Give the value after 5.9 years of a capital of $\$ 3000$ invested at $3.9 \%$ using continuous compounding. Round your answer to the nearest cent.

Step 1 ：Given a principal amount (P) of $3000, an annual interest rate (r) of 3.9%, and a time period (t) of 5.9 years, we are to find the value of the investment after 5.9 years using the formula for continuous compounding: \(A = P * e^{rt}\).

Step 2 ：First, convert the annual interest rate from a percentage to a decimal by dividing by 100: \(r = \frac{3.9}{100} = 0.039\).

Step 3 ：Substitute P = $3000, r = 0.039, and t = 5.9 years into the formula: \(A = 3000 * e^{0.039 * 5.9}\).

Step 4 ：Calculate the value of the investment after 5.9 years: \(A = 3776.18\).

Step 5 ：\(\boxed{The value of the investment after 5.9 years is \$3776.18}\).