Final answer:
The payback period for the machine is approximately 4 years.
Step-by-step explanation:
To calculate the payback period, we need to divide the cost of the machine by the annual savings it provides. In this case, the cost of the machine is $72,000 and the annual savings is $18,000. Therefore, the payback period is calculated as:
Payback Period = Cost of Machine / Annual Savings
Payback Period = $72,000 / $18,000
Payback Period = 4 years
The payback period for the machine is approximately 4 years, so the closest option is 2) 4 years.