Question

Please check for me and if any are incorrect please explain!

Answer 1

Answer:  (1) 14.4%   (2) 3.78%   (3) $222.48     (4) 21,176.47    

               (5) $425    (6) 14.3 cents per mile

Step-by-step explanation:

1) This is a calculator question. I = 0.144    --> 14.4%

$A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\bullet \text{A = Accrued amount (total amount paid)}\\\bullet \text{P = Principal (initial cost of the car)}\\\bullet \text{r = rate (interest rate in decimal form)}\\\bullet \text{n = number of times in a year (number of months)}\\\bullet \text{t = number of years}\\\\A = m \times nt\\\bullet \text{m = monthly payment amount}\\\bullet \text{nt = number of payments made}\\\implies m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}$

2) m = 93.33

   nt = 36

   P = 3000

   n = 12

$m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\\93.33\times 36=3000\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\3359.88=3000\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\1.11996=\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\1.00315198=1+\dfrac{r}{12}\\\\\\0.00315198=\dfrac{r}{12}\\\\\\0.0378=r\\\\\\\large\boxed{3.78\%}=r$

3) same equation as #2 but deduct the down payment from the Principal

   nt = 42

   P - d = 5,555 - 555 = 5,000

   r = 18% --> 0.18

   n = 12

$m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\\m\times 42=(5,555-555)\bigg(1+\dfrac{.18}{12}\bigg)^{42}\\\\\\42m=5000(1.015)^{42}\\\\\\42m=5000(1.868847)\\\\\\42m=9344.23557\\\\\\m=\large\boxed{222.48}$

4)  Gas  +  Oil  = cost per mile × number of miles

   1000 + 800 = 0.085x

               1800 = 0.085x

        $\large\boxed{21,176.47}=x$

5)  $\text{Annual Depreciation}=\dfrac{\text{Cost of car - Trade-in value}}{\text{Years driven}}$

$.\qquad =\dfrac{3800-1250}{6}\\\\\\.\qquad =\dfrac{2550}{6}\\\\\\.\qquad = \large\boxed{425}$

6) $\dfrac{\text{(Cost of car - Market value) + Gas & Oil + Parts, Maintenance + Insurance}}{\text{Miles driven}}$

$=\dfrac{(5000-3800)+750+250+300}{17,500}\\\\\\=\dfrac{2500}{17,500}\\\\\\=0.142857\\\\=\large\boxed{14.3\ cents\ per\ mile}$