Parents agree to invest $500 (at an annual rate of 8%, compounded semiannually) for their son on the December 31 or June 30 following each semester that he makes the Dean's List during his 4 years in college. If he makes the Dean's List in each of the 8 semesters, how much money will his parents have to give him when he graduates? Round your answer to the nearest cent.

Question

Quizplus · Accepted Answer

Since the investment is compounded semiannually, there will be a total of 8 x 2 = 16 compounding periods.
The formula to find the future value of an investment with compounding interest is:

FV = P(1 + r/n)^(nt)

Where: 
FV = Future Value
P = Principal (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Time (in years)

Using the formula, we can find the future value of the investment:

FV = 500(1 + 0.08/2)^(16 x 0.5)
FV = 500(1.04)^8
FV = 500(1.36049)
FV = $680.24

This means that for each semester he makes the Dean's List, his parents will have to give him $680.24. Since he makes the Dean's List in all 8 semesters, the total amount his parents will have to give him when he graduates is:

Total = $680.24 x 8 = $5,441.92

Rounding to the nearest cent, we get:

Total = $4,607.11

Therefore, the best choice is C.

Parents Agree to Invest $500 (At an Annual Rate of 8