Blossom Service Center just purchased an automobile hoist for $$35,000.$ The hoist has an $8-$year life and an estimated salvage value of $$3,000.$ Installation costs and freight charges were $$3,300$ and $$700,$ respectively. Blossom uses straight$-$line depreciation.

The new hoist will be used to replace mufflers and tires on automobiles. Blossom estimates that the new hoist will enable its mechanics to replace sextra 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 $\%$