Find \( A \) in the equation below \[ A=13000\left(1+\frac{0.04-3}{2}\right)^{12} \]

To solve for \( A \), we start with simplifying the expression inside the parentheses: \[ A = 13000 \left(1 + \frac{0.04 - 3}{2}\right)^{12} \] Calculating \( 0.04 - 3 \): \[ 0.04 - 3 = -2.96 \] Now, dividing by 2: \[ \frac{-2.96}{2} = -1.48 \] Next, adding this value to 1: \[ 1 - 1.48 = -0.48 \] Now we substitute back into the equation for \( A \): \[ A = 13000 \left(-0.48\right)^{12} \] Since raising a negative number to an even power results in a positive number, we compute \( (-0.48)^{12} \): \[ (-0.48)^{12} = 0.48^{12} \] Calculating \( 0.48^{12} \) gives a very small positive number. Using a calculator: \[ 0.48^{12} \approx 0.0000000197 \] Now, substituting this back in to find \( A \): \[ A \approx 13000 \times 0.0000000197 \approx 0.0002561 \] Thus, the value of \( A \) is approximately \( 0.0002561 \).