Present Value Calculator

How to use the present value calculator

Enter the amount you will receive in the future, the annual discount rate, the number of years until you receive it and how often the rate compounds. The calculator returns the present value — the amount that, invested today at that rate, would grow to exactly the future sum. If you will also receive a regular amount each period (such as a bond coupon or a rent payment), enter it as the optional payment; its present value is added to the result.

The step-by-step working shows the discount factor and every multiplication, and the table shows how the present value changes if you pick a slightly higher or lower discount rate.

The present value formula

FV is the future amount, r the annual discount rate, n the compounding periods per year and t the number of years. For a stream of equal payments at the end of each period, add:

where i = r/n and N = n × t.

Worked example

Someone promises you 10,000 in 10 years. If you could otherwise earn 5% a year, compounded annually, the discount factor is 1 ÷ 1.05¹⁰ = 0.613913, so the promise is worth 10,000 × 0.613913 = 6,139.13 today. Put another way, 6,139.13 invested at 5% grows to 10,000 in ten years. At an 8% discount rate the same promise is worth only 4,631.93 — the higher your alternative return, the less a distant payment is worth.

Now suppose it is a bond paying 400 a year for 10 years plus 10,000 at the end. Discounted at 5%, the coupons are worth 400 × 7.7217 = 3,088.69, giving a total present value of 9,227.83 — so the bond should trade below its face value.

Why present value matters

A sum of money today is worth more than the same sum in the future, because today's money can be invested, and because inflation and risk reduce the value of later money. This idea — the time value of money — underpins almost all of finance:

• Investment decisions: discount a project's future cash flows to compare them with its cost, as the NPV calculator does.
• Lottery and legal settlements: compare a lump sum with an annuity of payments.
• Bonds: a bond's price is the present value of its coupons and face value.
• Retirement planning: how much you need today to fund a future goal.

Choosing a discount rate

The discount rate should reflect your opportunity cost and the risk of the payment. For a near-certain payment, use a safe rate such as a government bond yield of matching length. For an uncertain business cash flow, use your required return or cost of capital, which may be 8–15% or more. To express future money in today's purchasing power, discount at the expected inflation rate instead — the inflation calculator does this directly.

Common mistakes

The most frequent error is mixing periods — using an annual rate with monthly periods, or forgetting that a semi-annual bond pays two coupons a year. Make sure the rate, the payment and the number of periods all refer to the same interval. A second mistake is using a discount rate that ignores risk: discounting an uncertain payment at a bank deposit rate makes it look far more valuable than it is.

Results are for education and planning; they are not investment advice.