Question

You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $40,000 per year per child, payable at the beginning of each school year. The annual interest rate is 7 percent. Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume four years of college. How much money must you deposit in an account each year to fund your children’s education?

Answer 1

First, we need to find the total amt. For both childrens' education --to be saved by the end of Yr.15/ beg. Yr. 1----in the a/c.

as it is given that --You will make your last deposit when your oldest child enters college,ie.end of Yr.15/ beg. Yr. 16

As fees are paid in the beginning of the year, we need to use the PV of annuity due formula,

PV(due)=(Pmt.*(1-(1+r)^-n)/r)*(1+r)

Where, PV(due) is the amt. to be found out

pmt.= the annual fees --$ 40000

r=rate of interest given as 7% p.a. or 0.07

n= no.of yearly pmts.= 4

so, plugging in these values, in the formula,

40000*(1-1.07^-4)/0.07*(1.07)

we get the PV at end Yr.15/Yr. 16 as

144973

PV of the younger one's education expenses

is the PV at end yr. 15/Beg. Yr. 16 of the

above PV of annuity due at end yr. 17/ Beg. Yr. 18

ie. PV(PVOAdue)

ie. 144973/1.07^2=

126625

So, the total sum needed to be in the savings a/c at end yr. 15/beg yr. 16 will be

144973+126625=

271598

This $ 271598 is the future value of annual deposits made from end yr. 1 to end yr.15

Using the FV of ordinary annuity formula,

FV(OA)=Pmt.*((1+r)^n-1)/r

Where, FV(OA) is the amt. known-- $ 271598

pmt.= the annual deposit--to be found out--??

r=rate of interest given as 7% p.a. or 0.07

n= no.of yearly deposits= 15

so, plugging in these values, in the formula,

271598=Pmt.*((1+0.07)^15-1)/0.07

Pmt.=271598/(((1+0.07)^15-1)/0.07)

10808

The required annual deposits from end yr. 1 upto end yr. 15 will be

$10,808