new six speed automatic transmission for automobiles offers an estimated 4% impr
ID: 1100272 • Letter: N
Question
new six speed automatic transmission for automobiles offers an estimated 4% improvement in fuel economy compared to the traditional four-speed transmissions in front wheel drive cars. If a four-speed transmission car averages 30 miles per gallon and gasoline costs three dollars per gallon, how much extra can a motorist pay for fuel-efficient six speed transmission? Assume that the car will be driven for 120,000 miles over its lifetime of 10 years. The motorist can earn 6.69 % per year on an investment. Instructor hint: to get the correct answer you ust assume the person buys his gasoline at the end of each year.
Explanation / Answer
four-speed transmission car
miles driven per year = 120000/10 = 12000 miles
number of gallons required per year = 12000/30= 400 gallons
Money spent on fuel per year= 400*3 = $1200
Present cost of fuel = 1200/(1+6.69%) + 1200/(1+6.69%)^2 + 1200/(1+6.69%)^3.....1200/(1+6.69%)^10
Present cost of fuel = 1200*(1-1/1.0669^10)6.669%= $8,550.41
new six speed automatic transmission automobiles
miles driven per year = 120000/10 = 12000 miles
new mileage = 30*(1+4%) = 31.2
number of gallons required per year = 12000/31.2= 384.62 gallons
Money spent on fuel per year= 384.62*3 = $1,153.85
Present cost of fuel = 1,153.85/(1+6.69%) + 1,153.85/(1+6.69%)^2 + 1,153.85/(1+6.69%)^3.....1,153.85/(1+6.69%)^10
Present cost of fuel = 1,153.85*(1-1/1.0669^10)6.669%= $8,221.55
Difference in the cost = $8,550.41 - 8,221.55=$328.86
extra amount can a motorist pay for fuel-efficient six speed transmission=$328.86
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