Find the compound amount for the deposit and the amount of interest earned. $\$ 5300$ at $5 \%$ compounded quarterly for 8 years Identify the formula needed to find the compound amount, and substitute the appropriate values into it. Select the correct answer below, and fill in any answer boxes within your choice. A. $A=\square\left(1+\frac{0.05}{\square}\right)$ B. $A=\square[1+0.05(\square)$ C. $A=\left[e^{0.05(\square)}\right.$ The compound amount after 8 years 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.)

Step 1 ：Given the principal amount (P) is $5300, the annual interest rate (r) is 5% or 0.05 in decimal, the number of times that interest is compounded per year (n) is 4 (since it is compounded quarterly), and the number of years the money is invested for (t) is 8 years.

Step 2 ：The formula for compound interest is \(A = P(1 + \frac{r}{n})^{nt}\), where A is the amount of money accumulated after n years, including interest.

Step 3 ：Substitute these values into the formula: \(A = 5300(1 + \frac{0.05}{4})^{4*8}\)

Step 4 ：Simplify the expression inside the parentheses: \(A = 5300(1 + 0.0125)^{32}\)

Step 5 ：Calculate the power: \(A = 5300 * 1.488864\)

Step 6 ：Multiply to find the compound amount: \(A = \$7896.98\) (rounded to the nearest cent)

Step 7 ：The compound amount after 8 years is \(\boxed{\$7896.98}\)

Step 8 ：The amount of interest earned is the compound amount minus the principal: \(Interest = A - P\)

Step 9 ：Substitute the values: \(Interest = \$7896.98 - \$5300\)

Step 10 ：Calculate to find the interest: \(Interest = \$2596.98\)

Step 11 ：So, the amount of interest earned is \(\boxed{\$2596.98}\)