Question

You own a house worth $400,000 on a river. If the river floods moderately, the house will be completely destroyed. This happens about once every 50 years. If you build a seawall, the river would have to flood heavily to destroy your house, and this only happens about once every 200 years.

What would be the annual premium to the nearest dollar for an insurance policy that offers full insurance?                               $
What would be the annual premium to the nearest dollar for an insurance policy that only pays 75% of the home value?   $

What are your expected annual costs to the nearest dollar without a seawall with full insurance?                                                      $
What are your expected annual costs to the nearest dollar without a seawall with partial coverage?  

Answer 1

Solution: The insurance premium is based on the probability of flooding:

Without seawall: 1 in every 50 years: 1/50 = 0.02 = 2%

With seawall: 1 in every 200 years: 1/200 = 0.005 = 0.5%

So, the annual premium to the nearest dollar for an insurance policy that offers full insurance is computed as below:

Amount of premium= Value of House× Probability of flooding

Without seawell = $400,000× 2%

= $8000

With seawell = $400,000× 0.5%  

= $2000

The premium to the nearest dollar for an insurance policy that only pays 75% of the home value is as computed below:

Amount of premium= Value of House× Probability of flooding

Without Seawell = ($400,000× 75%)× 2%  

= $6000

With Seawell = ($400,000× 75%)× 0.5%  

= $1500

The difference in the annual premium with or without seawell is calculated as below:

A. With Full Coverage

= $8000- $2000

= $6000

If the seawall cost less than this amount, it is better to build it as it would minimize the annual expected cost.

B. With Partial Coverage i.e. 75%

= $6000- $1500

= $4500

If the seawall cost less than this amount, it is better to build it as it would minimize the annual expected cost.