Use the compound interest formula to determine the final value of the following amount. $\$ 1100$ at $10.2 \%$ compounded monthly for 1.5 years What is the final value of the amount? $\$ \square$ (Simplify your answer. Round to the nearest cent.)

Step 1 ：We are given that the principal amount (P) is $1100, the annual interest rate (r) is 10.2% or 0.102 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 1.5 years.

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

Step 3 ：Substituting the given values into the formula, we get: \(A = 1100 (1 + \frac{0.102}{12})^{12*1.5}\)

Step 4 ：Solving the above expression, we find that A is approximately 1281.0289103288474

Step 5 ：Rounding to the nearest cent, we get the final value of the amount as $1281.03

Step 6 ：\(\boxed{\$1281.03}\) is the final value of the amount after 1.5 years.