Future Value of a Growing Annuity
End-of-period payments that grow at a constant rate, accumulated to a future date.
FV of Growing Annuity
Future value of a finite series of payments that grow at a constant rate.
When to use: Use to find what growing savings deposits will accumulate to.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| FVA | Future Value of Annuity | Accumulated value of all growing payments | $ |
| PMT | First Payment | The first payment amount | $ |
| k | Interest Rate | Rate of return | % |
| g | Growth Rate | Payment growth rate | % |
| n | Number of Years | Number of periods | years |
Real-Life Examples
Example 1: Growing 401k Contributions
Start saving $6,000/year, increasing contributions by 3%/year for 30 years at 8% return.
Given
Step-by-Step
For these inputs, Future Value of Annuity is $916,247.33 under the stated payment, compounding and accounting assumptions.
Example 2: Growing Business Revenue
First year revenue of $100,000, growing 5%/year, invested at 10% for 20 years.
Given
Step-by-Step
For these inputs, Future Value of Annuity is $8,148,404.49 under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
Enter your first contribution as PMT, the annual growth rate of contributions as g, the investment return as k, and years as n. The formula calculates how much all the growing deposits will accumulate to, including investment returns.
Increasing contributions with your income maintains your savings rate as you earn more. The future value of growing contributions is substantially higher than flat contributions — a 3% annual increase over 30 years can boost your final balance by 30-50% or more.
The growth rate (g) is how fast your payments increase each period — like annual salary raises. The interest rate (k) is the return earned on invested money. Both must be positive, and k must exceed g for the standard formula to work.