Question

You have a couple who are 31 years old, and want to retire at the age of 67. Knowing that, the couple has a combined annual income of $95,000 today.

1. They are curious to find out if college costs $90,000 per year when their child gets into college in 19 years, how much is the total cost of a college education (that lasts for 4 years) in today’s dollars if the cost of money is 8%? Assume you pay the tuitions at the beginning of each year and the annual tuition cost will grow at a 6% annual rate. [Hint: first compute the beginning value (at 19th year) of the tuition payment stream over the 4 year period]

Answer 1

Answer)

Calculation of Present value of College fees

Year Beginning	Annual fees	Present value factor at 8%	Present value
19	90,000.00	0.250249	22,522.41
20	95,400.00	0.231712	22,105.32
21	101,124.00	0.214548	21,695.95
22	107,191.44	0.198656	21,294.22
Total	87,617.91

Therefore total cost of education in today’s dollars if $ 87,617.91 or $ 87,618 (Approximately).

Working Notes:

Calculation of amount of tuition fees for each of four year of college

As specified in the question,

The college fees for 1st year to be paid in the beginning of 19th year from now will be $ 90,000.

Since the fees is expected to grow at 6% annual rate, the fees will be:

For 2nd year of college (to be paid in the beginning of 20th year from today) = $ 90,000 + ($ 90,000 X 6%)

                               = $ 90,000 + $ 5,400                                                                                                                      

                               = $ 95,400

For 3rd year of college (to be paid in the beginning of 21st year from today) = $ 95,400 + ($ 95,400 X 6%)

                               = $ 95,400 + $ 5,724                                                                                                                      

                               = $ 101,124

For 4th year of college (to be paid in the beginning of 22nd year from today) = $ 101,124 + ($ 101,124 X 6%)

                               = $ 101,124 + $ 6,067.44                                                                                                                      

                               = $ 107,191.44