Problem says you drive 30,000 miles per year and gas averages $4 per gallon.
a. If you own a hybrid car averaging 30 miles per gallon, then annually you will consume the next amount of gallons:
[tex]30,000\text{miles x}\frac{1gallon}{30miles}=1,000gallons[/tex]And you will pay for 1000 gallons:
[tex]1000\text{gallons}\frac{4dollars}{1gallon}=4000\text{ dollars}[/tex]But, if you own a SUV averaging 9 miles per gallon, you'll consume the next amount of gallons:
[tex]30,000\text{miles x}\frac{1gallon}{9miles}=3,333.3gallons[/tex]And you will spend in fuel:
[tex]3333.3\text{gallons}\frac{4dollars}{1gallon}=13333.3\text{ dollars}[/tex]Thus, if you own a hybrid car, you will save in annual fuel expenses:
[tex]13333.3-4000=9333.3\approx9333dollars[/tex]b. If you deposit your monthly fuel savings at the end of each month into an annuity that pays 4.8% compounded monthly, at the end of four years you will save:
The formula is:
[tex]A=\frac{P\lbrack(1+\frac{r}{n})^{nt}-1\rbrack}{(\frac{r}{n})}[/tex]Where A is the balance in the account after t years, P is the amount you deposit each month, r is the annual interest rate in decimal form and n is the number of compounding periods in one year (12 as it is monthly).
Then, if you save annually $9333, each month you save $9333/12=$777.75
At the end of 4 years, you will save then:
[tex]\begin{gathered} A=\frac{777.75\lbrack(1+\frac{0.048}{12})^{12\cdot4}-1\rbrack}{(\frac{0.048}{12})} \\ A=\frac{777.75\lbrack(1+0.004)^{48}-1\rbrack}{(0.004)} \\ A=\frac{777.75\lbrack(1.004)^{48}-1\rbrack}{(0.004)} \\ A=\frac{777.75\lbrack1.2112-1\rbrack}{(0.004)} \\ A=\frac{777.75\times0.2112}{(0.004)} \\ A=41066.5\approx41067 \end{gathered}[/tex]After 4 years you will save $41067