You are saving for the college education of your two children They are two years

Question

You are saving for the college education of your two children They are two years apart in age: one will begin college 11 years from today and the other will begin 13 years from today You estimate your children's college expenses to be $34,000 per your per child payable at the beginning of each school year The annual interest rate is 7.7 percent Your deposits begin one year from today You will make your last deposit when your oldest child enters college Assume tour years of college tor each child. How much money must you deposit in an account each year to fund your cMdren's education? Annual savings References eBook & Resources Worksheet Difficulty: 3 Challenge

Explanation / Answer

First, we will calculate the present value of the college expenses for each child.

The expenses are an annuity,

so the present value of the college expenses is:

PVA = C ({1 – [1/ (1 + r)] ^t} / r)

PVA= $34,000({1 – [1/ (1 + .077)] ^4} / .077)

PVA = $113368.40

This is the cost of each child’s college expenses one year before they enter college.

So, the cost of the oldest child’s college expenses today will be:

PV = FV/ (1 + r) t

PV = $113368.40/ (1 + 0.077) ^11

PV = $ 50132.49

And the cost of the youngest child’s college expenses today will be:

PV = FV/ (1 + r) t

PV = $ 113368.40/ (1 + .077)^13

PV = $ 43220.31

Therefore, the total cost today of your children’s college expenses is:

Cost today = $ 50132.49+$ 43220.31

Cost today = $ 93352.80

This is the present value of your annual savings, which are an annuity.

So, the amount you must save each year will be:

PVA = C ({1 – [1/(1 + r)]t } / r )

$93,352.80 = C ({1 – [1/(1 + .077)]^12} / .077

C = $ 12195.59

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