Question Kremena took out a \( \$ 500 \) discounted loan for a period of 3 months. The amount she actually received into her bank account was \( \$ 460 \). Assuming simple interest rates, what is effective interest rate \( r_{e} \) ? Give your answer as a percentage to the nearest percent.

To find the effective interest rate \( r_{e} \), we can use the formula for simple interest: \[ r_{e} = \frac{I}{P} \times \frac{1}{t} \] where \( I \) is the interest earned, \( P \) is the principal amount, and \( t \) is the time period in years. First, calculate the interest \( I \): \[ I = P - A = 500 - 460 = 40 \] Next, plug in the values into the formula. The principal \( P = 500 \), the interest \( I = 40 \), and the time \( t = \frac{3}{12} \) years (which is \( 0.25 \) years): \[ r_{e} = \frac{40}{500} \times \frac{1}{0.25} = \frac{40}{500} \times 4 = 0.32 \] To express it as a percentage: \[ r_{e} \times 100 = 0.32 \times 100 = 32\% \] So, the effective interest rate \( r_{e} \) is \( 32\% \).