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Future Value of an Annuity Calculator

Project the future value of recurring payments with ordinary or annuity-due timing plus an optional starting balance.

What this tool does

Project the future value of recurring payments with ordinary or annuity-due timing plus an optional starting balance. You fill in these fields: Payment per period, Starting amount, Annual interest rate, Length, Payments per year, and Payment timing. Some fields are optional. It shows future value, total contributions, interest earned, and number of payments.

Inputs

  • Payment per period (USD): A number. Must be at least 0. The same amount paid into the account each period. Enter 0 for a lump sum only.
  • Starting amount (USD): A number. Must be at least 0. Optional. Money already in the account at the start. Leave empty for none.
  • Annual interest rate (%): A number. Accepts 0 to 100. Yearly rate. It is divided by the payments per year to get the rate for each period.
  • Length (years): A whole number. Accepts 1 to 100.
  • Payments per year: A whole number. Accepts 1 to 365. Starts at 12. 12 for monthly, 4 for quarterly, 1 for yearly.
  • Payment timing: Choose one: End of each period (ordinary annuity), Start of each period (annuity due). Starts as End of each period (ordinary annuity).

How to use

  1. Enter the payment per period in USD.
  2. Enter the starting amount in USD. This one is optional.
  3. Enter the annual interest rate as a percentage.
  4. Enter the length in years.
  5. Enter the payments per year.
  6. Choose End of each period (ordinary annuity) or Start of each period (annuity due) for "Payment timing".
  7. Read the result: future value, total contributions, interest earned, and number of payments. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • Payment per period: 100 USD
  • Annual interest rate: 12%
  • Length: 2 years
  • Payments per year: 12
  • Payment timing: End of each period (ordinary annuity)

Results:

  • Future value: $2,697.35
  • Total contributions: $2,400.00
  • Interest earned: $297.35
  • Number of payments: 24

How this is worked out: Ordinary annuity FV = P x ((1 + r)^n - 1) / r, with r = 0.12 / 12 = 0.01 and n = 2 x 12 = 24. (1.01)^24 = 1.26973465, so the factor is (1.26973465 - 1) / 0.01 = 26.973465 and FV = 100 x 26.973465 = 2697.3465, shown as 2697.35. Contributions = 100 x 24 = 2400. Interest = 2697.3465 - 2400 = 297.3465, shown as 297.35.

Example 2. Inputs:

  • Payment per period: 100 USD
  • Starting amount: 1,000 USD
  • Annual interest rate: 10%
  • Length: 2 years
  • Payments per year: 1
  • Payment timing: Start of each period (annuity due)

Results:

  • Future value: $1,441.00
  • Total contributions: $1,200.00
  • Interest earned: $241.00
  • Number of payments: 2

How this is worked out: Annuity due with a starting amount. r = 0.10, n = 2. Payments: ordinary factor ((1.1)^2 - 1) / 0.1 = 0.21 / 0.1 = 2.1, times (1 + r) = 1.1 for start-of-period payments, gives 100 x 2.1 x 1.1 = 231. Starting amount: 1000 x (1.1)^2 = 1210. FV = 231 + 1210 = 1441. Contributions = 1000 + 100 x 2 = 1200. Interest = 1441 - 1200 = 241.

Example 3. Inputs:

  • Payment per period: 200 USD
  • Starting amount: 500 USD
  • Annual interest rate: 0%
  • Length: 5 years
  • Payments per year: 12
  • Payment timing: End of each period (ordinary annuity)

Results:

  • Future value: $12,500.00
  • Total contributions: $12,500.00
  • Interest earned: $0.00
  • Number of payments: 60

How this is worked out: Zero rate: nothing grows, so the future value is the money paid in. Periods = 5 x 12 = 60. Payments = 200 x 60 = 12000. Plus the starting amount 500 gives 12500. Interest = 0.

Example 4. Inputs:

  • Payment per period: 0 USD
  • Starting amount: 1,000 USD
  • Annual interest rate: 5%
  • Length: 10 years
  • Payments per year: 1
  • Payment timing: End of each period (ordinary annuity)

Results:

  • Future value: $1,628.89
  • Total contributions: $1,000.00
  • Interest earned: $628.89
  • Number of payments: 10

How this is worked out: Lump sum only: FV = 1000 x (1 + 0.05)^10. 1.05^10 = 1.62889463, so FV = 1628.89. Interest = 1628.89 - 1000 = 628.89.

Limitations

  • Assumes the same payment every period and one fixed annual rate for the whole term.
  • Interest compounds once per payment period, at the annual rate divided by the payments per year.
  • Does not include taxes, fees, inflation or missed payments.
  • The length must be from 1 to 100 whole years.

FAQs

Q: Does the result include taxes or fees?
A: No. The result is the growth of your payments and starting amount at the rate you enter. Taxes, account fees and inflation are not included.
Q: What does the payment timing option change?
A: End of each period is an ordinary annuity: each payment is made at the end of its period. Start of each period is an annuity due: each payment earns one extra period of interest, so the future value is higher.
Q: Can I see how a lump sum grows?
A: Yes. Enter 0 as the payment and the amount you have as the starting amount. Leave the starting amount empty to calculate payments only.
Q: Why is the length in whole years?
A: The number of payments is the length in years times the payments per year, so the length is entered as whole years to give a whole number of payments.

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