Questions: account pays 2% interest compounded semiannually. (a) State the type. - sinking fund - amortization - future value - ordinary annuity - present value (b) Answer the question. (Round your answer to the nearest cent.)

Solution Steps

To solve this problem, we need to determine the future value of an investment with interest compounded semiannually. We will use the future value formula for compound interest, which is \( FV = P \times (1 + \frac{r}{n})^{nt} \), where \( P \) is the principal amount, \( r \) is the annual interest rate, \( n \) is the number of times interest is compounded per year, and \( t \) is the time in years.

We are given the following values:

• Principal amount \( P = 1000 \)
• Annual interest rate \( r = 0.02 \)
• Number of times interest is compounded per year \( n = 2 \) (semiannually)
• Time in years \( t = 5 \)

The future value \( FV \) can be calculated using the formula: \[ FV = P \times \left(1 + \frac{r}{n}\right)^{nt} \] Substituting the values: \[ FV = 1000 \times \left(1 + \frac{0.02}{2}\right)^{2 \times 5} \]

Calculating the expression: \[ FV = 1000 \times \left(1 + 0.01\right)^{10} = 1000 \times (1.01)^{10} \] Calculating \( (1.01)^{10} \): \[ (1.01)^{10} \approx 1.1046221254112045 \] Thus, \[ FV \approx 1000 \times 1.1046221254112045 \approx 1104.6221254112045 \]

Rounding \( FV \) to the nearest cent: \[ FV \approx 1104.62 \]

Final Answer