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

Explanation:

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

`A=P\bigg(1+(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 * nt\\\bullet \text{m = monthly payment amount}\\\bullet \text{nt = number of payments made}\\\implies m* nt=P\bigg(1+(r)/(n)\bigg)^(nt)`

2) m = 93.33

nt = 36

P = 3000

n = 12

`m* nt=P\bigg(1+(r)/(n)\bigg)^(nt)\\\\\\93.33* 36=3000\bigg(1+(r)/(12)\bigg)^(36)\\\\\\3359.88=3000\bigg(1+(r)/(12)\bigg)^(36)\\\\\\1.11996=\bigg(1+(r)/(12)\bigg)^(36)\\\\\\1.00315198=1+(r)/(12)\\\\\\0.00315198=(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* nt=P\bigg(1+(r)/(n)\bigg)^(nt)\\\\\\m* 42=(5,555-555)\bigg(1+(.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}=\frac{\text{Cost of car - Trade-in value}}{\text{Years driven}}`

`.\qquad =(3800-1250)/(6)\\\\\\.\qquad =(2550)/(6)\\\\\\.\qquad = \large\boxed{425}`

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

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