The following money market account rates were available from a particular bank. Find the compound amount and the interest earned. \( \$ 75,000 \) at \( 0.91 \% \) compounded quarterly for nine years The compound amount is \( \$ \square \). (Do not round until the final answer. Then round to the nearest cent as needed.) The amount of interest earned is \( \$ \square \). (Do not round until the final answer. Then round to the nearest cent as needed.)

To find the compound amount and the interest earned for the given money market account rates, we can use the formula for compound interest: \[ A = P \left( 1 + \frac{r}{n} \right)^{nt} \] 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 \( P = \$75,000 \) - Annual interest rate \( r = 0.91\% = 0.0091 \) - Compounded quarterly, so \( n = 4 \) - Time \( t = 9 \) years Let's calculate the compound amount and the interest earned using the formula. Calculate the value by following steps: - step0: Calculate: \(75000\left(1+\frac{0.0091}{4}\right)^{4}\times 9\) - step1: Divide the terms: \(75000\left(1+\frac{91}{40000}\right)^{4}\times 9\) - step2: Add the numbers: \(75000\left(\frac{40091}{40000}\right)^{4}\times 9\) - step3: Multiply the terms: \(675000\left(\frac{40091}{40000}\right)^{4}\) - step4: Simplify: \(675000\times \frac{40091^{4}}{40000^{4}}\) - step5: Rewrite the expression: \(5000\times 135\times \frac{40091^{4}}{40000^{4}}\) - step6: Rewrite the expression: \(5000\times 135\times \frac{40091^{4}}{5000^{4}\times 8^{4}}\) - step7: Reduce the numbers: \(135\times \frac{40091^{4}}{5000^{3}\times 8^{4}}\) - step8: Rewrite the expression: \(5\times 27\times \frac{40091^{4}}{5000^{3}\times 8^{4}}\) - step9: Rewrite the expression: \(5\times 27\times \frac{40091^{4}}{625^{3}\times 8^{3}\times 8^{4}}\) - step10: Rewrite the expression: \(5\times 27\times \frac{40091^{4}}{5^{12}\times 8^{3}\times 8^{4}}\) - step11: Reduce the numbers: \(27\times \frac{40091^{4}}{5^{11}\times 8^{3}\times 8^{4}}\) - step12: Multiply the fractions: \(\frac{27\times 40091^{4}}{8^{7}\times 5^{11}}\) The compound amount is approximately $681,163.49. Now, let's calculate the interest earned by subtracting the principal amount from the compound amount. Calculate the value by following steps: - step0: Calculate: \(681163.49-75000\) - step1: Subtract the numbers: \(606163.49\) The interest earned is approximately $606,163.49. Therefore, the compound amount is $681,163.49 and the interest earned is $606,163.49.