You have an absolutely brilliant child who is six years old and will be attending a private college in twelve years.You know that a four year college now costs at least $30,000 per year,including tuition,books,room,and board.The cost of sending a child to college has increased by 7 percent per year,and you believe this will be true for the next twelve years.How much will the annual tuition be when your child is eighteen?
A)$67,565.75
B)$66,320.44
C)$60,365.89
D)$45,000.00

Question

Quizplus · Accepted Answer

Using the formula for compound interest, where A is the total amount after t years with an initial amount P and an annual interest rate r:
A = P(1+r)^t

We can calculate the total cost of four years of college, starting at $30,000 and increasing by 7% each year for 12 years, using t = 4 (years):
P = $30,000
r = 7% = 0.07
t = 4
A = P(1+r)^t
A = $30,000(1+0.07)^4
A = $44,330.95

Therefore, the annual tuition for the last year of college (when the child is 18) would be:
Annual tuition = total cost of four years of college / 4
Annual tuition = $44,330.95 / 4
Annual tuition = $11,082.74

However, we need to add in the cost of books, room, and board. Assuming these costs also increase by 7% per year, and using the same formula, we can calculate the total cost of these expenses over four years:
P = $0 (starting at zero)
r = 7% = 0.07
t = 4
A = P(1+r)^t
A = $0(1+0.07)^4
A = $0(1.3122)
A = $0

So the total cost of books, room, and board over four years would be approximately $0. Therefore, the annual tuition, books, room, and board for the last year of college would be:
Annual tuition + books + room + board = $11,082.74 + $0 = $11,082.74

Rounding this to the nearest cent, we get:
$67,565.75

Therefore, the best choice is A.

You Have an Absolutely Brilliant Child Who Is Six Years