Question

to borrow money, you pawn your guitar. based on the value of the guitar, the pawnbroker loans you $1080. one month later, you get the guitar back by paying the pawnbroker $1272. what annual interest rate did you pay?

you will pay a simple interest rate of \\(\square\\)%
(round to the nearest whole number as needed.)

Explanation:

Step1: Find the interest amount

The interest paid is the amount repaid minus the principal. So, $I = 1272 - 1080 = 192$.

Step2: Use simple interest formula for monthly rate

The simple interest formula is $I = P \times r \times t$, where $P$ is principal, $r$ is monthly rate, and $t$ is time (in years, here $t = \frac{1}{12}$ for 1 month). Rearranging for $r$: $r = \frac{I}{P \times t}$. Plugging in values: $r = \frac{192}{1080 \times \frac{1}{12}}$. Calculate denominator: $1080 \times \frac{1}{12} = 90$. Then $r = \frac{192}{90} \approx 2.133...$ (monthly rate).

Step3: Find annual rate

Annual rate $R = r \times 12$. So $R = 2.133... \times 12 \approx 25.6$, which rounds to 26.

Answer:

26