PV of Growing Annuity
Present value of a finite series of payments that grow at a constant rate g per period.
When to use: Use to value salary streams, growing dividends, or any payments that increase each period.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PVA | Present Value of Annuity | Present value of all growing payments | $ |
| PMT | First Payment | The first payment amount | $ |
| k | Interest Rate | Discount rate as a decimal | % |
| g | Growth Rate | Rate at which payments grow each period | % |
| n | Number of Years | Number of payment periods | years |
Real-Life Examples
Example 1: Growing Salary
A job pays $60,000/year, growing 3%/year, for 30 years. Discount rate is 8%. What is the PV of total compensation?
Given
Step-by-Step
The present value of 30 years of growing salary is $908,464.62.
Example 2: Growing Dividends
A stock pays $2/share dividend, growing 4%/year for 20 years. Required return is 10%.
Given
Step-by-Step
The present value of 20 years of growing dividends is $22.45 per share.
Frequently Asked Questions
A growing annuity is a finite series of payments that increase at a constant rate each period. Unlike a regular annuity with equal payments, each payment is larger than the last by a fixed percentage — like a salary that grows 3% per year.
When g equals k, the standard formula produces a division by zero. In this special case, the present value simplifies to PMT × n / (1 + k), which is the first payment times the number of periods, discounted back one period.
To value a career's total compensation, treat the first year salary as PMT, annual raise percentage as g, expected return as k, and working years as n. The result is the present value of your entire future earnings stream.
A growing annuity has a finite number of payments (n periods), while a growing perpetuity continues forever. The growing annuity formula includes a term that accounts for the stream ending, which the perpetuity formula does not need.