arah invested \( \$ 2,500 \) in an account aying an interest rate of \( 2.1 \% \) ompounded continuously. Assumin o deposits or withdrawals are nade, how much money, to the earest hundred dollars, would be he account after 14 years?

To find the amount in Sarah's account after 14 years, we use the formula for continuous compound interest: \[ A = Pe^{rt} \] where: - \( A \) is the amount of money accumulated after time \( t \), - \( P \) is the principal amount (the initial investment), - \( r \) is the annual interest rate (in decimal), - \( t \) is the time the money is invested for (in years), - \( e \) is the base of the natural logarithm (approximately 2.71828). Plugging in the values: - \( P = 2500 \) - \( r = 0.021 \) (2.1% as a decimal) - \( t = 14 \) \[ A = 2500 \times e^{0.021 \times 14} \] Calculating this: 1. Calculate \( 0.021 \times 14 = 0.294 \). 2. Find \( e^{0.294} \approx 1.3415 \). 3. Now multiply \( 2500 \times 1.3415 \approx 3353.75 \). Rounding to the nearest hundred dollars, the amount after 14 years would be approximately \( \$3,400 \).