Question

Use the information for the​ question(s) below.

Suppose that a young couple has just had their first​ baby, a​ daughter, and they wish to ensure that enough money will be available to pay for her college education.​ Currently, college​ tuition, books,​ fees, and other​ costs, average​ $12,500 per year. On​ average, tuition and other costs have historically increased at a rate of​ 4% per year.

Assuming that college costs continue to increase an average of​ 4% per year and that all her college savings are invested in an account paying​ 7% interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest​ to:

A.

​$101,291.

B.

​$97,110.

Your answer is correct.

C.

​$107,532.

D.

​$50,000.

Answer 1

Correct answer: B.$97,110

Current College fee = $12,500

Years until first day of college = 18

Assuming college fee paid at beginning of each of year of college.

Fee for year-1 = 12,500*(1+0.04)^18 = $25,322.71

Fee for year-2 = 25,322.71*(1+0.04) = $26,335.61

Fee for year-3 = 26,335.61*(1+0.04) = $27,389.04

Fee for year-4 = 27,389.04*(1+0.04) = $28,484.60

Annual interest rate = 7%

Thus, Present value of College fee on first of college (i.e at age 18)

26.335.61 27, 389.04 = 25,322.71 + = (1+0.07)/(1+0.07) 2 28, 484.60 140.07)3

$\large = \$97,110$

Please note: Intermediate calculation is not rounded off. (figures are rounded off to 2 decimal just to show)

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.