Find the compound amount for the deposit and the amount of interest earned. $\$ 16,000$ at $2 \%$ compounded monthly for 15 years The compound amount after 15 years is $\$ \square$. (Do hot round until the final answer. Then round to the nearest cent as needed.)

Step 1 ：We are given that the principal amount (P) is $16,000, the annual interest rate (r) is 2% or 0.02 in decimal form, the number of times the interest is compounded per year (n) is 12 (since it's compounded monthly), and the time the money is invested for (t) is 15 years.

Step 2 ：We can use the compound interest formula A = P(1 + r/n)^(nt) to find the amount of money accumulated after 15 years, including interest.

Step 3 ：Substituting the given values into the formula, we get A = 16000(1 + 0.02/12)^(12*15).

Step 4 ：Calculating the expression, we find that A = 21592.348151245355.

Step 5 ：Rounding to the nearest cent, we get the final amount as $21592.35.