Question

Matt and Kristin 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 6 percent discount if they install dead-bolt locks on all exterior doors. The couple can also receive a 3 percent discount 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 $45 each. At the local hardware store, smoke detectors cost $6 each, and the new house has two floors. Kristin and Matt can install them themselves.

How many years will it take Kristin and Matt to earn back in discounts the cost of the dead-bolts? (Round your answer to 2 decimal places.)

Answer 1

2.50 years

Step-by-step explanation:

Data provided:

yearly premium on their homeowner’s insurance policy = $ 600

Discount offered if dead-bolt locks are installed = 6%

the amount of discount of yearly premium = 0.06 × $ 600 = $ 36 / year

Cost of dead-bolts = $ 45

Total number of dead-bolts installed = 2

Thus, the total cost of the dead-bolt = 2 × $ 45 = $ 90

Now, the year taken by the Matt and Kristin to earn back the cost of dead-bolt can be calculated as:

Year to earn back the cost = Total cost of the dead-bolts / discount earned per year

or

the year taken by the Matt and Kristin to earn back the cost of dead-bolt

= 90/36

or

= 2.50 years