Questions: To borrow money, you pawn your guitar. Based on the value of the guitar, the pawnbroker loans you 600. One month later, you get the guitar back by paying the pawnbroker 470. What annual interest rate did the pawnbroker charge? (Round to the nearest whole number as needed.)

Solution Steps

To find the annual interest rate charged by the pawnbroker, we need to determine the interest paid and then calculate the equivalent annual interest rate. First, calculate the interest paid by subtracting the amount paid back from the loan amount. Then, calculate the monthly interest rate by dividing the interest by the loan amount. Finally, convert the monthly interest rate to an annual interest rate by multiplying by 12 and convert it to a percentage.

The interest paid can be calculated as follows: \[ \text{Interest Paid} = \text{Loan Amount} - \text{Amount Paid Back} = 600 - 470 = 130 \]

The monthly interest rate is determined by dividing the interest paid by the loan amount: \[ \text{Monthly Interest Rate} = \frac{\text{Interest Paid}}{\text{Loan Amount}} = \frac{130}{600} \approx 0.2167 \]

To find the annual interest rate, we multiply the monthly interest rate by 12 and convert it to a percentage: \[ \text{Annual Interest Rate} = \text{Monthly Interest Rate} \times 12 \times 100 = 0.2167 \times 12 \times 100 = 260 \]

Final Answer