To determine the payback period when purchasing a 2019 Tesla Model 3 compared to a conventional car, we'll follow these steps:
1. Calculate the annual cost of gas for the conventional car:
- The average driver covers 15,000 miles per year.
- Assume the conventional car gets an average of 25 miles per gallon, and the price of gas is [tex]$2.5 per gallon.
- We calculate the number of gallons used per year by dividing the total miles driven per year by the car's miles per gallon:
\[
\text{Gallons per year} = \frac{15000 \, \text{miles}}{25 \, \text{miles/gallon}} = 600 \, \text{gallons}
\]
- Multiply the number of gallons used per year by the price per gallon:
\[
\text{Annual cost of gas} = 600 \, \text{gallons} \times 2.5 \, \text{\$[/tex]/gallon} = 1500 \, \text{\[tex]$}
\]
2. Calculate the annual cost of electricity for the Tesla:
- Assume the Tesla Model 3 gets 4 miles per kWh, and the price of electricity is $[/tex]0.13 per kWh.
- Calculate the number of kWh needed per year by dividing the total miles driven per year by the car's miles per kWh:
[tex]\[
\text{kWh per year} = \frac{15000 \, \text{miles}}{4 \, \text{miles/kWh}} = 3750 \, \text{kWh}
\][/tex]
- Multiply the number of kWh used per year by the price per kWh:
[tex]\[
\text{Annual cost of electricity} = 3750 \, \text{kWh} \times 0.13 \, \text{\$/kWh} = 487.5 \, \text{\$}
\][/tex]
3. Calculate the annual savings when driving a Tesla instead of a conventional car:
- Calculate the difference between the annual cost of gas and the annual cost of electricity:
[tex]\[
\text{Annual savings} = 1500 \, \text{\$} - 487.5 \, \text{\$} = 1012.5 \, \text{\$}
\][/tex]
4. Determine the payback period in years:
- The base price of the Tesla Model 3 is [tex]$30,000.
- Divide the base price of the Tesla by the annual savings to find out how many years it will take to recover the initial investment:
\[
\text{Payback period} = \frac{30000 \, \text{\$[/tex]}}{1012.5 \, \text{\$/year}} \approx 29.63 \, \text{years}
\]
In conclusion, it would take approximately 29.63 years of average driving for the cost savings on fuel and electricity to "pay back" the initial investment in a Tesla Model 3, compared to purchasing a conventional Fusion.
