Exercise 2 Marcus Fitzgerald plans to retire 32 years from n

Exercise 2. Marcus Fitzgerald plans to retire 32 years from now. He expects that he will live 28 more years after retiring. Marcus wants to have enough money upon reaching retirement age to withdraw $120,000 from the account at the end of each year he expects to live, and yet still have $250,000 left in the account at the time of his expected death (60 years from now) Marcus plans to accumulate the retirement fund by making equal annual deposits at the end of each year for the next 32 years. He expects that he will be able to earn 9% per year on his deposits. However, he only expects to earn 5% per year on his investment after he retires since he will choose to place the money in less risky investments. What equal annual deposits must Marcus make each year to reach his retirement goal?

Solution

You plan to retire 32 years from now so when you retire you must have accumulated enough to cover the expenses in after retirement life. Let the initial annual deposits be A. Then its present value at the time of retirement will be

A(F/A, 9%, 32).

When you are at your retirement age 32 years from now you will have an accumulated amount of A(F/A, 9%, 32) which you will spend in the following manner so that you are left with 250,000 at the end of 28^th year from then

A(F/A, 9%, 32) = 120,000(P/A, 5%, 28) + 250,000(P/F, 5%, 28)

A*164.03699 = 120,000*14.89813 + 250,000*0.25509

This gives A = 11287.38. This is the required amount of annual deposits