Question

You want to save money for your newborn niece’s college education. Assume that today’s all-in cost of attending a prestigious college for four years is $250,000. This number is already discounted back to the beginning of the four years in college, i.e., you need $250,000 in your savings account today to fully fund a college student for the next four years. This all-in cost of college is expected to increase by 5 percent per year forever. You expect your niece to start attending college in 18 years, and to take 4 years to finish college.

a.  If the discount rate is 6 percent, what is the present value of the cost of her college education?

b. Your plan is to hand your niece a check on her 18th birthday for an amount sufficient to cover the cost of her college education. To achieve this goal, you would like to save the same amount every year for the next 18 years. Assume that you can invest your savings at an interest rate of 6 percent (EAR). What dollar amount do you need to save every year for the next 18 years?

Please show details of calculations.

Answer 1

Expected College cost after 18 years,when niece will start the college = 250000*1.05^{18 =}   250000*2.4066 = $ 601,652.5

a) If discount rate is 6% then, Present value of College fees = 601652.5/(1.06¹⁸)

                                                                             = 601650/2.85433 = 210785.89 or 210786 (Approximately)

b)

Assumption : Since question is silent, We are assuming that I will save the amount "P" for my Niece at the end of every year.

Since we know,

Present value of Annuity = P * [1-(1+r)^-n]/r          (where, (1+r)^{-n =} 1/([1+r)ⁿ] , r = 0.06, n = 18 years)

So, 210786 = P * [1-(1+0.06)^-18]/0.06      

So, 210786 = P * [1- (1/2.85433)]/0.06

So, 210786 = P* [1-0.350345]/0.06

So, 210786 = P*10.82758

So, P = 19467.50

So, P = $19,467.50

So, I will save $ 19,467.50 for my niece every year for her college cost.