Question

You've purchased a new car and have agreed to a loan with payments of $ 336 per month. Your loan is for 8 years loan at 3.3 % simple interest. How much total money will you pay the loan company?

Answer 1

$32,256

Step-by-step explanation:

We'll use the below formula to solve the given question;

`P_0=(d(1-(1+(r)/(k))^(-Nk)))/(((r)/(k)))`

where P = the principal amount

d = the loan payment per month = $336

r = annual interest rate in decimal = 3.3% = 3.3/100 = 0.033

k = number of compounding periods in one year = 12

N = length of loan in years = 8

Let us substitute the above values into our formula and solve for P as seen below;

`P_0=(200(1-(1+(0.033)/(12))^(-8\cdot12)))/((0.033)/(12))_{}`
`P_0=(200(1-(1.00275)^(-96)))/(0.00275)`
`P_0=(200(0.23174814556))/(0.00275)`
`P_0=\text{\$}16,854.41`

We can see from the above that the starting amount of the loan is $16,854.41. But the total money to be paid to the loan company will be $32,256 that is $336 per month for 96 months (8 years)