If $\$ 13,000$ is invested at $12 \%$ interest compounded monthly, find the interest earned in 13 years.

The interest earned in 13 years is $\$ \square$.
(Do not round until the final answer. Then round to two decimal places as needed.)

Step 1 ：Given that the principal amount (P) is \$13,000, the annual interest rate (r) is 12% or 0.12 in decimal form, the number of times that interest is compounded per year (n) is 12, and the time the money is invested for (t) is 13 years.

Step 2 ：We can 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: \(A = 13000(1 + \frac{0.12}{12})^{12*13}\)

Step 4 ：Calculate the value of A to get \$61387.17705289992

Step 5 ：The interest earned is calculated by subtracting the principal amount from A: \(interest\_earned = A - P = 61387.17705289992 - 13000 = \$48387.17705289992\)

Step 6 ：Round the final answer to two decimal places to get \(\boxed{\$48387.18}\)