Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner$$s insurance policy is $$550$ for the coverage they need. Their insurance company offers an annual discount of $6$ percent if they install dead$-$bolt locks on all exterior doors. The couple can also receive an annual discount of $4$ 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 $$78$ each. At the local hardware store, smoke detectors cost $$20$ each, and the new house has two floors. Dave and Ellen can install the smoke detectors themselves.

a$.$ What discount will Dave and Ellen receive if they install the dead$-$bolt locks? $($Round your answer to $2$ decimal places.$)$

b$.$ What discount will Dave and Ellen receive if they install smoke detectors?

PART B

Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner$$s insurance policy is $$650$ for the coverage they need. Their insurance company offers a discount of $8$ percent if they install dead$-$bolt locks on all exterior doors. The couple can also receive a discount of $4$ 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 $$110$ each. At the local hardware store, smoke detectors cost $$24$ 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.$)$

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.$)$