Question

Find the future value of an \(\$ 8000\) investment if the interest rate is \(4.5 \%\) compounded monthly for 2 years.

Short answer

The future value of an \$8000 investment with an interest rate of 4.5\% compounded monthly for 2 years will be calculated with above steps using the formula for compound interest.

Step-by-step solution

Identify the parameters

The parameters for the problem are as follows - Principal amount, \(P = \$ 8000\), Annual interest rate, \(r = 4.5\% = 0.045\) (converted to decimal by dividing by 100), Number of compounding periods, \(n = 12\) (since the interest is compounded monthly), Time period, \(t = 2\) years.

Apply parameters in the future value formula

Substitute all the parameters into the future value formula: \(A = \$ 8000 \times \left(1 + \frac{0.045}{12}\right)^{12 \times 2}\)

Solve the formula

Calculate the value within the brackets first as per the BODMAS rule, then raise it to the power of \(12 \times 2\) and finally multiply the result with \$8000.

Compute the future value

The computed future value of the investment is then typically rounded to two decimal places to represent cents in the monetary value.