\( \$ 200 \) are deposited in an account with 60 interest rate, compounded continuously. What is the balance after 5 years? \[ F=\$[?] \]

To calculate the future balance \( F \) of an account with continuous compounding, you can use the formula: \[ F = P \times e^{rt} \] where: - \( P \) is the principal amount (\$200), - \( r \) is the annual interest rate (60% or 0.60 as a decimal), - \( t \) is the time in years (5 years), - \( e \) is the base of the natural logarithm (approximately 2.71828). Plugging in the values: \[ F = 200 \times e^{0.60 \times 5} = 200 \times e^{3} \] Calculate \( e^{3} \): \[ e^{3} \approx 20.0855369232 \] Now, multiply by the principal: \[ F = 200 \times 20.0855369232 \approx 4017.11 \] **Final Balance:** \[ F = \$4,\!017.11 \]