Future Value of an Annuity
A level stream of end-of-period payments accumulated to a future date. Solve for the future value, the payment needed to reach a target, or how long it takes to get there.
FV of Ordinary Annuity (Annual Compounding)
Calculates the future value of a series of equal end-of-year payments.
When to use: Use to find how much a series of regular annual savings deposits will grow to.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| FVA | Future Value of Annuity | Total future value of all payments | $ |
| PMT | Payment | Periodic payment amount | $ |
| k | Interest Rate | Nominal annual interest rate as a decimal | % |
| n | Number of Years | Time period in years | years |
Real-Life Examples
Example 1: Annual Retirement Contributions
You contribute $6,000/year to a retirement fund earning 8% for 30 years.
Given
Step-by-Step
For these inputs, Future Value of Annuity is $679,699.27 under the stated payment, compounding and accounting assumptions.
Example 2: Vacation Fund
Save $2,000/year at 5% annual return for 10 years.
Given
Step-by-Step
For these inputs, Future Value of Annuity is $25,155.79 under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
An ordinary annuity is a series of equal payments made at the end of each period. Most loans, bond coupon payments, and retirement contributions are structured as ordinary annuities.
The future value of an annuity is the total amount accumulated after making a series of equal periodic payments, including all interest earned. It tells you how much your regular savings will grow to.
In an ordinary annuity, payments are made at the end of each period. In an annuity due, payments are made at the beginning. An annuity due is always worth more because each payment has one extra period to earn interest.
The basic annual formula works for annual payments. For monthly savings, use the m-times-per-year version of the formula, which adjusts the rate and number of periods for the compounding frequency.
The calculator uses the finite zero-rate limit: an annuity’s value is payment times payment count; a solved payment is the target value divided by a positive payment count. Deferral has no effect at zero interest. Values require whole payment counts, even under continuous interest compounding.