Cori's Dog House is considering the installation of a new computerized pressure cooker for hot dogs. The cooker will increase sales by $$7,800$ per year and will cut annual operating costs by $$13,900.$ The system will cost $$54,700$ to purchase and install. This system is expected to have a $6-$year life and will be depreciated to zero using straight$-$line depreciation and have no salvage value. The tax rate is $40$ percent and the required return is $11\mathrm{.}4$ percent. What is the NPV of purchasing the pressure cooker?

Group of answer choices

$$$$3,147$

$$$$24,142$

$$15,004$

$$4,479$

$$22,629$