1. **State the problem:** An initial amount of 3200 is invested at an interest rate of 7% per year, compounded continuously. We need to find the amount in the account after 5 years. 2. **Formula used:** For continuous compounding, the amount $A$ after time $t$ years is given by: $$A = P e^{rt}$$ where: - $P$ is the principal (initial amount), - $r$ is the annual interest rate (as a decimal), - $t$ is the time in years, - $e$ is Euler's number (approximately 2.71828). 3. **Substitute the known values:** $$P = 3200, \quad r = 0.07, \quad t = 5$$ 4. **Calculate the exponent:** $$rt = 0.07 \times 5 = 0.35$$ 5. **Calculate the amount:** $$A = 3200 \times e^{0.35}$$ 6. **Evaluate $e^{0.35}$:** $$e^{0.35} \approx 1.4190675$$ 7. **Multiply to find $A$:** $$A = 3200 \times 1.4190675 = 4540.616$$ 8. **Round to the nearest cent:** $$\boxed{4540.62}$$ So, the amount in the account after 5 years is 4540.62.