Question

Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner’s insurance policy is $600 for the coverage they need. Their insurance company offers a discount of 7 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 $89 each. At the local hardware store, smoke detectors cost $22 each, and the new house has two floors. Dave and Ellen can install them 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? (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? (Round your answer to 2 decimal places.)

Answer 1

Initial Outlay:

Dead Bolt Locks = 89*2 = 178

Smoke Alarms(assuming 1 for each floors) = 22*2 = 44

Year	Cash Flow	Cumulative Cashflow (currecnt cash flow + all previous cashflows)		Year	Cash Flow	Cumulative Cashflow (currecnt cash flow + all previous cashflows)
1	42	42		1	24	24
2	42	84		2	24	48
3	42	126		3	24	72
4	42	168		4	24	96
5	42	210		5	42	138
6	42	252		6	42	180
		As Initial Outlay is 178, it will be recoverd in between year 4 & 5. Therefore, Payback Period will be between 4th and 5th year.				As Initial Outlay is 44, it will be recoverd in between year 1 & 2. Therefore, Payback Period will be between 1st and 2nd year.
		Payback Period will be 4 years + proportionate of 5th year Payback Pariod = 4+[(178-168)/(210-168)]				Payback Period will be 1 year + proportionate of 2nd year Payback Pariod = 1+[(44-24)/(48-24)]
		Payback Period = 4.238 years				Payback Period = 1.833 years

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