Elisa needs money to repair her home air conditioner, so she pawns her bicycle. The pawnbroker loans Elisa \( \$ 270 \). Ten days later, Elisa gets her bicycle back by paying the pawnbroker \( \$ 288.00 \). What annual simple interest rate did the \( 80.95 \%, 17 \) of 21 pawnbroker charge Elisa? Assume 360 days in a year. Tle pawnbroker charged Elisa a simple interest rate of (Round to the nearest whole number as needed.)

To find the annual simple interest rate charged by the pawnbroker, we can use the formula for simple interest: \[ I = P \times r \times t \] Where: - \( I \) is the interest paid, - \( P \) is the principal amount (the initial loan), - \( r \) is the annual interest rate (in decimal form), - \( t \) is the time in years. ### Step 1: Identify the known values - The principal amount \( P = 270 \) (the amount loaned). - The total amount paid back \( A = 288 \). - The time \( t = \frac{10}{360} \) years (since we are assuming a 360-day year). ### Step 2: Calculate the interest paid The interest \( I \) can be calculated as: \[ I = A - P = 288 - 270 = 18 \] ### Step 3: Substitute the known values into the formula Now we can substitute the known values into the simple interest formula: \[ 18 = 270 \times r \times \frac{10}{360} \] ### Step 4: Solve for \( r \) First, simplify the equation: \[ 18 = 270 \times r \times \frac{1}{36} \] Now, multiply both sides by 36: \[ 18 \times 36 = 270 \times r \] Calculating \( 18 \times 36 \): \[ 648 = 270 \times r \] Now, divide both sides by 270 to solve for \( r \): \[ r = \frac{648}{270} \] ### Step 5: Calculate \( r \) Now, let's calculate \( r \): \[ r = 2.4 \] ### Step 6: Convert \( r \) to a percentage To convert \( r \) to a percentage, multiply by 100: \[ r = 2.4 \times 100 = 240\% \] ### Conclusion The annual simple interest rate charged by the pawnbroker is approximately \( 240\% \). Thus, the pawnbroker charged Elisa a simple interest rate of \( 240\% \).