Practice Question
Your job pays you at the end of the year and today, December 31, you just received your salary of $125,000 and you plan to spend all of it.
However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 20%
of your annual salary in an account that will earn 4.5% per year. Your salary will increase 3% per year throughout your career.
How much money will you have when you retire 50 years from today?
Step 1: Define Variables
- Initial Salary = $125,000
- Annual Savings = 20% of salary = $25,000 (Year 1 contribution)
- Interest Rate \( r = 4.5\% \)
- Growth Rate \( g = 3\% \)
- Number of Years \( n = 50 \)
Step 2: Use Future Value of Growing Annuity Formula
\[
FV = PMT \times \frac{(1 + r)^n - (1 + g)^n}{r - g}
\]
Where:
- \( PMT = 25,000 \)
- \( r = 0.045 \)
- \( g = 0.03 \)
- \( n = 50 \)
Step 3: Compute FV
\[ FV = 25,000 \times \frac{(1.045)^{50} - (1.03)^{50}}{0.045 - 0.03} \] \[ = 25,000 \times \frac{8.9606 - 4.3839}{0.015} = 25,000 \times \frac{4.5767}{0.015} = 25,000 \times 305.1133 = 7,980,320.23 \]
Conclusion: After 50 years of contributing 20% of your annually growing salary into an account earning 4.5%, you will have approximately $7,980,320.23 saved for retirement.