acalculator

What is the discount rate?

Enter what an amount is worth today, what it will be worth later and the years in between to see the discount rate that links them. Pick how often the rate compounds to see the nominal rate, and compare it with the effective yearly rate.

Your numbers

Discount rate (yearly)
6.194%

Discounting $25,000.00 back to $15,000.00 over 8.5 years takes a discount rate of 6.194% a year.

Effective yearly rate
6.194%
Discount factor
0.6

Discount rate (yearly): 6.194%. Discounting $25,000.00 back to $15,000.00 over 8.5 years takes a discount rate of 6.194% a year.

The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use

How to calculate

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.

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.

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.

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Present value $1,000.00, Future value $1,125.51, Years 4, Compounding Yearly gives Discount rate (yearly) 3.000027%, Discount 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. Present value $15,000.00, Future value $25,000.00, Years 8.5, Compounding Yearly gives Discount rate (yearly) 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. Present value $100.00, Future value $200.00, Years 10, Compounding Continuous gives Discount rate (yearly) 6.931472%, Effective yearly rate 7.177346%.
  4. Present value $10,000.00, Future value $15,000.00, Years 5, Compounding Monthly gives Discount rate (yearly) 8.136764%, Effective yearly rate 8.447177%, Discount factor 0.666667.

How it works

The future value FV and present value PV are linked by FV = PV × (1 + r ÷ m)^(m × t), where t is the years and m the compounding periods a year (1 yearly, 2 twice a year, 4 quarterly, 12 monthly, 365 daily). Solved for the yearly rate r:

  • Discount rate r = m × ((FV ÷ PV)^(1 ÷ (m × t)) − 1)
  • With continuous compounding, FV = PV × e^(r × t), so r = ln(FV ÷ PV) ÷ t
  • Effective yearly rate = (FV ÷ PV)^(1 ÷ t) − 1, whatever the compounding
  • Discount factor = PV ÷ FV

The rates show as percents.

Rules:

  • The present and future values are each from $0.01 to $1 trillion. The years are more than 0 and at most 1,000, and may have decimals.
  • A rate above 1 billion percent (or below −1 billion percent with continuous compounding) gives no answer.
  • Rates show to 4 decimals and the discount factor to 6, with halves rounded up (away from 0).

Assumptions

  • There is one amount today and one at the end, with no payments in between.
  • The rate stays the same for the whole time.

Worked examples by hand

$1,000 to $1,125.51 in 4 years, yearly. r = (1,125.51 ÷ 1,000)^(1 ÷ 4) − 1 = 1.0300003 − 1 = 3.0000%. Discount factor = 1,000 ÷ 1,125.51 = 0.888486.

$15,000 to $25,000 in 8.5 years, yearly. r = (25,000 ÷ 15,000)^(1 ÷ 8.5) − 1 = 6.1940%.

$100 to $200 in 10 years, continuous. r = ln(2) ÷ 10 = 6.9315%. Effective rate = e^0.069315 − 1 = 7.1773%.

$10,000 to $15,000 in 5 years, monthly. r = 12 × (1.5^(1 ÷ 60) − 1) = 8.1368%. Effective rate = 1.5^(1 ÷ 5) − 1 = 8.4472%. Discount factor = 10,000 ÷ 15,000 = 0.666667.

Other questions people ask

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.