Present Value Calculator

Present value answers a simple question: what is money you will receive later worth today? A dollar in ten years is worth less than a dollar now, because money you hold today can earn a return in the meantime. This calculator discounts future money back to the present in three ways: a single amount received on a future date, a series of equal payments such as a pension, annuity or bond coupons, and a list of uneven cash flows such as the expected returns from a project.

Each result shows the working, the discount factor used and a chart of how the value builds up. For the payments mode, the schedule lists the present value of every payment.

PV = FV ÷ (1 + r/m)^m·t (lump sum, m compounding periods a year)

PV = PMT × (1 − (1 + i)⁻ⁿ) ÷ i (payments at the end of each period)

PV = Σ CF_t ÷ (1 + r)^t (uneven cash flows)

r is the annual discount rate, i the rate per payment period and n the number of payments. Payments at the start of each period (an annuity due) are worth (1 + i) times more, because each arrives one period sooner. With continuous compounding the lump-sum formula becomes PV = FV × e^−rt.

A lump sum. $10,000.00 received in 10 years, discounted at 5% a year, is worth $6,139.13 today.

Lottery annuity or cash? $50,000 a year for 20 years, with the first payment today, is worth $679,665 at a 4.5% discount rate, although the payments total $1,000,000. A lump-sum offer below that figure is worth less than the annuity at that rate.

A bond. A five-year bond paying $25.00 every six months and $1,000 at maturity is worth $957.35 when similar bonds yield 6%, which is why its price is below face value.

Project cash flows of $3,000, $4,000, $5,000 and $8,000 in years 1, 2, 3 and 5 are worth $15,620.96 at 8%. Subtract the upfront cost to get the net present value.

Present value of $1.00 received after the number of years shown, with annual compounding:

Present value turns money at different dates into one comparable figure. People use it to compare a lump-sum pension or lottery payout with a stream of payments, to decide whether a settlement paid over time is fair, and to value a bond, a lease or a rental property. Businesses use it to compare projects whose returns arrive in different years, and courts use it to value future lost earnings.

It also works in reverse as a check on offers that sound large. A promise of $1,000,000 paid over 40 years is worth far less than $1,000,000 today, and the calculator shows exactly how much less at the rate you choose.

The discount rate is the return you could earn elsewhere on money with similar risk. For a guaranteed payment, use a safe rate such as the yield on a Treasury of similar maturity. For an uncertain business project, use a higher rate that reflects the risk, often a company's cost of capital. The result is sensitive to this choice, especially over long periods: the table shows that $1.00 in 30 years is worth about 41 cents at 3% but only about 6 cents at 10%. Inflation is a separate question: to express a future amount in today's purchasing power, discount at the expected inflation rate instead. For decisions that include an upfront cost, the net present value calculator adds it and finds the internal rate of return.