You deposit $\$ 3000$ in an account earning $4 \%$ interest compounded continuously. How much will you have in the account in 15 years?

Step 1 ：We are given that the principal amount (P) is $3000, the annual interest rate (r) is 4% or 0.04 in decimal form, and the time (t) is 15 years. We are asked to find the amount of money (A) accumulated after 15 years with continuous compound interest.

Step 2 ：The formula for continuous compound interest is \(A = P * e^{rt}\).

Step 3 ：Substituting the given values into the formula, we get \(A = 3000 * e^{0.04*15}\).

Step 4 ：Calculating the above expression, we find that \(A = 5466.356401171527\).

Step 5 ：Rounding to the nearest cent, we get \(A = 5466.36\).

Step 6 ：Final Answer: You will have \(\boxed{\$5466.36}\) in the account in 15 years.