Question

Geometric-Gradient Series 2.53 Joe's starting salary as a mechanical engineer is around $80,000. Joe is planning to place a total of 10% of his salary each year in the mutual fund. Joe expects a 5% salary increase each year for the next 30 years of employment. If the mutual fund will average 7% annual return over the course of his career, what can Joe expect at retirement?

please explain why each factor is being used.

Answer 1

Joe’s salary = $80,000

He plans to place 10%of his salary in mutual fund each year

Therefore, yearly deposits in mutual fund = $80,000*10% = 8,000

The salary is expected to increase by 5% every year for 30 years. Therefore, the annual deposits to mutual fund also increase by 5% every year for 5 years

Gradient = 5%

Number of years = 30 years

Average annual rate of return is 7%

Calculate what can Joe expect at retirement.

Calculate Future value (amount expected at 30year).

In this case we cannot directly calculate the future value. Instead calculate the present value and then take that present value to the future. Use the following formula to calculate the present value of the geometric gradient cash flow series.

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

Present Value = $8,000 [1 – (1+.05) ³⁰ (1+.07) ^–30 ÷ .07 – .05]

Present Value = $8,000 [21.61194448] = $172,896

Future Value of $172,896

Future Value = P (F/P, 7%, 30)

Future Value = $172,896 (7.61226) = $1,316,129

Calculate Future value (amount expected at 30th year) will be $1,316,129.