Question

1. A client plans to send her child to college starting in the fall of 2038. She estimates that tuition will cost $40,000 per year and that room and board will cost $14,000 per year, with $20,000 payable for tuition and $7,000 payable for room and board on each January 1 and July 1 during the four years in college, starting on July 1, 2038 and ending on January 1, 2042. She can invest in a fund that will pay 6% a year compounded monthly and plans to make equal deposits to the fund every month, on the first of the month. When her child is in college, she will make the payments for tuition and room and board from the fund while she is still making monthly deposits into the fund. If she makes deposits for 21 years and 8 months starting June 1, 2020, and ending on January 1, 2042, how much should each deposit be in order for the fund balance on January 1, 2042, to be sufficient to make the last payment for tuition and room and board?

Answer 1

Let an amount A be deposited each month

The Future value of both deposits and requirements should be equal

Monthly interest rate = 6%/12 = 0.5%

No of deposits = 21*12+8 = 260

So, FV = A/0.005*(1.005^260-1)

The first requirement will be on July 1,2038 and the last on Jan 1,2042 (3.years or 42 months) and total there will be 8 payments

FV of requirements = 27000*1.005^42+ 27000*1.005^36+ 27000*1.005^30+...+ 27000

=27000*1.005^42*(1-(1/1.005^6)^8)/(1-1/1.005^6)

=240414.95

So, A/0.005*(1.005^260-1) = 240414.95

=> A * 531.486 = 240414.95

=> A = 452.34

So, the monthly deposit should be $452.34