1. **State the problem:** We want to find the future value $A$ of an investment of $396$ at an interest rate of $13\%$ per year compounded continuously for $3$ years. 2. **Formula:** The continuous compound interest formula is $$A = Pe^{rt}$$ where: - $P$ is the principal amount (initial investment), - $r$ is the annual interest rate (as a decimal), - $t$ is the time in years, - $e$ is Euler's number (approximately $2.71828$). 3. **Substitute values:** $$P = 396, \quad r = 0.13, \quad t = 3$$ 4. **Calculate the exponent:** $$rt = 0.13 \times 3 = 0.39$$ 5. **Calculate $A$:** $$A = 396 \times e^{0.39}$$ 6. **Evaluate $e^{0.39}$:** $$e^{0.39} \approx 1.477$$ 7. **Multiply:** $$A \approx 396 \times 1.477 = 584.892$$ 8. **Round to two decimal places:** $$A \approx 584.89$$ **Final answer:** The investment will be worth approximately $584.89$ after 3 years. Among the given options, the closest is $584.88$.