Question

The cost of health insurance is $900 per month. The cost of an operation for a dramatic injury is $500,000. The chances of someone needing such an operation are 47.3% over a twenty year period. From a purely financial point of view, it is better for you to buy the insurance. True or False

Answer 1

Yes, It is better to buy the insurance.

Explanation:

Given Data:

Cost of Health Insurance for a month = 900$ per month

As 20 Years = 20*12 months = 240 months

Cost of Health Insurance for 20 years = 900 * 240

Cost of Health Insurance for 20 years = 216,000$

Insurance claim in case of having dramatic injury = Cost of Dramatic Injury = 500,000$

Insurance claim in case of having no dramatic injury = 0$

Chances of dramatic injury in 20 years = P(A) = 47.3%

Chances of not having dramatic injury in 20 years = P(B) = 100% - 47.3%

Chances of not having dramatic injury in 20 years = P(B) = 52.7%

Expected Insurance Claim for 20 years:

Expected Insurance Claim for 20 years = (Chances of having dramatic injury in 20 years * Insurance claim) + (Chances of not having dramatic injury * Insurance claim)

Expected Insurance Claim for 20 years = P(A) * 500,000$ + P(B) * 0$

Expected Insurance Claim for 20 years = 47.3% * 500,000 + 52.7% * 0

Expected Insurance Claim for 20 years = 236500 + 0

Expected Insurance Claim for 20 years = 236,500$

Expected Profit:

As expected insurance claim is 236,500$ is more than the cost of health insurance for 20 years and we are expected to have profit of 20,500$, thus we should take the health insurance.