Question

Assume your starting salary as a young engineer is$65,000. You expect annual raises of 2.5%. You will deposit a constant percentage of your annual salary at the end of each year in a savings account that earns 5%. What percentage must be saved so that there will be$1,000,000 in savings for retirement after 25 years?

Answer 1

Interest Rate = 5%

Starting salary = 65,000

Annual increase in salary = 2.5% each year

You will deposit a constant percentage of annual salary at the end of each year. As the salary increases by 2.5%, the deposit at the end of each year also increases by 2.5% each year.

Future value at the 25 year = 1,000,000

Calculate the what percentage must be saved to get 1,000,000.

Step 1 – Calculate PW of the Future Value

PW = 1,000,000 (P/F, 5%, 25)

PW = 1,000,000 (0.2953) = 295,300

Step 2 – Calculate the Deposit in Year 1

Using the geometric gradient formula

Present Value = A1 [1 – (1+g) N (1+i) –N ÷ i – g]

295,300 = A1 [1 – (1 + 0.025) 25 (1 + 0.05) –25 ÷ 0.05 – 0.025]

295,300 = A1 [18.10100677]

A1 = 16,314

Step 3 – Calculate the Percentage of Salary

% of salary = (16,314 ÷ 65,000) * 100

% of salary = 25.09% (rounded to nearest value, it will be 25%)

Answer – 25% of salary must be saved so that there will be$1,000,000 in savings for retirement after 25 years.