rate ÷ 12, and an effective annual rate becomes (1 + rate)^(1/12) − 1.

Worked examples

1. $10,000 in 10 years at 5%

The discount factor is 0.613913, so the present value is $6,139.13. Put differently, $6,139.13 invested today at 5% a year grows to $10,000 in 10 years.

2. Pricing a 10-year bond

A $10,000 bond paying a $500 coupon at the end of each year, valued at different market yields:

When the yield equals the coupon rate the bond is worth its face value; when yields rise, its price falls.

3. $50,000 now or $6,000 a year for 10 years?

At 4%, ten yearly payments of $6,000 are worth $48,665.37 today if paid at the end of each year and $50,611.99 if paid at the start. At that rate, $50,000 now beats end-of-year payments but not start-of-year payments.

Choosing a discount rate

The rate drives the result: the higher it is, the less future money is worth today. Use the return you could earn elsewhere on money with similar risk. For safe, fixed amounts, Treasury yields of a matching maturity are a common benchmark; the Federal Reserve's H.15 release publishes Treasury constant-maturity yields every business day, from one month to 30 years. Add a margin for uncertain cash flows, and use a real (inflation-adjusted) rate only if the amounts are in today's dollars.