suppose that you borrow $11,000 for five years at 5% toward the purchase of a car. use pmt = p * (r / n) / 1…

suppose that you borrow $11,000 for five years at 5% toward the purchase of a car. use pmt = p * (r / n) / 1 - (1 + r / n)^(-nt) to find the monthly payments and the total interest for the loan. the monthly payment is $ (do not round until the final answer. then round to the nearest cent as needed.)

suppose that you borrow $11,000 for five years at 5% toward the purchase of a car. use pmt = p * (r / n) / 1 - (1 + r / n)^(-nt) to find the monthly payments and the total interest for the loan. the monthly payment is $ (do not round until the final answer. then round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify the values

$P = 11000$, $r=0.05$, $n = 12$ (month - ly payments), $t = 5$

Step2: Calculate the exponent

$-nt=-12\times5=-60$

Step3: Calculate the value inside the brackets

$1+\frac{r}{n}=1+\frac{0.05}{12}\approx1 + 0.004167=1.004167$

Step4: Calculate $(1+\frac{r}{n})^{-nt}$

$(1.004167)^{- 60}\approx0.779205$

Step5: Calculate $1-(1+\frac{r}{n})^{-nt}$

$1 - 0.779205=0.220795$

Step6: Calculate $\frac{r}{n}$

$\frac{0.05}{12}\approx0.004167$

Step7: Calculate the monthly - payment PMT

$PMT=\frac{P\times\frac{r}{n}}{1-(1 + \frac{r}{n})^{-nt}}=\frac{11000\times0.004167}{0.220795}=\frac{45.837}{0.220795}\approx207.69$

Answer:

$207.69$