So let's say a company sells life insurance policies, which require customers to pay an annual fee. Assume that if the customer happens to die in that year, the company does not charge the customer's beneficiaries the fee and will also pay out the amount that the policy is worth. If the average customer has a 2.5% chance of dying in the next year and the policy is worth $100,000 then what is the minimum amount the company should charge for the yearly payment so that on average they won't lose any money? I'm having trouble starting out this question. I've learned about things like how to calculate profit however those questions give me the mean and standard deviation and this one doesn't.
If 2.5% of people will not be paying the fee, and will be receiving $100 000, then we have 97.5% of people who will be paying.
What we need is that the money payed out equals the money taken in :
100000 * 0.025 = 0.975 * p
Solving for the premium (p) we get :
2500 = 0.975p 2564.1025641 = p
The company should therefore charge a minimum of 2564.11 (rounding up) to not lose money.