Question

A couple wishes to establish a college fund at a bank for their seven-years-old child. The college fund will earn 10% interest compounded monthly. Assuming that the child enters university at age 18, the family estimates that amount of SR18,000 per year, in terms of today's dollars will be required to support the child's university expenses for four years. College expenses are estimated to increase at an annual rate of 9%. Determine the equal monthly deposit amounts the family must save until they send their child to university. Assume that the first deposit will be made at the end of first month and that deposit will continue until the child reaches age 17. The child will enter college at age 18, and annual college expense will be paid at the beginning of each college year. In other words, the first withdrawal will be made when the child is 18.

Answer 1

Solution:

first we have to calculate the present value of annual payment of SR 18,000 at the begining of year 18.Since the annual payment will be made at the begining of year,hence we should use the formula of annuity due to calculate the present value:

Present Value=(Annuity/Rate)*[1-(1/1+rate)^no. of years)]*(1+rate)

=(SR18,000/0.09)*[1-1/(1.09)^4)]*(1+0.09)

=SR 63,563.30

It means that couple need SR 63,563.30 at the end of the year 17.Now determining the monthly payment using the following formula:

Monthly Payment(Annuity)=Future Value/[(1+rate/no. of compounding in a year)^no. of years*no. of compounding in a year-1/(rate/no. of compounding in a year)

Annuity=SR 63,563.30/[(1+0.10/12)^17*12)-1/(0.10/12)

=SR 63,563.30/532.4754

=SR 119.37

Thus,couple is required to make monthly deposit of SR 119.37(approx).