Oriole Service Center just purchased an automobile hoistfor $$34,700.$ The hoist has an $8-$year life and an estimated salvage value of $$3,800.$ Installation costs and freight charges were $$3,600$ and $$700,$ respectively. Oriole uses straight$-$line depreciation.

The new hoist will be used to replace mufflers and tires on automobiles. Oriole estimates that the new hoist will enable its mechanics to replace $5$ extra mufflers per week. Each muffler sells for $$72$ installed. The cost of a muffler is $$35,$ and the labor cost to install a muffler is $$12.$

$($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 $\%$