The principal \( P \) is borrowed and the loan's future value \( A \) at time \( t \) is given. Determine the loan's simple interest rate \( r \). \( P=\$ 5000.00, A=\$ 5900.00, t=4 \) years \( \square \% \) (Round to the nearest tenth of a percent as needed.)

To find the simple interest rate \( r \), we can use the formula for the future value of a loan with simple interest, which is: \[ A = P(1 + rt) \] Rearranging this formula to solve for \( r \): \[ r = \frac{A - P}{Pt} \] Now, we can plug in the values: - \( P = 5000.00 \) - \( A = 5900.00 \) - \( t = 4 \) First, calculate \( A - P \): \[ 5900.00 - 5000.00 = 900.00 \] Next, plug in the values into the rearranged formula: \[ r = \frac{900.00}{5000.00 \times 4} \] Calculating the denominator: \[ 5000.00 \times 4 = 20000.00 \] Now, divide the values: \[ r = \frac{900.00}{20000.00} = 0.045 \] To express \( r \) as a percentage, we multiply by 100: \[ r = 0.045 \times 100 = 4.5\% \] So, the simple interest rate \( r \) rounded to the nearest tenth of a percent is: \( 4.5\% \)