James and Karen have just moved into a new home. Their homeowner's insurance policy is $$590$ each year. Their insurance company is offering a $9$ percent discount if they install dead$-$bolt locks on all exterior doors. The couple can also receive a $2$ percent discount if they install smoke detectors on each floor. They have contacted a local locksmith, who will provide and install dead$-$bolt locks on the two exterior doors for $$72$ each. At the hardware store, smoke detectors cost $$16$ each, and the home has two floors. James and Karen plan to install the smoke detectors themselves.

Assuming their insurance rates remain the same, how many years will it take them to earn back in discounts the cost of the smoke detectors? $($Round your answer in years to the nearest whole number.$)$