Find the interest eamed on $\$ 15,000$ invested for 6 years at $7 \%$ interest compounded as follows.
a. Annually
b. Semiannually (twice a year)
c. Quarterly
d. Monthly
e. Continuously
a. Compounding annually, the interest earned is $\$ 7,510.96$.
(Round to the nearest cent as needed.)
b. Compounding semiannually, the interest earned is $\$ 7666.03$.
(Round to the nearest cent as needed.)
c. Compounding quarterly, the interest earned is $\$ \square$
(Round to the nearest cent as needed.)

Step 1 ：Given that the principal amount (P) is $15,000, the annual interest rate (r) is 7% or 0.07, the number of times that interest is compounded per year (n) is 4 (since interest is compounded quarterly), and the time the money is invested for (t) is 6 years.

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

Step 3 ：Substitute the given values into the formula: \(A = 15000(1 + \frac{0.07}{4})^{4*6}\)

Step 4 ：Calculate the value of A to get the total amount of money accumulated after 6 years, including interest: \(A = 22746.641795875494\)

Step 5 ：To find the interest earned, subtract the principal amount from the total amount: \(interest\_earned = A - P = 22746.641795875494 - 15000 = 7746.641795875494\)

Step 6 ：Round the interest earned to the nearest cent to get the final answer: \(\boxed{\$7746.64}\)