Answer:
Option d - 4%; $46.50
Step-by-step 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 = [tex]\frac{1674.32}{36}=\$46.05[/tex]
Monthly payment, M=$46.05
Now, we have to find the APR=x (let)
Applying monthly payment formula,
[tex]M=\frac{A}{\frac{1-(1+i)^{-n}}{i}}[/tex]
[tex]M=\frac{A\times \frac{x}{12}}{1-(1+\frac{x}{12})^{-n}}[/tex]
Substituting the value,
M=$46.50 , A=$1575 , n=36
[tex]46.50=\frac{1575\times \frac{x}{12}}{1-(1+\frac{x}{12})^{-36}}[/tex]
We solve the equation using graph,
First we plot the graph of [tex]\frac{1575\times \frac{x}{12}}{1-(1+\frac{x}{12})^{-36}}[/tex] 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 [tex]x=0.04\times 100=4\%[/tex]
The APR is 4%.
Therefore, Option d is correct.
