Automobiles of the future will most likely be mafactured largely with carbon fib
ID: 1155341 • Letter: A
Question
Automobiles of the future will most likely be mafactured largely with carbon fibers made from recycled plastics, wood pulp, and cellulose. Replacing half the ferrous metals in current automobiles could reduce a vehicle's weight by 55% and fuel consumption by 20%. One impediment to using carbon fibers in cars is cost. If the justification for the extra sticker price of carbon-fiber cars is solely based on fuel savings, how much extra sticker price can be justified over a six-year life span if the carbon-fiber car would average 36 miles per gallon of gasoline compared to a convlr averaging 30 miles per gallon? Assume that gasoline costs $3.20 per gallon, the interest rate is 20% per year, and 1 16,000 miles are driven uniformly over sx years. ? Click the icon to view the interest and annuity table or discrete compounding when is 20% per month. The extra sticker price that can be afforded is (Round to the nearest dolar.)Explanation / Answer
ANSWER:
Miles driven per year = miles driven over 6 years / no of years = 116,000 / 6 = 19,333.33
Gas needed with conventional car = miles driven per year / conventional car average = 19,333.33 / 30 = 644.44 gallons per year
Gas needed with carbon fibre car = miles driven per year / carbon fibre car average = 19,333.33 / 36 = 537.07 gallons per year
Annual savings = gasoline cost * ( Gas needed with conventional car - Gas needed with carbon fibre car)
Annual savings = 3.2 * ( 644.44 - 537.07) = 3.2 * 107.40 = $343.70
i = 20% and n = 6 years
Justification = annual savings(p/a,i,n) = 343.7(p/a,20%,6) = 343.7 * 3.326 = $1,142.99
so the extra sticker price justified is $1,142.99 or $1,143 ( rounded to the nearest dollar)
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