Carla Vista Manufacturing purchases equipment with an expected life of $10$ years for $$47600.$ The equipment has an estimated salvage value of $$1920.$ Carla Vista expects the new equipment to generate annual cost savings of $$7680.$ What is the payback period of the equipment?

$5\mathrm{.}95$ years

$10\mathrm{.}00$ years

$6\mathrm{.}45$ years

$6\mathrm{.}20$ years