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Holly would like to plan for her daughter's college education. She would like for her daughter, who was born today, to attend college for 4 years, beginning at age 18. Tuition is currently $13,000 per year and tuition inflation is 7%. Holly can earn an after-tax rate of return of 10%. How much must Holly save at the end of each year, if she wants to make the last payment at the beginning of her daughter's first year of college

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Answer:

Holly saved $3,362.76 at the end of each year.

Explanation:

Solution

Given that:

We solve for the computation  of Tuition Fees given as:

First Year tuition fees will be $13,000 with inflation at 7% for 18 years.

That is, $13,000 * (1.07)^18 = $13,000 * 3.38 = $43,940

Now,

For the remaining three years we have the following given below:

College Year 1= $43,940

College Year 2 = $47,015.80, $43,940 * 1.07

College Year 3 = $50,306.91, $47,015.80 * 1.07

College Year 4 = $53,828.39, $50,306.91 * 1.07

Thus,

The Present Value of the college fees at the beginning of college at 10% is given as follows:

Year          PVF at 10%        College Fees       Present Value

1                     0.91                $43,940.00     $39,985.40

2                    0.83                $47,015.80     $39,023.11

3                    0.75                $50,306.91     $37,730.18

4                    0.68                $53,828.39     $36,603.31

TOTAL :                                                         $153,342.00

Thus,

Holly should have accumulated $153,342 till beginning of her daughter's college.

Let us recall  the accumulation factor for annual annuity is given as:

(1 + .10)^18 - 1/. 10

=45.60

Therefore, the Annual Investment should be $153,342 / 45.60

= $3,362.76

     

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