Question

Suppose that you drive 30000 miles per year and gas averages ​$4 per gallon. Complete parts a. and b. below.

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Part 1
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?
​$

enter your response here
​(Round to the nearest dollar as​ needed.)
Part 2
If you deposit your monthly fuel savings at the end of each month into an annuity that pays ​%4.8 compounded​ monthly, how much will have saved at the end of 8 ​years?
​$

enter your response here
​(Round to the nearest dollar as​ needed.)

Answer 1

Part 1:

To calculate the annual fuel expense savings, we need to find the difference in fuel consumption between the hybrid car and the SUV.

For the hybrid car:

Fuel consumption = 30 miles per gallon

Annual fuel consumption = 30,000 miles / 30 miles per gallon = 1,000 gallons

For the SUV:

Fuel consumption = 9 miles per gallon

Annual fuel consumption = 30,000 miles / 9 miles per gallon ≈ 3,333.33 gallons

Difference in fuel consumption = 3,333.33 gallons - 1,000 gallons = 2,333.33 gallons

Fuel cost savings = Difference in fuel consumption * Price per gallon

Fuel cost savings = 2,333.33 gallons * $4 per gallon = $9,333.33

Therefore, you would save approximately $9,333.33 in annual fuel expenses by owning a hybrid car instead of an SUV.

Part 2:

To calculate the amount saved at the end of 8 years, we will use the formula for the future value of an annuity:

Future Value = Payment * [(1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years) - 1] / (Interest Rate / Number of Compounding Periods)

Monthly fuel savings = $9,333.33 / 12 months = $777.78

Interest rate = 4.8% = 0.048

Number of compounding periods per year = 12

Number of years = 8

Plugging these values into the formula:

Future Value = $777.78 * [(1 + (0.048 / 12))^(12 * 8) - 1] / (0.048 / 12)

Calculating the expression within the square brackets and then dividing by (0.048 / 12), we find:

Future Value ≈ $9,477.03

Therefore, at the end of 8 years, you would have saved approximately $9,477.03 by depositing your monthly fuel savings into an annuity that pays a 4.8% interest rate compounded monthly.