Thomas Taylor is evaluating a new ticketing system for his theater. The system will cost $$312,600$ and will save the theater $$59,020$ in annual cash operating costs. Thomas expects the new system to last $10$ years, at which time the system will have a salvage value of $$21,000.$ If Thomas purchases the new system, he will be able to sell his existing system for $$14,000.$

$($a$)$ Calculate the accounting rate of return for the proposed ticketing system.

Accounting rate of return $\%$

$($b$)$ Thomas Taylor wants to earn a minimum accounting rate of return of $9\%$ on his projects. Should he invest in the new equipment?

Thomas Taylor $$ invest in the new equipment.