Question

You have 35 years left until retirement and want to retire with $2.5 million. Your salary is paid annually, and you will receive $75,000 at the end of the current year. Your salary will increase at 2 percent per year, and you can earn a return of 8 percent on the money you invest.

  

If you save a constant percentage of your salary, what percentage of your salary must you save each year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Percentage of salary

%

Answer 1

Year end salary = $75,000
Annual Growth in salary = 2%
Annual return = 8%
Time to retirement = 35 years

Future Value of salary received = $75,000*1.08^34 + $75,000*1.02*1.08^33 + $75,000*1.02^2*1.08^32 + ... + $75,000*1.02^34
Future Value of salary received = $75,000 * 1.08^34 * [1 - (1.02/1.08)^35] / [1 - (1.02/1.08)]
Future Value of salary received = $75,000 * 1.08^35 * [1 - (1.02/1.08)^35] / 0.06
Future Value of salary received = $75,000 * 213.09091
Future Value of salary received = $15,981,818.25

Desired Sum at retirement = $2,500,000

Percentage of Salary saved = Desired Sum at retirement / Future Value of salary received
Percentage of Salary saved = $2,500,000 / $15,981,818.25
Percentage of Salary saved = 15.64%

So, you need to save 15.64% of your annual salary to achieve desired goal