Question

Cipro Milda is planning a college fund for her child. When the child joins college in 15 years, the tuition payment for the first semester is expected to be $21,000. Thereafter, tuition payments will be due every six months for the following semester. These payments are expected to increase at an annual inflation rate of 3 percent. The child will graduate in eight semesters, so she will have to make a total of eight tuition payments. If she can earn 8 percent annual rate compounded monthly, how much will she have to deposit monthly in the college fund so that the balance in the fund is zero when the last tuition payment is made? She plans to continue making these deposits until the last tuition bill is paid.

$403.04

$283.92

$423.70

$331.62

$348.35

$270.49

Answer 1

Let's assume the monthly deposit to be x. it is paid for 18.5 years.( 15 years + till start of last semester when last fees is paid)

total months for which deposits are made = 18.5*12 = 222 months

we can calculate total payment made for college fund by finding the future value of all the monthly payments using r = 0.08/12(as there is monthly compounding) and use n= 222 months because we have just calculated the approximate time till the last fees payment.

total payment made = x(1+0.08/12)^221 + x(1+0.08/12)^221 + .........x(1+0.08/12)^0 =

x( (1+0.08/12)^222 - 1) / ((1+0.08/12)-1) = 505.713865x

total requirement = 2*(21000 + 21000(1.03) + 21000(1.03)^2 + 21000(1.03)^3) = 175712.334

505.713865x = 175712.334

=>x = 175712.334/505.713865 = 348.35(approximately)