Question

Millhouse graduated 5 years ago with a degree in business administration and is currently employed as a middle level manager for the same firecracker company his dad already worked for. His current annual salary of $60,000 has increased at an average rate of 5% per year and is projected to increase at that rate for the future. The firm has had a voluntary retirement savings program in place, whereby, employees can contribute up to 11% of their gross annual salary (up to a maximum of $11,000 per year) and the company will match every dollar that the employee contributes. Unfortunately, Millhouse did not listen to his finance instructor (which is understandable, because you can’t really trust those Germans) and has not yet taken advantage of the retirement savings program. He opted instead to buy a new car, rent an expensive apartment and go out to Moe’s every night. However, with wedding plans on the horizon, Millhouse has finally come to the realization (with the help of his fiancée Lisa) that he had better start putting away some money. Millhouse figures that the two largest expenses down the road would be those related to the wedding and down payment on a house. He estimates that the wedding, which will take place in twelve months, should cost about $10,000. Furthermore, he plans to move into a $200,000 house in 5 years and would need 20% for a down payment. Millhouse knows that an automatic payroll deduction is probably the best way to go since he is not a very disciplined investor.

) If Millhouse saves up a million dollars by the time he retires (at age 65), how much can he withdraw each month in equal dollar amounts, if he figures he will live up to the age of 85 years? Assume that his investment fund yields a rate of return of 8% compounded monthly.

Answer 1

This is a payout annuity pronblem

The equation to figure out payout annuity is,

Here,

P₀ = $1000000

r= 0.08

k = 12 (compounded monthly)

N = 20 (ie, 85-65)

And d is the unknown

Thus,

1000000=d(1-(1+0.08/12)^-20*12)/0.08/12

1000000=d*0.79702861134/0.00666666666

d(aka equal monthly withdrawals possible) = $8364.40068167