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 appropriate 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 for each child. How much money must you deposit in an account each year to fund your children’s education?

Answer 1

Answer:

It will deposit $ 10,082.68 per yearto fund their children tuiton

Explanation:

We calculate the present value of the tuiton:

We must notice payment are made atthe beginning of the year. So this will be an annuity-due

$C \times \frac{1-(1+r)^{-time} }{rate}(1+r) = PV$

C 40,000 per year

time 4 year

rate          7% = 7/100 = 0.07

$40000 \times \frac{1-(1+0.07)^{-4} }{0.07} (1+0.07) = PV$

PV $144,972.6418

we round to 144,972.64

Then, we have two children and we stop the payment when the oldest children goes into college.

so one tuiton must be carryied two years into the future:

$Principal \: (1+ r)^{time} = Amount$

Principal $144,972.64

time              2 years

rate                      0.07000

$144972.64 \: (1+ 0.07)^{2} = Amount$

Amount 165,979.18

We add both to get the total value of our fund:

144,972.64 + 165,979.18 = 310,951.82 = 310,952

Finally we calculate the couta of this annuity for 17 years

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $310,952.00

time      17 years

rate               7% = 0.07

$310952 \times \frac{1-(1+0.07)^{-17} }{0.07} = C$

C  $ 10,082.68