Question Kremena took out a \( \$ 500 \) discounted loan for a period of 3 months. The amount she actually received into her bank accoun 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 \( r_{e} \) for Kremena's loan, we can use the formula for simple interest: \[ I = P \cdot r \cdot t \] Where: - \( I \) is the interest paid, - \( P \) is the principal amount (the amount of the loan), - \( r \) is the interest rate (as a decimal), - \( t \) is the time in years. ### Step 1: Identify the known values - The principal amount \( P = 500 \) (the total loan amount). - The amount received \( A = 460 \) (the amount deposited into her account). - The time \( t = \frac{3}{12} = 0.25 \) years (3 months). ### Step 2: Calculate the interest paid The interest paid \( I \) can be calculated as the difference between the principal and the amount received: \[ I = P - A = 500 - 460 = 40 \] ### Step 3: Rearrange the simple interest formula to find \( r \) We can rearrange the formula to solve for \( r \): \[ r = \frac{I}{P \cdot t} \] ### Step 4: Substitute the known values into the formula Now we can substitute the values we have into the rearranged formula: \[ r = \frac{40}{500 \cdot 0.25} \] ### Step 5: Calculate \( r \) Let's calculate \( r \): \[ r = \frac{40}{125} = 0.32 \] ### Step 6: Convert \( r \) to a percentage To express \( r \) as a percentage, we multiply by 100: \[ r_{e} = 0.32 \times 100 = 32\% \] Thus, the effective interest rate \( r_{e} \) is \( \boxed{32\%} \).