## Future Value of an Annuity Calculator

## Definition – What is a Future Value (FV) of an annuity?

Future value (FV) of an annuity is a financial calculation used to find out the value of a set of payments at some point in the future. The payments occur at the end of each time period (compared with annuity due when payments occur at the start of each time period).

## Future Value of an Annuity Formula – How FV of an annuity is calculated

Future Value = Annuity Payment x ((1 + Interest Rate)^{Number of Periods}-1) ÷ Interest Rate)

Where:

- “Payment” is the payment amount each period.
- “Rate of return” is a decimal value rate of return per period (the calculator above uses a percentage). A return of “2.2%” per year would be calculated as “0.022.”
- “Number of Periods” are the number of compounding periods.

### Example

We will receive $100 each year for the next 10 years. The interest rate at the moment is 2.2% compounded annually. What is the future value of this annuity after the 10th compounding period?

Future Value = 100 x ((1.022^{10} – 1) ÷ 0.022)

Future Value = 100 x ((1.243108 – 1) ÷ 0.022)

Future Value = 100 x (0.243108 ÷ 0.022)

Future Value = 100 x 11.5036

Future Value = 1,105.04

## Future Value of an Annuity Chart

## FAQ

### What is the difference between the future value of an annuity and an annuity due?

An annuity has the payments occur at the end of the time period. An annuity due has payments occur at the beginning of the time period.

For a financial stream of $1,000/year compounded at 2.2%/year for 3 years starting on January 1 of 2025:

- An annuity would: have payments occur on December 31 of 2025, December 31 of 2026, and December 31 of 2027. The value of the annuity would be calculated on December 31, 2027. The final value would be $3,066.48.
- An annuity due would: have payments occur on January 1 of 2025, January 1 of 2026, and January 1 of 2027. The value of the annuity due would be calculated on December 31, 2027. The final value would be $3,133.94.

In this case, the value of the annuity due would be worth slightly more than the annuity due to the extra compounding achieved by receiving the payments at the beginning of each period instead of the end.

### How do you calculate the future value of an annuity with a lump sum amount at the beginning of the time periods?

The lump sum amount at the beginning acts as a direct future value of a lump sum.

The annuity is calculated separately from the lump sum.

Finally, both amounts are added together (assuming they end at the same time period) to find the future value of both amounts.

## Sources and External Resources

- Wikipedia – Time Value of Money & Future Value – Wikipedia’s explanation of future value. The future value of an annuity formula is on the time value of money page.
- Dummies.com – How to calculate the future value of an annuity – An explanation of the formula behind the future value of an annuity.
- Houston Chronicle – Formula for the Future Value of an Annuity – Explains the formula as well as some of the terms behind annuities.