Connor invested \( \$ 59,000 \) in an account paying an interest rate of \( 2.6 \% \) compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 12 years?
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To find the amount of money in the account after 12 years with continuous compounding, we can use the formula for continuously compounded interest: \[ A = Pe^{rt} \] where: - \( A \) is the amount of money accumulated after time \( t \), - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (as a decimal), - \( t \) is the time in years, - \( e \) is the Euler's number (approximately \( 2.71828 \)). Plugging in the values: - \( P = 59000 \), - \( r = 0.026 \) (which is \( 2.6\% \)), - \( t = 12 \). Now calculating \( A \): \[ A = 59000 \times e^{0.026 \times 12} \] \[ A = 59000 \times e^{0.312} \] \[ A \approx 59000 \times 1.3656 \quad (\text{using } e^{0.312} \approx 1.3656) \] \[ A \approx 80496.40 \] Rounding to the nearest hundred dollars, the total amount in the account after 12 years would be approximately \( \$80,500 \).
