Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner's insurance policy is $$500$ for the coverage they need. Their insurance company offers a discount of $5$ percent if they install dead$-$bolt locks on all exterior doors. The couple can also receive a discount of $2$ percent if they install smoke detectors on each floor. They have contacted a locksmith, who will provide and install dead$-$bolt locks on the two exterior doors for $$65$ each. At the local hardware store, smoke detectors cost $$8$ each, and the new house has two floors. Dave and Ellen can install the smoke detectors themselves.

a$.$ Assuming their insurance rates remain the same, how many years will it take Dave and Ellen to earn back in discounts the cost of the dead$-$bolts? $($Do not round intermediate calculations. Round your$-$answer to $2$ decimal places.$)$

Recovery period years

b$.$ How many years will it take Dave and Ellen to earn back in discounts the cost of the smoke detectors? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Recovery period

years