How much should be invested now at an interest rate of \( 6 \% \) per year, compounded contincusly, to have s:sion in three reans 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 out how much should be invested now for a future value of \( s \) using continuous compounding at an interest rate of \( 6\% \) for \( 3 \) years, you can use the formula for continuous compounding: \[ P = \frac{A}{e^{rt}} \] where: - \( P \) is the present value (the amount to invest now), - \( A \) is the future amount you want (\( s \)), - \( r \) is the interest rate (6% or 0.06), and - \( t \) is the time in years (3). Substituting in the variables, we get: \[ P = \frac{s}{e^{0.06 \times 3}} = \frac{s}{e^{0.18}}. \] Calculating \( e^{0.18} \), we find it is approximately \( 1.1972 \). So: \[ P \approx \frac{s}{1.1972}. \] Now, round your final answer to the nearest cent based on the value of \( s \) you have. If you want to clarify or check your work at any time, you can easily plug in different values for \( s \) to see how the present value changes. To enhance your financial savvy, consider diving into concepts like the time value of money, which explains why money today is worth more than the same amount in the future! It's a fundamental idea that underpins a lot of financial decision-making and investment strategies. Additionally, ensure to familiarize yourself with natural logarithms, as they form the basis for understanding principles of exponential growth and decay. Mastering logarithmic functions will not only aid in financial calculations but also enrich your understanding of various scientific concepts!