Harper invested \( \$ 3,200 \) in an account paying an interest rate of \( 7 \% \) compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 6 years?

To calculate the amount in an account with continuous compounding interest, we use the formula \( A = Pe^{rt} \), where \( A \) is the amount after time \( t \), \( P \) is the principal amount (initial investment), \( r \) is the interest rate, and \( t \) is the time in years. In this case: - \( P = 3200 \) - \( r = 0.07 \) (7% as a decimal) - \( t = 6 \) Plugging in the values, we have: \( A = 3200 \times e^{0.07 \times 6} \) \( A = 3200 \times e^{0.42} \) Using \( e \approx 2.71828 \), we calculate: \( e^{0.42} \approx 1.519 \) (you can use a calculator for a more precise value). So, \( A \approx 3200 \times 1.519 \approx 4860.8 \) Rounding to the nearest ten dollars, the amount in the account after 6 years would be approximately \( \$ 4,860 \).