Question

Question 7 4 pts To borrow money, you pawn your mountain bike. Based on the value of the bike, the pawnbroker loans you $552. One month later, you get the bike back by paying the pawnbroker $851. What annual interest rate did you pay? Write as a percentage.

Answer 1

650.2%

Explanation:

We have to calculate annual interest rate by this formula :

A = P( 1 + rt )

A = Future value of loan ( $851 )

P = Principal amount ( $552 )

r = Rate of interest

t = Time in years

As we know, 1 year = 12 months . By converting 1 month to year we get

1 month =
`(1)/(12)` year = 0.0833 year

Now we put the values in the formula

$851 = $552( 1 + r × 0.0833 )

=
`(851)/(552) =(552(1+(0.0833r)))/(552)`

= 1.5417 = 1 + 0.0833r

= 1.5417 - 1 = 0.0833r

= 0.5417 = 0.0833r

r = 6.502

r is in decimal form so we have to multiply with 100 to convert the value in percentage.

6.502 × 100 = 650.2%

The annual interest rate that you pay is 650.2%

Answer 2

The annual rate of interest is 650 %.

Explanation:

Given,

The amount of loan = $ 552,

Total amount paid after one month = $ 851,

So, the interest for one month = $ 851 -$ 552 = $ 299,

Thus, the monthly interest =
`\frac{\text{Interest for a month}}{\text{Total amount of loan}}* 100`

`=(299)/(552)* 100`

`=(29900)/(552)`

Since, 1 year = 12 month ⇒ 1 month = 1/12 year,

Hence, the annual rate of interest =
`(29900)/(552)* 12=(358800)/(552)=650\%`