Soft Touch Car Wash is considering the purchase of a new automated sudser and has narrowed it down to $2$ possible machines: One, which costs more but lasts longer, and one that is less expensive but has a shorter useful life. The expected cash flows associated with the $2$ machines are as follows:

Expected cash flow of two machines Year Machine A Machine B

$0(50,000)(30,000)$

$120,00020,000$

$220,00020,000$

$320,000$ NA

$420,000$ NA

What is the Payback Period for Machine A and Machine B$?$