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.

How much would Millhouse have to save each month, starting from the end of next month, in order to accumulate enough money for his wedding expenses, assuming a rate of return of 10% compounded monthly?

Millhouse would have to save $46613.56 each month in order to accumulate enough money for his wedding expenses.

***If Millhouse starts saving at the end of next month for the down payment on his house, how much money (in addition to the wedding expenses) will he have to save each month? Assume the same terms as in question 3.

Answer 1

Since Millhouse needs to pay 20% down payment after 5 years, amount required after 5 years =

20% * 200000 = 40000.

So he needs to accumulate 40000 over the 5 years through monthly savings.

Since he will start at the end of next months, the total months will be (5 * 12) - 1 = 59 months.

We need to calculate monthly savings required for 59 months to accumulate 40000.

This is the case of ordinary annuity where we will save equal amount every month for a specific time period (59 months) with an interest rate of 10% p.a.

Since the installments are monthly, the interest rate will be 10% / 12 = 0.8333%

Now, 40000 is the future value hence we can use the below formula to calculate the monthly requirement:

Putting FV, i & n as 40000, (10%/12) & 59, we get,

C = 527.67 per month.