# What is the discount rate?

Computes the yearly discount rate that turns a future value into a present value over a number of years, with the effective rate and the discount factor.

- Page: https://www.acalculator.org/finance/discount-rate-calculator
- JSON spec: https://www.acalculator.org/finance/discount-rate-calculator.json
- Version: a9ef4fcc5fa8

## Default answer

Example with the default inputs (Present value $15,000.00, Future value $25,000.00, Years 8.5, Compounding Yearly): Discounting $25,000.00 back to $15,000.00 over 8.5 years takes a discount rate of 6.194% a year.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| pv | Present value | What the amount is worth today. |
| fv | Future value | The amount at the end of the period. |
| years | Years | The time between the present and the future value, in years. Decimals are fine. |
| compounding | Compounding | How often the rate compounds. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| rate | Discount rate (yearly) | The nominal yearly rate, compounded as chosen. |
| effective | Effective yearly rate | The rate compounded once a year that gives the same growth. |
| factor | Discount factor | Present value ÷ future value: what $1 at the end is worth today. |

## Method

r = m × ((FV ÷ PV)^(1 ÷ (m × t)) − 1) for m compounding periods a year over t years; continuous: r = ln(FV ÷ PV) ÷ t. Effective rate = (FV ÷ PV)^(1 ÷ t) − 1. Discount factor = PV ÷ FV.

## Assumptions

- One amount today and one amount at the end, with no payments in between.
- The rate is the same every year. A future value below the present value gives a negative rate.

## Worked examples

1. pv = $1,000.00, fv = $1,125.51, years = 4, compounding = annually gives rate = 3.000027%, factor = 0.888486. Source: OpenStax, Principles of Finance, 7.3 Methods for Solving Time Value of Money Problems (solving for the rate: $1,000 to $1,125.51 in 4 years is 3%; $15,000 to $25,000 in 8.5 years is 6.194%). https://openstax.org/books/principles-finance/pages/7-3-methods-for-solving-time-value-of-money-problems: 3% (Python 3: (1,125.51 ÷ 1,000)^(1 ÷ 4) − 1 = 3.00003%).
2. pv = $15,000.00, fv = $25,000.00, years = 8.5, compounding = annually gives rate = 6.193969%. Source: OpenStax, Principles of Finance, 7.3 Methods for Solving Time Value of Money Problems (solving for the rate: $1,000 to $1,125.51 in 4 years is 3%; $15,000 to $25,000 in 8.5 years is 6.194%). https://openstax.org/books/principles-finance/pages/7-3-methods-for-solving-time-value-of-money-problems: 6.1940% (Python 3: (25,000 ÷ 15,000)^(1 ÷ 8.5) − 1).
3. pv = $100.00, fv = $200.00, years = 10, compounding = continuous gives rate = 6.931472%, effective = 7.177346%.
4. pv = $10,000.00, fv = $15,000.00, years = 5, compounding = monthly gives rate = 8.136764%, effective = 8.447177%, factor = 0.666667.

## FAQ

### What is a discount rate?

A discount rate is the yearly rate used to turn money you will get in the future into its value today. The higher the rate, the less a future dollar is worth now.

### How do I calculate the discount rate?

Divide the future value by the present value, raise the result to the power 1 ÷ years, and subtract 1. $15,000 today and $25,000 in 8.5 years give (25,000 ÷ 15,000)^(1 ÷ 8.5) − 1 = 6.194% a year.

### What is a discount factor?

The discount factor is what $1 at the end is worth today: the present value divided by the future value, or 1 ÷ (1 + r)ᵗ. A factor of 0.8885 means each future dollar is worth about 89 cents now.

### What discount rate should I use?

Use the return you could earn elsewhere on an investment of the same risk. Companies often use their weighted average cost of capital (WACC). For a safe amount, a government bond yield for the same term is a common choice.

### What is the difference between the nominal and the effective rate?

The nominal rate compounds as often as you choose (monthly, daily). The effective rate is the rate compounded once a year that gives the same growth. With yearly compounding they are the same; with more frequent compounding the nominal rate is lower.

### Can the discount rate be negative?

Yes. If the future value is less than the present value, the money shrinks over time and the rate is below 0.

## Sources

- OpenStax, Principles of Finance, 7.3 Methods for Solving Time Value of Money Problems: solving for the rate ($1,000 to $1,125.51 in 4 years is 3%; $15,000 to $25,000 in 8.5 years is 6.194%). https://openstax.org/books/principles-finance/pages/7-3-methods-for-solving-time-value-of-money-problems (retrieved 2026-10-05)
- OpenStax, Principles of Finance, 7.2 Time Value of Money (TVM) Basics: FV = PV × (1 + i)^n and present value as discounting. https://openstax.org/books/principles-finance/pages/7-2-time-value-of-money-tvm-basics (retrieved 2026-10-05)