How much would you have to deposit in an account with a \( 9 \% \) interest rate, compounded continuously, to have \( \$ 1500 \) in your account 5 years later? \[ P=\$[?] \] Round to the nearest cent.

To determine how much you need to deposit today (\( P \)) to have \$1,500 in your account after 5 years with a continuously compounded interest rate of 9%, we can use the formula for continuous compounding: \[ A = P \cdot e^{rt} \] Where: - \( A \) is the future amount (\$1,500), - \( r \) is the annual interest rate (0.09), - \( t \) is the time in years (5), - \( e \) is the base of the natural logarithm (approximately 2.71828). **Step-by-Step Calculation:** 1. **Rearrange the Formula to Solve for \( P \):** \[ P = \frac{A}{e^{rt}} \] 2. **Plug in the Known Values:** \[ P = \frac{1500}{e^{0.09 \times 5}} = \frac{1500}{e^{0.45}} \] 3. **Calculate \( e^{0.45} \):** \[ e^{0.45} \approx 1.5683 \] 4. **Compute \( P \):** \[ P = \frac{1500}{1.5683} \approx 956.44 \] **Final Answer:** \[ P = \$956.44 \]