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Present Value Calculator

Find what a future sum of money is worth today, using a discount rate and how often the rate compounds.

What this tool does

Find what a future sum of money is worth today, using a discount rate and how often the rate compounds. You fill in these fields: Future value, Annual discount rate, Number of years, and Compounding periods per year. It shows present value, future value, and total interest earned.

Inputs

  • Future value (USD): A number. Must be at least 0. The lump sum you expect to receive at the end of the term.
  • Annual discount rate (%): A number. Must be at least 0. The yearly rate you could earn elsewhere, for example 5 for 5 percent.
  • Number of years (years): A number. Must be at least 0. How long until the sum is received. Decimals are allowed, for example 2.5.
  • Compounding periods per year: A whole number. Accepts 1 to 365. Starts at 1. 1 for yearly, 2 for semi-annually, 4 for quarterly, 12 for monthly, 365 for daily.

How to use

  1. Enter the future value in USD.
  2. Enter the annual discount rate as a percentage.
  3. Enter the number of years in years.
  4. Enter the compounding periods per year.
  5. Read the result: present value, future value, and total interest earned. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • Future value: 1,000 USD
  • Annual discount rate: 10%
  • Number of years: 2 years
  • Compounding periods per year: 1

Results:

  • Present value: $826.45
  • Future value: $1,000.00
  • Total interest earned: $173.55

How this is worked out: Yearly compounding: PV = FV / (1 + r)^n = 1000 / 1.10^2 = 1000 / 1.21 = 826.4463. Discount = 1000 - 826.4463 = 173.5537.

Example 2. Inputs:

  • Future value: 1,000 USD
  • Annual discount rate: 12%
  • Number of years: 1 year
  • Compounding periods per year: 12

Results:

  • Present value: $887.45
  • Future value: $1,000.00
  • Total interest earned: $112.55

How this is worked out: Monthly compounding: r per period = 12 / 100 / 12 = 0.01, periods = 1 x 12 = 12. PV = 1000 / 1.01^12. 1.01^12 = 1.12682503, so PV = 1000 / 1.12682503 = 887.45. Discount = 1000 - 887.45 = 112.55.

Example 3. Inputs:

  • Future value: 5,000 USD
  • Annual discount rate: 0%
  • Number of years: 3 years
  • Compounding periods per year: 4

Results:

  • Present value: $5,000.00
  • Future value: $5,000.00
  • Total interest earned: $0.00

How this is worked out: Zero rate: (1 + 0/4)^(3 x 4) = 1, so PV = 5000 / 1 = 5000. Nothing is discounted, so the interest is 0.

Example 4. Inputs:

  • Future value: 2,000 USD
  • Annual discount rate: 6%
  • Number of years: 0 years
  • Compounding periods per year: 1

Results:

  • Present value: $2,000.00
  • Future value: $2,000.00
  • Total interest earned: $0.00

How this is worked out: Zero years: the exponent is 0, so (1.06)^0 = 1 and PV = 2000 / 1 = 2000. No time passes, so no interest.

Limitations

  • Assumes one lump sum received at the end of the term, with no other payments.
  • The rate is a nominal yearly rate, applied once per compounding period. Taxes, fees and inflation are not included.
  • Assumes the discount rate stays the same for the whole term.

FAQs

Q: What does the compounding setting change?
A: It sets how often the discount rate is applied within each year. More frequent compounding gives a slightly lower present value for the same yearly rate.
Q: Does the tool handle a series of payments?
A: No. It works for one lump sum received at the end of the term. Discount each payment separately and add the results to handle a series.
Q: Can I enter part of a year?
A: Yes. Enter decimals in the number of years, such as 2.5 for two and a half years.
Q: What is the total interest earned?
A: It is the future value minus the present value, which is the amount the money grows by over the term at the rate you entered.

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