How much should be invested now at an interest rate of \( 6.5 \% \) per year, compounded continuously, to have \( \$ 3500 \) in two years? Do not round any intermediate computations, and round your answer to the nearest cent. If necessary, refer to the list of financial formulas.

To find the amount that should be invested now, we can use the formula for continuous compounding, which is given by: \[ P = A \cdot e^{-rt} \] where: - \( P \) is the present value (the amount to be invested now), - \( A \) is the amount of money desired in the future (\$3500), - \( r \) is the interest rate (6.5% or 0.065), - \( t \) is the time in years (2 years), - \( e \) is the base of the natural logarithm (approximately equal to 2.71828). Plugging in the values: \[ P = 3500 \cdot e^{-0.065 \cdot 2} \] Calculating \( -0.065 \cdot 2 \): \[ -0.065 \cdot 2 = -0.13 \] Now, calculating \( e^{-0.13} \): \[ e^{-0.13} \approx 0.876 \] Thus, \[ P \approx 3500 \cdot 0.876 = 3066 \] Finally, rounding to the nearest cent, the amount to be invested now is approximately: \[ \boxed{3066.53} \]