Present Value Calculator

What present value tells you

A dollar you receive in ten years is worth less than a dollar today, because today’s dollar could be invested and grow in the meantime. Present value answers the reverse question: how much would you need to invest today, at a given rate, to end up with the future amount? That sum is the future money’s value in today’s terms.

Use it to compare offers that pay at different times:

• a lump sum now versus a larger payment later (a settlement, a prize, a buyout);
• a lump sum versus a series of payments (a pension option, a structured payout, a lease);
• the price of a bond: its coupons plus its face value at maturity, discounted at the market yield.

The discount rate is the return you give up by waiting — what the money could earn elsewhere at a similar risk. A higher rate or a longer wait makes the present value smaller. This calculator only discounts; to grow money forward use the compound interest calculator, and to project a portfolio with regular contributions use the investment calculator.

Present value formulas

For a single amount received after t years, with the annual rate compounded m times a year:

With continuous compounding the growth factor becomes e^(r × t), so PV = FV × e^(−r × t).

For n equal payments PMT, discounted at i per payment period:

A final lump sum F adds F ÷ (1 + i)ⁿ. At a 0% rate the present value is simply the total received.

FV

the future amount

r

annual discount rate as a decimal (5% → 0.05)

m

compounding periods per year

t

years until the money arrives

PMT

the level payment

i

discount rate per payment period — normally the annual rate ÷ payments a year

n

number of payments

An ordinary annuity pays at the end of each period (loan repayments, bond coupons); an annuity due pays at the start (rent, insurance premiums). Each payment of an annuity due arrives one period sooner, so it is worth exactly (1 + i) times as much.

If you choose a compounding frequency that differs from the payment frequency, the calculator converts the annual rate into the equivalent rate per payment period: i = (1 + r ÷ m)^(m ÷ p) − 1, where p is the number of payments a year.

Worked examples

A single amount. You are promised $10,000 in 10 years and could earn 5% a year elsewhere.

1. Growth factor: 1.05¹⁰ = 1.628895
2. Present value: $10,000 ÷ 1.628895 = $6,139.13
3. Discount: $10,000 − $6,139.13 = $3,860.87

With monthly compounding at the same 5% the present value is $6,071.61, and with continuous compounding $6,065.31 — more frequent compounding means a slightly larger discount.

Regular payments. You will receive $500 at the end of every month for 5 years and use a 6% annual rate, so i = 0.06 ÷ 12 = 0.005 and n = 60.

1. Annuity factor: (1 − 1.005^−60) ÷ 0.005 = 51.725561
2. Present value: $500 × 51.725561 = $25,862.78, against $30,000 received in total
3. If each payment arrives at the start of the month instead: $25,862.78 × 1.005 = $25,992.09

A bond. A 10-year bond with a $1,000 face value pays a $50 coupon once a year. If similar bonds yield 6%, it is worth $50 × 7.360087 + $1,000 ÷ 1.790848 = $926.40 — below face value, because its 5% coupon is less than the market rate.

Matching Excel and Google Sheets

Spreadsheets have the same calculation as PV(rate, nper, pmt, [fv], [type]). The rate and the number of periods must use the same period: for monthly payments, divide the annual rate by 12 and multiply the years by 12. Type 0 means payments at the end of each period, 1 at the start.

The spreadsheet treats money as cash flows with a sign: what you receive is positive and what you pay out is negative. =PV(6%/12, 60, 500) therefore returns −$25,862.78 — the amount you would have to pay today to receive those payments. This calculator shows the present value as a positive amount; the formula under the result enters the payments as negative numbers so a spreadsheet gives the same positive figure.

Limits of the calculation

• One rate for the whole period. Real discount rates and yields change; the result is only as good as the rate you choose.
• Level payments only. Payments that rise each year, or irregular cash flows, need a separate cash-flow (net present value) calculation.
• No tax, fees or default risk. A promised payment that might not arrive is worth less than the formula says; lenders account for that with a higher rate.
• Inflation is separate. Discounting at a nominal rate gives a nominal present value. To see purchasing power instead, use the inflation calculator.