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?

To find the amount of money in the account after 12 years, we can use the formula for continuous compounding: \[ A = P \times e^{rt} \] Where: - \( A \) is the amount of money in the account after \( t \) years, - \( P \) is the principal amount (initial investment), - \( r \) is the interest rate, - \( t \) is the time in years. Given: - \( P = \$59,000 \) - \( r = 2.6\% = 0.026 \) - \( t = 12 \) years Substitute the values into the formula: \[ A = 59000 \times e^{0.026 \times 12} \] Now, we can calculate the amount of money in the account after 12 years. Calculate the value by following steps: - step0: Calculate: \(59000e^{0.026\times 12}\) - step1: Multiply the numbers: \(59000e^{0.312}\) - step2: Convert the expressions: \(59000e^{\frac{39}{125}}\) - step3: Rewrite the expression: \(59000\sqrt[125]{e^{39}}\) The amount of money in the account after 12 years is approximately $80,603.13. Rounded to the nearest hundred dollars, the amount of money in the account after 12 years is $80,600.