Question 5 of 9, Step 1 of 1 $3 / 9$ Correct Incorr Suppose that $\$ 47,600$ is invested in a certificate of deposit for 2 years at $10.2 \%$ annual interest to be compounded semi-annually. How much interest will this investment earn? Round your answer to the nearest cent, if necessary. Note: 365 days in a year and 30 days in a month. Answer How to enter your answer (opens in new window) Keypa Keyboard Shortc $\$ 52,453.20$

Step 1 ：The problem is asking for the amount of interest earned from an investment in a certificate of deposit. The initial investment is $47,600, the annual interest rate is 10.2%, and the interest is compounded semi-annually for 2 years.

Step 2 ：To solve this problem, we can use the formula for compound interest, which is \(A = P(1 + r/n)^{nt}\), where: \n- A is the amount of money accumulated after n years, including interest. \n- P is the principal amount (the initial amount of money). \n- r is the annual interest rate (in decimal). \n- n is the number of times that interest is compounded per year. \n- t is the time the money is invested for in years.

Step 3 ：First, we need to calculate the total amount after 2 years, and then subtract the initial investment to find the interest earned. Using the given values, we have \(P = 47600\), \(r = 0.102\), \(n = 2\), and \(t = 2\).

Step 4 ：Substituting these values into the formula, we get \(A = 47600(1 + 0.102/2)^{2*2} = 58078.82437396759\).

Step 5 ：The interest earned is then calculated by subtracting the initial investment from the total amount, which gives us \(interest\_earned = 58078.82437396759 - 47600 = 10478.824373967589\).

Step 6 ：However, the question asks to round the answer to the nearest cent. So, we need to round the result to two decimal places. This gives us \(interest\_earned\_rounded = 10478.82\).

Step 7 ：Final Answer: The interest earned from the investment is approximately \$10478.82. So, the final answer is \(\boxed{\$10478.82}\).