Midterm 1 Exponential Discounting

Suppose your uncle Chris was going to make a deposit of \$20K on the date of your
child’s birth to fund a college education. The cost of college starts at \$20K
and increases by 8% per year for four years starting in year 18 and continuing
through year 21.

How much will college cost in your child’s 21st year?

(a) \$25,194.24
(b) \$20,000.00
(c) \$100,676.67
(d) \$26,400.00

The first thing you want to do for this problem is to notice that we are looking for future worth, knowing that the present worth is \$20K. The equation we want to use here is

F = P(1 + i)N

Where F is the future worth, P is the present worth, i is the interest rate, and N is the number of years projected. \$20K is the present worth for this problem because this is the cost college starts at, given in the problem statement. The present worth then increases at a rate of 8%, which is i. N is equal to 3 years, because the cost starts increasing in year 18 and continues through 21.

21 – 18 = 3

Substituting these values into the equation

F = \$20K(1 + 0.08)3

Solving this equation gives

F = \$25,194.24