to borrow money, you pawn your guitar. based on the value of the guitar, the pawnbroker loans you $720. one…

to borrow money, you pawn your guitar. based on the value of the guitar, the pawnbroker loans you $720. one month later, you get the guitar back by paying the pawnbroker $1170. what annual interest rate did you pay?\nyou will pay a simple interest rate of \n(round to the nearest whole number as needed.)

to borrow money, you pawn your guitar. based on the value of the guitar, the pawnbroker loans you $720. one month later, you get the guitar back by paying the pawnbroker $1170. what annual interest rate did you pay?\nyou will pay a simple interest rate of \n(round to the nearest whole number as needed.)

Answer

Explanation:

Step1: Calculate the interest for 1 - month

The amount of interest $I$ paid in 1 month is the difference between the amount repaid and the amount borrowed. So, $I = 1170 - 720=450$.

Step2: Use the simple - interest formula $I = Prt$

The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Here, $P = 720$, $t=\frac{1}{12}$ years (since 1 month $=\frac{1}{12}$ of a year), and $I = 450$. Substitute the values into the formula: $450=720\times r\times\frac{1}{12}$.

Step3: Solve for $r$

First, simplify the right - hand side of the equation: $720\times\frac{1}{12}\times r = 60r$. So, the equation becomes $450 = 60r$. Then, solve for $r$ by dividing both sides of the equation by 60: $r=\frac{450}{60}=7.5$. To convert $r$ from a decimal to a percentage, multiply by 100. So the annual interest rate as a percentage is $r = 750%$.

Answer:

750