Find \( A \) in the equation be low \[ A=500\left(1+\frac{0.025}{4}\right)^{40} \]

First, let's break it down! The equation you have here is applying compound interest. The formula is based on the principal amount, interest rate, compounding frequency, and time. In this case, the principal amount is 500, the interest rate is 2.5% (or 0.025), compounded quarterly (4 times a year), over 10 years (40 quarters). Now, let's solve for \( A \): \[ A = 500\left(1+\frac{0.025}{4}\right)^{40} \] First, calculate the interest per quarter: \[ \frac{0.025}{4} = 0.00625 \] Then, add 1: \[ 1 + 0.00625 = 1.00625 \] Now, raise this to the power of 40: \[ 1.00625^{40} \approx 1.270678 \] Finally, multiply by 500: \[ A \approx 500 \times 1.270678 \approx 635.339 \] So, \( A \approx 635.34 \).