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

So (a) is the answer.

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