\( \$ 1250 \) are deposited in an account with a \( 6.5 \% \) interest rate, compounded continuously. What is the balance after 8 years? \[ F=\$[?] \]

To find the balance after 8 years with continuous compounding, we can use the formula for continuous compounding: \[ F = P \times e^{rt} \] Where: - \( F \) is the final balance - \( P \) is the principal amount (initial deposit) - \( r \) is the interest rate - \( t \) is the time in years Given: - Principal amount \( P = \$1250 \) - Interest rate \( r = 6.5\% = 0.065 \) - Time \( t = 8 \) years Substitute the values into the formula: \[ F = 1250 \times e^{0.065 \times 8} \] Now, we can calculate the final balance. Calculate the value by following steps: - step0: Calculate: \(1250e^{0.065\times 8}\) - step1: Multiply the numbers: \(1250e^{0.52}\) - step2: Convert the expressions: \(1250e^{\frac{13}{25}}\) - step3: Rewrite the expression: \(1250\sqrt[25]{e^{13}}\) The balance after 8 years with continuous compounding is approximately $2102.53.