What is the formula for present value?

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

What discount rate should I use?

Use the return you could earn on an alternative investment of similar risk: a savings or bond rate for safe cash flows, a higher required return for risky ones.

How do I handle monthly compounding?

Divide the annual rate by 12 and multiply the years by 12. Ten years at 6% compounded monthly is r = 0.5% and n = 120.

Why is present value lower than future value?

Because money available now can be invested to earn interest. The present value is the amount that would grow into the future value at the chosen rate.

Present Value Formula and Calculator

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Present Value Calculator

Present value answers a simple question: how much money today is equivalent to a payment you will receive later? Because money can earn interest, 1,000 in five years is worth less than 1,000 in your hand now. The present value formula removes that interest by dividing the future amount by the growth factor (1 + r)ⁿ, a process called discounting.

Formula

PV = FV(1 + r)ⁿ

Where

PV: present value: what the future amount is worth today
FV: future value: the amount received at the end of period n
r: interest (discount) rate per period, as a decimal
n: number of compounding periods

Calculator

Future value (FV)

Rate per period (r) (%)

For monthly periods divide the annual rate by 12.

Number of periods (n)

Years × periods per year.

Result and step-by-step solution

Present value

6,139.13

10,000.00 received after 10 periods at 5% per period is worth 6,139.13 today.

Convert the rate to a decimal
r = 5% = 0.05
Compound factor
(1 + r)ⁿ = (1 + 0.05)¹⁰ = 1.628895
Divide the future value by the factor
PV = 10,000.001.628895 = 6,139.13
Discount (time value lost)
FV − PV = 10,000.00 − 6,139.13 = 3,860.87

How to use the formula

The rate r and the number of periods n must use the same time unit. With an annual rate of 6% and monthly periods, use r = 0.5% and multiply the years by 12. The rate you choose is the return you could earn elsewhere at similar risk; a higher rate or a longer wait both shrink the present value.

In the default example, 10,000 received after 10 years at 5% a year is worth 6,139.13 today. Put another way, 6,139.13 invested at 5% grows to exactly 10,000 in ten years, which you can confirm with the future value formula. Present value is the building block for bond pricing, NPV and loan maths.

Frequently asked questions

What is the formula for present value?: PV = FV ÷ (1 + r)ⁿ, where FV is the future amount, r is the discount rate per period as a decimal and n is the number of periods.
What discount rate should I use?: Use the return you could earn on an alternative investment of similar risk: a savings or bond rate for safe cash flows, a higher required return for risky ones.
How do I handle monthly compounding?: Divide the annual rate by 12 and multiply the years by 12. Ten years at 6% compounded monthly is r = 0.5% and n = 120.
Why is present value lower than future value?: Because money available now can be invested to earn interest. The present value is the amount that would grow into the future value at the chosen rate.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.