Practice Question
You have decided that one year from today you will begin depositing 5% of your annual salary in an account that will earn 11% per year. Your salary will increase 4% per year throughout your career. How much money will you have when you retire 40 years from today?
Step 1: Identify Known Variables
- Initial Salary = $50,000
- Annual Deposit = 5% of salary
- Deposit starts in year 1 and increases with salary
- Interest Rate = 11% annually
- Salary Growth Rate = 4% annually
- Time Horizon = 40 years
Step 2: Formula for Future Value of a Growing Annuity
This is a growing annuity because your salary—and therefore your deposit—increases every year.
The formula is:
\[
FV = PMT \times \frac{(1 + r)^n - (1 + g)^n}{r - g}
\]
Where:
- \( PMT = 2,500 \) (i.e., 5% of $50,000)
- \( r = 0.11 \) (interest rate)
- \( g = 0.04 \) (salary/deposit growth rate)
- \( n = 40 \) (number of years)
Step 3: Plug in the Values
\[ FV = 2,500 \times \frac{(1.11)^{40} - (1.04)^{40}}{0.11 - 0.04} \] \[ FV = 2,500 \times \frac{67.274 - 4.801}{0.07} = 2,500 \times 892.448 = 2,231,119.47 \] Then, account for growth of initial payment stream: \[ FV_{\text{adjusted}} = 2,231,119.47 \times (1 + r) = 2,231,119.47 \times 1.11 \approx 2,532,753.39 \]
Conclusion: After 40 years of increasing deposits into a growing annuity, you will have accumulated approximately $2,532,753.39.