Bill deposits \( \$ 8300 \) with his credit union in an account paying \( 4 \% \) compounded quarterly. Find the compound amount and the interest in 6 years. Use the compound interest table. 7 Click the icon to view the compound interest table. What is the compound amount? \( \$ \square \) (Round to the nearest cent as needed.) What is the interest amount? \( \$ \square \) (Round to the nearest cent as needed.)

To find the compound amount and the interest in 6 years, we can use the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( A \) is the compound amount - \( P \) is the principal amount (initial deposit) - \( r \) is the annual interest rate - \( n \) is the number of times the interest is compounded per year - \( t \) is the time in years Given: - Principal amount (\( P \)) = $8300 - Annual interest rate (\( r \)) = 4% = 0.04 - Compounded quarterly, so \( n = 4 \) - Time (\( t \)) = 6 years Substitute the values into the formula: \[ A = 8300 \left(1 + \frac{0.04}{4}\right)^{4 \times 6} \] Now, we can calculate the compound amount using the formula. Calculate the value by following steps: - step0: Calculate: \(8300\left(1+\frac{0.04}{4}\right)^{4\times 6}\) - step1: Divide the terms: \(8300\left(1+\frac{1}{100}\right)^{4\times 6}\) - step2: Add the numbers: \(8300\left(\frac{101}{100}\right)^{4\times 6}\) - step3: Multiply the numbers: \(8300\left(\frac{101}{100}\right)^{24}\) - step4: Simplify: \(8300\times \frac{101^{24}}{100^{24}}\) - step5: Rewrite the expression: \(100\times 83\times \frac{101^{24}}{100^{24}}\) - step6: Reduce the numbers: \(83\times \frac{101^{24}}{100^{23}}\) - step7: Multiply: \(\frac{83\times 101^{24}}{100^{23}}\) The compound amount after 6 years is approximately $10,538.80. To find the interest amount, we subtract the principal amount from the compound amount: Interest = Compound amount - Principal amount Interest = $10,538.80 - $8,300 Interest = $2,238.80 Therefore, the interest amount after 6 years is $2,238.80.