suppose that you decide to borrow $17,000 for a new car. you can select one of the following loans, each…

Explanation:

Step1: Identify the values for Loan A

For Loan A, $P=$17000$, $r = 5.9%=0.059$, $n = 12$ (month - ly payments), $t = 3$ years.

Step2: Calculate the monthly - payment formula

The formula for the monthly payment $PMT=\frac{P\times\frac{r}{n}}{1-(1 + \frac{r}{n})^{-nt}}$. Substitute the values: $\frac{r}{n}=\frac{0.059}{12}$, $nt=12\times3 = 36$. $PMT=\frac{17000\times\frac{0.059}{12}}{1-(1+\frac{0.059}{12})^{-36}}$ First, calculate $(1+\frac{0.059}{12})^{-36}$. Let $x=\frac{0.059}{12}\approx0.0049167$. Then $(1 + x)^{-36}=\frac{1}{(1 + 0.0049167)^{36}}$. Using the formula $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$ or a calculator, $(1+0.0049167)^{36}\approx1.19097$. So $(1 + 0.0049167)^{-36}\approx\frac{1}{1.19097}\approx0.8396$. $1-(1+\frac{0.059}{12})^{-36}=1 - 0.8396 = 0.1604$. $17000\times\frac{0.059}{12}\approx17000\times0.0049167 = 83.5839$. $PMT=\frac{83.5839}{0.1604}\approx521.096$.

Step3: Calculate the total amount paid

The total amount paid over 3 years (36 months) is $PMT\times nt=521.096\times36=$18759.456$.

Step4: Calculate the total interest

The total interest $I$ is the total amount paid minus the principal. $I=18759.456 - 17000=$1759.456\approx$1759.46$.

Answer:

The monthly payment for Loan A is $$521.10$ and the total interest is $$1759.46$.