Try Again One of the digits in your answer is wrong. Check your work carefully. initial amount of \( \$ 2700 \) is invested in an account at an interest rate of \( 8 \% \) per year, compounded continuously. Assuming that no withdrawals are made, ind the amount in the account after five years. if not round any intermediate computations, and round your answer to the nearest cent. iner to the list of financial formulas.

To find the amount in an account with continuous compounding, you can use the formula \( A = Pe^{rt} \), where \( A \) is the amount of money accumulated after \( t \) years, \( P \) is the principal amount (initial investment), \( r \) is the annual interest rate (as a decimal), and \( e \) is approximately equal to 2.71828. Plugging in the values: \( P = 2700 \), \( r = 0.08 \), and \( t = 5 \): \[ A = 2700 \times e^{0.08 \times 5} \] Calculating this yields: \[ A \approx 2700 \times e^{0.4} \approx 2700 \times 1.49182 \approx 4027.91 \] So, the amount in the account after five years is approximately \( \$4027.91 \). If you're ever unsure about your calculations, it’s handy to double-check each step, especially with exponentials—it’s easy to slip up on decimal placements or exponents! Also, breaking down the calculations into smaller parts can help ensure accuracy. You can use a scientific calculator or software for complex exponentials, but always review your inputs for common mistakes!