The principal \( P \) is borrowed at simple interest rate \( r \) for a period of time \( t \). Find the loan's future value, \( A \), or the total amount due at time \( t \) \( P=\$ 4000, r=4.5 \%, t=9 \) months The future value is \( \$ \square \). (Simplify your answer. Type an integer or a decimal.)

To find the future value \( A \) using the simple interest formula, we first need to calculate the interest earned over the loan period. The formula for simple interest is: \[ I = P \times r \times t \] Where: - \( P = 4000 \) (the principal) - \( r = 0.045 \) (the annual interest rate expressed as a decimal) - \( t = \frac{9}{12} = 0.75 \) (the loan period in years) Now, let's calculate the interest: \[ I = 4000 \times 0.045 \times 0.75 = 135 \] Next, we find the future value \( A \): \[ A = P + I = 4000 + 135 = 4135 \] So, the future value is \( \$ 4135 \).