Question

Bought car for $30,635, $8000 towards down payment four year loan at a rate of 7.98% what is my monthly payment and what is the total interest for this loan

Answer 1

Step-by-step explanation:

We are to find the monthly payment and interest on the loan for the purchase of the car.

To do so, we will list some parameters to be used

`\begin{gathered} P=amount\text{ borrowed =Worth of the car - down payment} \\ P=\text{ \$30,635- \$8000 = \$22635} \end{gathered}`

then

`n=number\text{ of monthly payments =4 years }*12=84`

also, the rate

`r=rate=7.98\text{ \%=0.0798}`

So we can apply the formula

`M=(22635((0.0798)/(12))^(1+(0.0798)/(12))^(48))/((1+(0.0798)/(12))^(48)-1)=(22635*6.65*10^(-3)*(1+6.65*10^(-3))^(48))/((1+6.65*10^(-3))^(48)-1)`

simplifying further, we will have the monthly payment to be

`M=552.37`

Thus,

The monthly payment is $552.37

For the second part of the question, we are to get the total interest for the loan, to do so, we will multiply the monthly payments by the number of times and then subtract the original worth of the car

So we will have

`\text{ \$552.37}*48=\text{ \$26513.76}`

Then we will subtract the value of P from the value obtained

`\text{ \$26513.76- \$22635=\$3878.76}`

Therefore, the interest for the loan is $3878.76