suppose that you decide to buy a car for $29,635, including taxes and license fees. you saved $7000 for a…

Explanation:

Step1: Calculate loan amount

The cost of the car is $29,635 and the down - payment is $7000. So the loan amount $P$ is $P=29635 - 7000=22635$.

Step2: Determine interest rate and number of periods

The annual interest rate $r = 6.25%=0.0625$. The monthly interest rate $i=\frac{0.0625}{12}$. The loan is for 3 years, so the number of months $n = 3\times12 = 36$.

Step3: Calculate monthly payment using the formula

The formula for the monthly payment of a loan is $PMT=\frac{P\times i\times(1 + i)^{n}}{(1 + i)^{n}-1}$. Substitute $P = 22635$, $i=\frac{0.0625}{12}$, and $n = 36$ into the formula: First, calculate $(1 + i)^{n}=(1+\frac{0.0625}{12})^{36}$. Let $x=\frac{0.0625}{12}\approx0.00520833$. Then $(1 + x)^{36}\approx1.209499$. $PMT=\frac{22635\times0.00520833\times1.209499}{1.209499 - 1}$ $PMT=\frac{22635\times0.00520833\times1.209499}{0.209499}$ $PMT=\frac{22635\times0.0062937}{0.209499}$ $PMT=\frac{142.307}{0.209499}\approx679.27$.

Step4: Calculate total amount paid

The total amount paid over 36 months is $679.27\times36 = 24453.72$. The total interest paid is $24453.72-22635 = 1818.72$.

Answer:

The monthly payment is $$679.27$. The total interest for the loan is $$1818.72$.