Answer:
a. Compounded semiannually: $19,216.67
b. Compounded quarterly: $19,338.56
c. Compounded monthly: $19,416.32
d. Compounded continuously: $19,451.08
Explanation:
The formula for the accumulated value (A) of an investment with an initial principal (P), an interest rate (r) and a compounding period (n) for a number of years (t) is:
A = P(1 + r/n)^(n*t)
Using this formula, we can calculate the accumulated value for each of the compounding periods given:
a. Compounded semiannually:
A = $15,000(1 + 0.065/2)^(2*5) = $19,216.67
b. Compounded quarterly:
A = $15,000(1 + 0.065/4)^(4*5) = $19,338.56
c. Compounded monthly:
A = $15,000(1 + 0.065/12)^(12*5) = $19,416.32
d. Compounded continuously:
A = $15,000e^(0.0655) = $19,451.08
Therefore, the accumulated value of the investment varies depending on the compounding period, with more frequent compounding resulting in a higher accumulated value.