Stan Moneymaker has been informed of a major automobile$$ manufacturer's plan to conserve on gasoline consumption through improved engine design. The idea is called$$ "engine displacement," and it works by switching from$8-$cylinder operation to$4-$cylinder operation at approximately $40$ miles per hour. Engine displacement allows enough power to accelerate from a standstill and to climb hills while also permitting the automobile to cruise at speeds over $40$ miles per hour with little loss in driving performance. The trade literature studied by Stan makes the claim that the engine displacement option will cost the customer an extra $$$ on the$$ automobile's sticker price. This option is expected to save miles per gallon$($an average of$$ in$-$town and highway$$ driving$).$ A regular$8-$cylinder engine in the car that Stan is interested in buying gets an average of miles per gallon of gasoline. If Stan drives approximately miles per$$ month, how many months of ownership will be required to make this $$$ investment pay for$$ itself? Stan's opportunity cost of capital $($i$)$ is $\%$ per$$ month, and gasoline costs $$$ per gallon.

LOADING... Click the icon to view the interest and annuity table for discrete compounding when the MARR is $\%$ per month.

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Part $1$

Using the table given above and the interpolation$$ method,

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$9\mathrm{.}9$ months of ownership will be required to make this $$$ investment pay for itself. $($Round to one decimal$$ place.$)$