Answer:
The accumulated value of the investment after 5 years is
a. Compounded semiannually: $19,675
b. Compounded quarterly: $19,711
c. Compounded semiannually: $19,735
d. Compounded continuously: $19,747
Explanation:
Formula for a. b. c. : Future Value (FV) =
Formula for c: FV =
Where:
- PV = present value of the deposit/investment ($15,000)
- i = stated interest rate (5.5%)
- n = number of periods in a year
- t = number of years (5)
a. Compounded semiannually: n=2 => FV = 15,000 * [1+(5.5%/2)]^(2*5) = $19,675
b. Compounded quarterly: n=4 => FV = 15,000 * [1+(5.5%/4)]^(4*5) = $19,711
c. Compounded semiannually: n=12 => FV = 15,000 * [1+(5.5%/12)]^(12*5) = $19,735
d. Compounded continuously: FV = 15,000 * e^(5.5%*5) = $19,747