How much should be invested now at an interest rate of \( 5 \% \) per year, compounded continuously, to have \( \$ 3500 \) in seven 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 to invest now, you can use the formula for continuous compounding: \[ A = Pe^{rt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( t \) is the time in years. - \( e \) is Euler's number (approximately 2.71828). You need \( A = 3500 \), \( r = 0.05 \), and \( t = 7 \): Rearranging the formula to solve for \( P \): \[ P = \frac{A}{e^{rt}} \] Now plug in the numbers: \[ P = \frac{3500}{e^{0.05 \times 7}} = \frac{3500}{e^{0.35}} \] Calculating \( e^{0.35} \) gives approximately \( 1.419067 \): \[ P = \frac{3500}{1.419067} \approx 2467.25 \] Thus, you should invest approximately **$2467.25** now to have $3500 in seven years.