Question

When you land your first engineering job, you open a retirement account that will pay 6% interest each year. You plan to deposit 5% of your annual salary into the account. Your first years salary is $67,000, and you expect your salary to grow 3% each year.

A) How much will be in your account after 40 years?

B) What will be your final contribution in year 40?

Answer 1

Interest Rate = 6%

Plan to deposit 5% of the salary in retirement fund

Salary in first year = 67,000

5% of salary = 5% of 67,000 = 3,350

Salary grows up by 3% each year.

It implies the annual deposit in the retirement fund also increases by 3%.

a. Calculate the future value after 40 years.

This is a geometric gradient cash flow series. First calculate PW by using the following formula.

P = A1 [1 – (1+g) ^N (1+i) ^–N ÷ i-g], where g = 3% and i=6%

P = 3,350 [1 – (1 + 0.03) ⁴⁰ (1 + 0.06) ^–3 ÷ 0.06 – 0.03] = 76,252.43

Now calculate Future Value

FV = 76,252.43 (1 + 0.06) ⁴⁰

FV = 784,310.9

b. What will the final contribution at year 40?

Contribution at 40^th year = A1 (1 + g) ^{N – 1}

Contribution at 40^th year = 3,350 (1 + 0.03) ^{40 – 1}

Contribution at 40^th year = 3,350 (1 + 0.03) ³⁹

Contribution at 40^th year = 10,609.54