suppose that you decide to buy a car for $31,635, including taxes and license fees. you saved $8000 for a…

suppose that you decide to buy a car for $31,635, including taxes and license fees. you saved $8000 for a down - payment and can get a four - year car loan at 7.1%. use pmt = p * \\frac{r}{n} / (1-(\\frac{1}{1 + \\frac{r}{n}})^{nt}) to find the monthly payment and the total interest for the loan. the monthly payment is $567.84. (round to the nearest cent as needed.) the total interest for the loan is $ (round to the nearest cent as needed.)

suppose that you decide to buy a car for $31,635, including taxes and license fees. you saved $8000 for a down - payment and can get a four - year car loan at 7.1%. use pmt = p * \\frac{r}{n} / (1-(\\frac{1}{1 + \\frac{r}{n}})^{nt}) to find the monthly payment and the total interest for the loan. the monthly payment is $567.84. (round to the nearest cent as needed.) the total interest for the loan is $ (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Calculate the loan amount

The cost of the car is $31635$ and the down - payment is $8000$. So the loan amount $P$ is $31635 - 8000=23635$.

Step2: Determine the number of payments and interest rate per period

The loan is for 4 years. Since the payments are monthly, the number of payments $n = 4\times12=48$ months. The annual interest rate $r = 7.1%=0.071$, so the monthly interest rate $i=\frac{0.071}{12}$.

Step3: Use the loan - payment formula

The formula for the monthly payment $M$ of a loan is $M=\frac{P\times i\times(1 + i)^n}{(1 + i)^n-1}$. We are given that $M = 567.84$. To find the total interest paid, we first find the total amount paid over the life of the loan. The total amount paid $A$ is the monthly payment times the number of payments, so $A = 567.84\times48$. $A=567.84\times48 = 27256.32$. The loan amount is $P = 23635$. The total interest $I$ is the total amount paid minus the loan amount. So $I=A - P$. $I=27256.32-23635=3621.32$.

Answer:

$3621.32$