suppose that you decide to buy a car for $24,635, including taxes and license fees. you saved $6000 for a…

Explanation:

Step1: Calculate the loan amount

The car cost is $24,635 and the down - payment is $6000. So the loan amount $P$ is $P=24635 - 6000=18635$.

Step2: Determine the number of payments and monthly interest rate

The loan term is 5 years. Since there are 12 months in a year, the number of payments $n = 5\times12=60$. The annual interest rate $r=5.33%=0.0533$, so the monthly interest rate $i=\frac{0.0533}{12}$.

Step3: Use the PMT 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 $P = 18635$, $i=\frac{0.0533}{12}$, and $n = 60$ into the formula. [ \begin{align*} i&=\frac{0.0533}{12}\approx0.004442\ PMT&=\frac{18635\times0.004442\times(1 + 0.004442)^{60}}{(1+ 0.004442)^{60}-1}\ (1 + 0.004442)^{60}&\approx1.2937\ PMT&=\frac{18635\times0.004442\times1.2937}{1.2937 - 1}\ &=\frac{18635\times0.004442\times1.2937}{0.2937}\ &=\frac{18635\times0.005747}{0.2937}\ &=\frac{107.03}{0.2937}\ &\approx364.39 \end{align*} ]

Step4: Calculate the total amount paid

The total amount paid over 60 months is $364.39\times60 = 21863.4$.

Step5: Calculate the total interest

The total interest $I$ is the total amount paid minus the loan amount, so $I=21863.4-18635 = 3228.4$.

Answer:

The monthly payment is $$364.39$ and the total interest for the loan is $$3228.40$