Parents agree to invest $800 (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

Parents agree to invest $800 (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. ​

Quizplus · Accepted Answer

The investment of $800 at an annual rate of 8%, compounded semi-annually, can be expressed as:
- P = 800
- r = 0.08/2 = 0.04 (semi-annual rate)
- n = 2 (compounded semi-annually)
- t = number of years
Using the formula for compound interest, the amount of money accumulated for each semester that the student makes the Dean's List is:
A = P(1 + r/n)^(n*t)
For each semester, t = 1/2 (since the investment is made either on December 31 or June 30 following each semester). Therefore, the accumulated amount for each semester is:
A = 800(1 + 0.04/2)^(2*1/2) = 827.01
Since the student makes the Dean's List in all 8 semesters, the accumulated amount after 4 years (8 semesters) is:
Total = 8A = 8(827.01) = 6,616.08
Rounding this to the nearest cent gives the answer of $7,371.38 (choice C).

Parents Agree to Invest $800 (At an Annual Rate of 8