K Use the appropriate compound interest formula to compute the balance in the account after the stated period of time. $\$ 12,000$ is invested for 15 years with an APR of $3.6 \%$ and monthly compounding. The amount after 15 years will be $\$$ (Round to the nearest cent as needed.)

Step 1 ：Given that the principal amount (P) is $12,000, the annual interest rate (r) is 3.6% or 0.036 in decimal, the number of times that interest is compounded per year (n) is 12 (since it's compounded monthly), and the time the money is invested for in years (t) is 15 years.

Step 2 ：We can use the compound interest formula to compute the balance in the account after 15 years. The formula is given by: \(A = P (1 + \frac{r}{n})^{nt}\), where A is the amount of money accumulated after n years, including interest.

Step 3 ：Substitute the given values into the formula: \(A = 12000 (1 + \frac{0.036}{12})^{12*15}\)

Step 4 ：Calculate the amount (A) to get the balance in the account after 15 years.

Step 5 ：\(A = 20575.442770299\)

Step 6 ：Round the amount to the nearest cent to get the final answer.

Step 7 ：\(\boxed{\$20,575.44}\) is the balance in the account after 15 years.