Question

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

Answer 1

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

Step-by-step 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