Solve the following equation for \( P \). Round value to 2 decimal places if needed. \( 6400=P\left(1+\frac{0.0585}{12}\right)^{12 \cdot 7} \)

To solve for \( P \) in the equation \( 6400 = P\left(1+\frac{0.0585}{12}\right)^{12 \cdot 7} \), we first need to calculate the term inside the parentheses. 1. Calculate \( \frac{0.0585}{12} \) which is approximately \( 0.004875 \). 2. Therefore, \( 1 + 0.004875 \) equals approximately \( 1.004875 \). 3. Next, raise \( 1.004875 \) to the power of \( 12 \cdot 7 = 84 \): \[ (1.004875)^{84} \approx 1.4645 \] (using a calculator). Now, substitute back into the equation to isolate \( P \): \[ 6400 = P \times 1.4645 \] Now, divide both sides by \( 1.4645 \): \[ P = \frac{6400}{1.4645} \approx 4366.75 \] Thus, the value of \( P \) is approximately \( 4366.75 \) (rounded to two decimal places).