Legend Service Center just purchased an automobile hoist for $$32,100.$ The hoist has an $8-$year life and an estimated salvage value of $$3,200.$ Installation costs and freight charges were $$3,500$ and $$800,$ respectively. Legend uses straight$-$line depreciation.

The new hoist will be used to replace mufflers and tires on automobiles. Legend estimates that the new hoist will enable his mechanics to replace $5$ extra mufflers per week. Each muffler sells for $$74$ installed. The cost of a muffler is $$39,$ and the labor cost to install a muffler is $$15.$

$($a$)$

Compute the cash payback period for the new hoist.

Cash payback period years

$($b$)$

Compute the annual rate of return for the new hoist. $($Round answer to $2$ decimal places, e$.$g$.10\mathrm{.}52\%.)$

Annual rate of return $\%$