Question

An insurance company issues a 1-year $1000 policy insuring against an occurrence A that historically happens to 2 out of every 100 owners of the policy. Administrative fees are $15 per policy and are not part of the company’s "profit". How much should the company charge for the policy if it requires that the expected profit per policy be $50? (Hint: If C is the premium for the policy, the company’s "profit" is C – 15 if A does not occur and C – 15 – 1000 if A does occur.)

Answer 1

Answer:

$85

Step-by-step explanation:

For the insurance company mentioned in the question above, we have:

Outcome              AA_cc         AA

Profit (X)                CC-15      CC-15-1000

p(x)                   1-0.02=0.98       0.02

Therefore, we can deduce that the expected profit will be equivalent to:

E(X) = (CC-15)*0.98 +(CC-15-1000)*0.02 = 50

0.98CC-14.7+0.02CC-0.3-20 = 50

0.98CC+0.02CC = 50+14.7+0.3+20 = 85

CC = $85

Thus, the insurance company should charge $85 for the policy to obtain the estimated expected profit.