Answer:
1740%.
Step-by-step explanation:
We have been given that the pawnbroker loans you $600. One month later, you get the guitar back by paying the pawnbroker $1470.
We will use simple interest formula to solve our given problem.
[tex]A=P(1+rt)[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
1 month = 1/12 year
[tex]1470=600(1+r*\frac{1}{12})[/tex]
[tex]1470=600+\frac{600}{12}*r[/tex]
[tex]1470=600+50*r[/tex]
[tex]1470-600=600-600+50*r[/tex]
[tex]870=50*r[/tex]
[tex]50r=870=[/tex]
[tex]\frac{50r}{50}=\frac{870}{50}[/tex]
[tex]r=17.4[/tex]
Since our interest rate is in decimal form, so we will convert it into percentage by multiplying by 100 as:
[tex]17.4\times 100\%=1740\%[/tex]
Therefore, you paid an annual interest rate of 1740%.
