Question

Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner's insurance policy is $450 for the coverage they need. Their insurance company offers a 5 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 locksmith, who will provide and install dead-bolt locks on the two exterior doors for $50 each. At the local hardware store, smoke detectors cost $7 each, and the new house has two floors. Dave and Ellen can install them themselves.

a. How many years will it take Dave and Ellen to earn back in discounts the cost of the dead-bolts?
b. How many years will it take Dave and Ellen to earn back in discounts the cost of the smoke detectors?
c.Would you recommend Dave and Ellen invest in the safety items, if they plan to stay in that house for about 5 years?

Answer 1

1.Annual discount for dead-bolts $22.50

Recovery period 4.44 years

2.Annual discount for smoke alarms $9.00

Recovery period 1.5 years

3. Yes

Step-by-step explanation:

1. Calculation for the years it will take Dave and Ellen to earn back the cost of the dead-bolts

a. We were going to calculate for the Annual discount for dead-bolts using this formula Annual discount for dead bolts =Discount percent × Annual premium

Let plug in the formula

Annual discount for dead-bolts =0.05 × $450

Annual discount for dead-bolts =$22.50

b. We are to find Recovery period using this formula Recovery period=Cost of dead bolts / Annual discount for dead-bolts

Let plug in the formula

Recovery period= (2 × $50) / $22.50

Recovery period=100/$22.50

Recovery period= 4.44years

2. Calculation for the years it will take Dave and Ellen to earn back the cost of the smoke detectors

a. We are going to calculate for the Annual discount for smoke alarms using this formula Annual discount for smoke alarms =Discount percent × Annual premium

Let plug in the formula

Annual discount for smoke alarms =0.02 × $450

Annual discount for smoke alarms =$9.00

b. We are going to find the Recovery period using this formula Recovery period=Cost of smoke alarms / Annual discount for smoke alarms

Let plug in the formula

Recovery period=(2 × $7) / $9.00

Recovery period=14/$9.00

Recovery period= 1.5 years

3. Yes I Would recommend both Dave and Ellen to invest in the safety items, if they plan to stay in that house for about 5 years as they should recover most of their costs within the planned tenancy of the house and for their personal safety they should install the items regardless of all the recovery time period.