Katrice takes a textbook to a pawnshop to borrow some money and is given \( \$ 35.00 \). Katrice must pay Dack the \( \$ 35.00 \) in addition to a \( \$ 12.75 \) fee in 6 months. What simple interest rate is she being charged? Round to the nearest tenth of a percent and don't forget to include a percent sign, \%, in your answer. Katrice is being charged a simple interest rate of

To calculate the simple interest rate, we can use the formula for simple interest: \[ I = P \times r \times t \] where: - \( I \) is the interest amount, - \( P \) is the principal amount (the money borrowed), - \( r \) is the interest rate (in decimal form), - \( t \) is the time in years. In Katrice's case, the total she needs to pay back is \( 35.00 + 12.75 = 47.75 \). The interest charged is the amount she pays back minus what she borrowed, which is \( 12.75 \). The principal \( P \) is \( 35.00 \), the interest \( I \) is \( 12.75 \), and the time \( t \) is \( 0.5 \) years (since 6 months is half a year). We can rearrange the formula to solve for \( r \): \[ r = \frac{I}{P \times t} \] Substituting in the values: \[ r = \frac{12.75}{35.00 \times 0.5} = \frac{12.75}{17.5} \approx 0.7286 \] To convert this to a percentage, we multiply by 100: \[ r \approx 72.86\% \] Rounding to the nearest tenth of a percent, we find that Katrice is being charged a simple interest rate of **72.9%**.