What this calculator does
The discount rate is the annual rate used to convert a future amount of money into its equivalent value today, reflecting the fact that money available now is generally worth more than the same amount received later. Most calculators that use a discount rate treat it as a given input; this one solves for it instead, when you already know the present value, the future value, and how many periods separate them.
This is the mirror image of a standard compound growth calculation. Instead of asking "what will this amount grow to at a given rate," it asks "what rate would have to apply for this amount to grow into that one," using r = (FV ÷ PV)^(1/n) − 1.
The formula
Divide the future value by the present value, raise that ratio to the power of one divided by the number of periods, and subtract 1. The result is the rate per period that exactly reconciles the present and future values given.
| Term | Meaning |
|---|---|
| Discount rate | The implied rate per period: (future value ÷ present value)^(1/periods) − 1. |
| Present value | The value of the amount today. |
| Future value | The value of the amount at the end of the stated number of periods. |
The inputs explained
| Field | What to enter |
|---|---|
| Present value ($) | The value of the amount today, or at the start of the period being measured. |
| Future value ($) | The value of the amount at the end of the stated number of periods. |
| Number of periods (years) | The number of periods (typically years) between the present value and the future value. |
When to use it
Backing out the rate an investment actually earned
If you know what an amount started at and what it grew to over a known period, this works out the effective annual rate that connects the two, without needing to know the rate in advance.
Checking the rate implied by a quoted deal
A structured investment, bond, or business valuation that quotes a present value and an expected future value implies a specific discount rate; recomputing it independently checks whether that implied rate looks reasonable.
Comparing to a required rate of return
Once the implied discount rate is known, it can be compared directly against a required or benchmark rate of return to judge whether the numbers behind a deal are actually attractive.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the implied discount rate changes with the number of periods
A fixed present value of $10,000 growing to $13,000, across a range of period lengths.
| Number of periods | Discount rate |
|---|---|
| 1 years | 30.0% |
| 2 years | 14.0% |
| 5 years | 5.39% |
| 10 years | 2.66% |
| 20 years | 1.32% |
| 30 years | 0.878% |
How the implied discount rate changes with the future value
A fixed $10,000 present value and 5-year period, across a range of future values.
Questions
What is a discount rate?
It is the rate used to convert a future amount of money into its present-day equivalent, or equivalently, the rate at which a present amount would need to grow to reach a stated future value over a given number of periods.
How is this different from a normal compound interest calculation?
A standard compounding calculation takes a rate as a given input and computes the future value it produces. This calculator works backwards: it takes the present value, future value and time period as given, and solves for the rate that connects them.
What is the formula for discount rate?
r = (FV ÷ PV)^(1/n) − 1, where FV is the future value, PV is the present value, and n is the number of periods between them.
How do I calculate a discount rate in practice?
Take the future value divided by the present value, raise the result to the power of one over the number of periods, then subtract 1. Multiplying the result by 100 expresses it as a percentage per period.
To see the loss triangle created when a market price is pushed away from its equilibrium, use the deadweight loss calculator. For a present-value calculation that takes the discount rate as a starting input instead, see the human life value calculator.