Present Value Calculator

What is present value?

Present value (PV) is the amount of money today that is equivalent to a payment you will receive, or owe, at a later date. A dollar in hand can be saved or invested and will grow, so a dollar promised next year is worth less than a dollar available now. Present value puts both on the same footing by shrinking the future amount back to today's terms.

The shrinking is called discounting, and the rate used for it is the discount rate. It stands for the return you could earn on the money in the meantime, or the return you would demand for waiting. The higher the rate and the longer the wait, the smaller the present value.

This tool handles a single lump sum paid once at the end of the last period. For a stream of payments with different amounts, use the NPV calculator; to go the other way and grow a sum forward, use the future value calculator.

How to use the calculator

1. Type the future value: the amount you expect to receive or need to have at the end of the horizon.
2. Enter the discount rate as a percentage for one period, for example 6 for 6%.
3. Enter the number of periods as a whole number (1 or more). The period can be a year, a quarter or a month, as long as the rate is quoted for that same length of time.
4. Press the button. The first result is the present value; the second is the difference, the part of the future amount that discounting takes away.

The periods field accepts whole numbers only. If your horizon is 18 months, switch the period to months and convert the rate to a monthly rate instead of entering 1.5 years.

The present value formula

PV = FV ÷ (1 + r)^nFV is the future value, r the discount rate per period written as a decimal, and n the number of periods.

The term 1 ÷ (1 + r)ⁿ is the discount factor. At 5% over 10 periods it equals 0.6139, so every dollar due at the end of period 10 is worth about 61 cents today. The difference reported by the calculator is simply FV − PV.

The formula is the algebraic inverse of compound growth. Growing a present amount gives FV = PV × (1 + r)ⁿ; dividing both sides by (1 + r)ⁿ isolates PV.

Worked example

A buyer agrees to pay you $25,000 in 8 years. Money of similar risk earns 6% a year, so you use 6% as the discount rate.

1. Compute the growth multiple: 1.06⁸ = 1.5938.
2. Divide the future value by it: 25,000 ÷ 1.5938 = $15,685.31.
3. The difference is 25,000 − 15,685.31 = $9,314.69, the value lost to waiting eight years at 6%.

Put another way, if you invested $15,685.31 today at 6% a year, it would grow to $25,000 in eight years. Any offer to buy that future payment today for less than $15,685.31 undervalues it at a 6% discount rate.

Monthly periods: $12,000 due in 24 months with a 6% nominal annual rate means 0.5% per month, so PV = 12,000 ÷ 1.005²⁴ = $10,646.23. Using 6% for each of the 24 months by mistake would give only $2,963.74.

Present value of $10,000 at common rates

This table shows how quickly the present value of $10,000 falls as the rate or the horizon grows. The 5% and 10-year cell matches the calculator's answer for those inputs.

Choosing a discount rate

The arithmetic is simple; the hard part is the rate. Common choices are:

• The interest rate on a savings account, bond or loan you would otherwise use, when the payment is fairly certain.
• The expected return of an alternative investment of similar risk, when you are comparing opportunities.
• A company's cost of capital, such as the figure from the WACC calculator, when valuing business cash flows.

Riskier or less certain payments deserve a higher rate, which lowers their present value. Small changes in the rate matter a lot over long horizons, so it is worth trying a few values.

Assumptions and common mistakes

• One payment only. The result values a single sum. Recurring payments need an annuity formula or the time value of money calculator.
• Rate and period must match. A 6% annual rate belongs with years; for months, divide by 12 first.
• Percent, not decimal. Enter 5 for 5%. Entering 0.05 means 0.05%.
• Constant rate. The formula assumes the same rate in every period and ignores inflation, taxes and fees unless you build them into the rate.
• Rate is not a forecast. Present value depends on the rate you choose, and results are only as reliable as that assumption.

Results are mathematical estimates for general information and are not investment, tax or financial advice. See our disclaimer.

Related tools

• Future value calculator grows a present amount forward.
• NPV calculator sums the present values of several cash flows and subtracts the initial outlay.
• IRR calculator finds the discount rate at which an investment's net present value is zero.
• Compound interest calculator shows the growth side of the same formula.