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 on a money market account, you can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \(A\) is the amount of money accumulated after n years, including interest. - \(P\) is the principal amount (the initial amount of money). - \(r\) is the annual interest rate (decimal). - \(n\) is the number of times that interest is compounded per year. - \(t\) is the number of years the money is invested or borrowed. For your case: - \(P = 75,000\) - \(r = 0.0091\) (0.91% as a decimal) - \(n = 4\) (quarterly compounding) - \(t = 9\) Plugging in the values: \[ A = 75000 \left(1 + \frac{0.0091}{4}\right)^{4 \times 9} \] Calculating: \[ A = 75000 \left(1 + 0.002275\right)^{36} \] \[ A = 75000 \left(1.002275\right)^{36} \] \[ A = 75000 \left(1.087196\right) \approx 81539.70 \] Now, the interest earned: \[ \text{Interest} = A - P = 81539.70 - 75000 \approx 6539.70 \] The compound amount is \( \$ 81,539.70 \). The amount of interest earned is \( \$ 6,539.70 \).