Question

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 ​$1470. What annual interest rate did you​ pay?

Answer 1

1740%.

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.

`A=P(1+rt)`, 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

`1470=600(1+r*(1)/(12))`

`1470=600+(600)/(12)*r`

`1470=600+50*r`

`1470-600=600-600+50*r`

`870=50*r`

`50r=870=`

`(50r)/(50)=(870)/(50)`

`r=17.4`

Since our interest rate is in decimal form, so we will convert it into percentage by multiplying by 100 as:

`17.4* 100\%=1740\%`

Therefore, you paid an annual interest rate of 1740%.