Find the compound amount and the amount of interest earned by the deposit below. $\$ 4,000$ at $4.36 \%$ compounded continuously for 2 years. What is the compound amount?

Step 1 ：We are given a principal amount (P) of $4000, an annual interest rate (r) of 4.36%, and a time period (t) of 2 years. The interest is compounded continuously.

Step 2 ：We can calculate the compound amount using the formula for continuous compounding: \(A = P * e^{rt}\), where A is the amount of money accumulated after n years, including interest.

Step 3 ：First, we convert the annual interest rate from a percentage to a decimal by dividing by 100. So, \(r = \frac{4.36}{100} = 0.0436\).

Step 4 ：Next, we substitute the values of P, r, and t into the formula: \(A = 4000 * e^{0.0436 * 2}\).

Step 5 ：Calculating the above expression, we find that the compound amount A is approximately $4364.46.

Step 6 ：\(\boxed{The compound amount is \$4364.46}\)