Question

You are borrowing $1,575 to purchase a washer and dryer using a 36 month installment plan. Determine the annual percentage rate (APR) and the monthly payment given that the interest charge is $99.32. Round your answer to the nearest whole percent and to the nearest cent.

a. 5%; $47.20
c. 4%; $49.42
b. 5%; $50.18
d. 4%; $46.50

Answer 1

The Answer is d

Explanation:

Answer 2

Option d - 4%; $46.50

Explanation:

Given : You are borrowing $1,575 to purchase a washer and dryer using a 36 month installment plan. The interest charge is $99.32.

To find : The annual percentage rate (APR) and the monthly payment ?

Solution :

The amount borrowed = $1,575

The interest charge = $99.32

Total amount paid in 36 month is 1575+99.32=$1674.32

For monthly payment,

The amount paid in a month =
`(1674.32)/(36)=\$46.05`

Monthly payment, M=$46.05

Now, we have to find the APR=x (let)

Applying monthly payment formula,

`M=(A)/((1-(1+i)^(-n))/(i))`

`M=(A* (x)/(12))/(1-(1+(x)/(12))^(-n))`

Substituting the value,

M=$46.50 , A=$1575 , n=36

`46.50=(1575* (x)/(12))/(1-(1+(x)/(12))^(-36))`

We solve the equation using graph,

First we plot the graph of
`(1575* (x)/(12))/(1-(1+(x)/(12))^(-36))` represent by line in black.

Then, put y=46.50 represent by red line.

Refer the attached figure below.

The intersection of the lines is the solution of x

i.e, x=0.04

In the percentage
`x=0.04* 100=4\%`

The APR is 4%.

Therefore, Option d is correct.