Find the compound amount for the deposit and the amount of interest earned. $\$ 12,000$ at $3 \%$ compounded monthly for 19 years

Step 1 ：Given that the principal amount (P) is $12,000, the annual interest rate (r) is 3% or 0.03 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 19 years.

Step 2 ：We can use the compound interest formula to find the compound amount (A). The formula is given by: \(A = P (1 + \frac{r}{n})^{nt}\)

Step 3 ：Substitute the given values into the formula: \(A = 12000 (1 + \frac{0.03}{12})^{12*19}\)

Step 4 ：Calculate the value of A to find the compound amount for the deposit. The compound amount is approximately $21204.12

Step 5 ：The amount of interest earned would then be the compound amount minus the initial principal. So, the interest earned is \(21204.12 - 12000 = 9204.12\)

Step 6 ：Final Answer: The compound amount for the deposit is \(\boxed{21204.12}\) and the amount of interest earned is \(\boxed{9204.12}\)