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

Answer:

$32,256

Explanation:

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

$P_0=\frac{d(1-(1+\frac{r}{k})^{-Nk})}{(\frac{r}{k})}$

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=\frac{200(1-(1+\frac{0.033}{12})^{-8\cdot12})}{\frac{0.033}{12}}_{}$$P_0=\frac{200(1-(1.00275)^{-96})}{0.00275}$$P_0=\frac{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)