Questions: Use the following formula A=P[(1+r/n)^(nt)-1]/(r/n) Suppose that you drive 30,000 miles per year and gas averages 4 per gallon. Complete parts a. and b. below. a. What will you save in annual fuel expenses by owning a hybrid car averaging 30 miles per gallon rather than an SUV averaging 9 miles per gallon? (Round to the nearest dollar as needed.)

Use the following formula
A=P[(1+r/n)^(nt)-1]/(r/n)

Suppose that you drive 30,000 miles per year and gas averages 4 per gallon. Complete parts a. and b. below.
a. What will you save in annual fuel expenses by owning a hybrid car averaging 30 miles per gallon rather than an SUV averaging 9 miles per gallon?
(Round to the nearest dollar as needed.)

Transcript text: Use the following formula \[ A=\frac{P\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\left(\frac{r}{n}\right)} \] Suppose that you drive 30,000 miles per year and gas averages $\$ 4$ per gallon. Complete parts a. and b. below. $\qquad$ a. What will you save in annual fuel expenses by owning a hybrid car averaging 30 miles per gallon rather than an SUV averaging 9 miles per gallon? $\$ \square$ (Round to the $\mathrm{I}^{\text {nearest dollar as needed.) }}$

Solution

Solution Steps

To solve this problem, we need to calculate the annual fuel expenses for both the hybrid car and the SUV, and then find the difference between the two to determine the savings. First, calculate the number of gallons used per year for each vehicle by dividing the total miles driven by the miles per gallon (mpg) of each vehicle. Then, multiply the number of gallons by the cost per gallon to find the total fuel cost for each vehicle. Finally, subtract the hybrid car's fuel cost from the SUV's fuel cost to find the savings.

Step 1: Calculate Gallons Used by the Hybrid Car

The number of gallons used by the hybrid car can be calculated using the formula: \[ \text{gallons}_{\text{hybrid}} = \frac{\text{miles per year}}{\text{hybrid mpg}} = \frac{30000}{30} = 1000.0 \]

Step 2: Calculate Gallons Used by the SUV

Similarly, the number of gallons used by the SUV is: \[ \text{gallons}_{\text{suv}} = \frac{\text{miles per year}}{\text{suv mpg}} = \frac{30000}{9} \approx 3333.3333 \]

Step 3: Calculate Annual Fuel Expenses for Each Vehicle

The annual fuel expenses for the hybrid car are: \[ \text{cost}_{\text{hybrid}} = \text{gallons}_{\text{hybrid}} \times \text{cost per gallon} = 1000.0 \times 4 = 4000.0 \] The annual fuel expenses for the SUV are: \[ \text{cost}_{\text{suv}} = \text{gallons}_{\text{suv}} \times \text{cost per gallon} \approx 3333.3333 \times 4 \approx 13333.3333 \]

Step 4: Calculate Savings

The savings by owning the hybrid car instead of the SUV can be calculated as: \[ \text{savings} = \text{cost}_{\text{suv}} - \text{cost}_{\text{hybrid}} \approx 13333.3333 - 4000.0 \approx 9333.3333 \]

Step 5: Round the Savings

Rounding the savings to the nearest dollar gives: \[ \text{savings}_{\text{rounded}} = 9333 \]