Question

Find the accumulated value of an investment of $15,000 for 5 years at an interest rate of 6.5% if the money is a. compounded​ semiannually; b. compounded​ quarterly; c. compounded monthly d. compounded continuously. Round answers to the nearest cent.

Answer 1

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.