Find both the compound amount and the compound interest an \( \$ 9900 \) at \( 2 \% \), compounded semiannually, for 3 years. a) Find the values using the compound interest table. Click the icon to view the compound interest table. b) Find the values using your TVM Solver. a) Use the Compound Interest Table. Round answers to the nearest cent. What is the compound amount? \( \$ \square \) What is the compound interest? \( \$ \square \) b) Use the Compound Interest Formula or our TVM Solver. Round answers to the aearest cent. What is the compound amount? \( \$ \square \) What is the compound interest? \( \$ \square \)

To find the compound amount and compound interest for an investment of \( \$9900 \) at \( 2\% \) compounded semiannually for 3 years, let's go through it step by step. ### a) Using the Compound Interest Table: The formula to compute the compound amount \( A \) using the compound interest table is: \[ A = P(1 + \frac{r}{n})^{nt} \] Where: - \( P = 9900 \) (the principal amount) - \( r = 0.02 \) (the annual interest rate as a decimal) - \( n = 2 \) (the number of times interest is compounded per year) - \( t = 3 \) (the number of years) First, we calculate \( nt \): \[ nt = 2 \times 3 = 6 \] Now, find \( (1 + \frac{r}{n}) \): \[ 1 + \frac{0.02}{2} = 1 + 0.01 = 1.01 \] Now substitute into the formula: \[ A = 9900 \times (1.01)^{6} \] Calculating \( (1.01)^{6} \) gives approximately \( 1.06152 \). Now, calculate \( A \): \[ A \approx 9900 \times 1.06152 \approx 10400.13 \] So, the compound amount is approximately \( \$10400.13 \). To find the compound interest: \[ \text{Compound Interest} = A - P = 10400.13 - 9900 = 500.13 \] So, the compound interest is approximately \( \$500.13 \). ### b) Using the Compound Interest Formula or TVM Solver: Using the same formula as above: \[ A = 9900(1 + \frac{0.02}{2})^{6} \Rightarrow A = 9900(1.01)^{6} \] As calculated before, \( A \approx 10400.13 \). Confirming the compound interest: \[ \text{Compound Interest} = A - P = 10400.13 - 9900 \approx 500.13 \] Hence, the answers remain consistent: - Compound Amount: \( \$10400.13 \) - Compound Interest: \( \$500.13 \) So, to recap: - The compound amount is \( \$10400.13 \). - The compound interest is \( \$500.13 \).