Payback Period and NPV of a Cost Reduction Proposal$$Differential Analysis

Mary Zimmerman decided to purchase a new automobile. Being concerned about environmental issues, she is leaning toward the hybrid rather than the completely gasoline four$-$cylinder model. Nevertheless, as a new business school graduate, she wants to determine if there is an economic justification for purchasing the hybrid, which costs $$1,500$ more than the regular VUE. She has determined that city$/$highway combined gas mileage of the Green VUE and regular VUE models are $27$ and $23$ miles per gallon respectively. Mary anticipates she will travel an average of $12,000$ miles per year for the next several years.

$($Round all of your answers to two decimal places. For example, enter $8\mathrm{.}84$ for $8\mathrm{.}844$ and $8\mathrm{.}85$ for $8\mathrm{.}845.)$

$($a$)$ Determine the payback period of the incremental investment if gasoline costs $$3\mathrm{.}50$ per gallon.