Scarlett is considering the purchase of a new Wolf gas range by Sub$-$Zero Group, Inc. to increase the quality of the food served in her restaurant. It will also enhance the cooking experience for her and her chefs, as they won't have to fuss with the finicky electric burners they currently use.

However, the new range is expensive. It will cost $$9,890$ to buy and properly install. On the upside, it should last for at least $7$ years, at which time Scarlett may consider trading it in for another new range. While her operating costs will not decrease as a result of this purchase, Scarlett will be able to generate additional gross margin of at least $$1,520$ in the first year. After that, she expects the additional gross margin to grow by $10\%$ each year for the next $4$ years, at which point it will become stable for the remainder of the $7$ year life. She believes the new range will be worth $$1,000$ at the end of this $7-$year period. Her current range can be salvaged today for $$250.$

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$($a$)$

Calculate the discounted payback period for this range $($using before$-$tax cash flows$),$ assuming Scarlett's cost of capital averages $6\%.($Round present value factor calculations to $5$ decimal places, eg$.1\mathrm{.}25124$ and final answer to $2$ dec$/$mal places eg$.15\mathrm{.}25.)$

Discounted payback period years