Question

A $7300 car is 27% off. How much will you pay for the car if the tax rate is 8%, and you take out a 5 year loan with a 12% simple interest rate?

Answer 1

so the car is regularly 7300 bucks, however today is your birthday and you get it 27% off, so 100% - 27% = 73%, so 73% of the regular price, hmm how much is that?

`\begin{array} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{73\% of 7300}}{\left( \cfrac{73}{100} \right)7300}\implies 5329`

now enter the taxman! to that will squeeze you for 8%

`\stackrel{\textit{8\% of 5329}}{\left( \cfrac{8}{100} \right)5329}\implies 426.32\hspace{5em}\underset{ total~cost }{\stackrel{ 5329~~ + ~~426.32 }{\text{\LARGE 5755.32}}}`

so how much will it be for 5755.32 at 12% for 5 years simple interest?

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$5755.32\\ r=rate\to 12\%\to (12)/(100)\dotfill &0.12\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 5755.32[1+(0.12)(5)] \implies \stackrel{ \textit{final pay for the car} }{\boxed{A \approx 9208.51}}`