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

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