Curvy Mathematics

Insurance : The Game (12 Oct 2017)

 The idea of minimizing risk is called insurance. Entrepreneurs are supposed to take risks. At least this is what they declare to the rest of the world. Shipping companies insure their cargo, financial corporations insure their loss probability, common people go with the flow and insure whatever they can, either because they are obliged by legislation or because they feel that insurance will repay them at all costs. In my opinion, insurance will only deceive common people's minds by allowing them to believe that in case of an unfortunate event, the insurance company will take care of everything. Practically, it will cause more trouble in the case that the unfortunate event finally occurs.

 Insurance companies make money. Neither they generate nor they mint money, they just wager (invest is their favourite term) with their clients' money. In exchange to the clients' goodwill to trust their money in the insurance broker's hands, they repay their clients with some interest. Interest can be high or low, acceptable or unacceptable but this is utterly subjective. Personally, if I could find repayment with an interest greater than the one banks offer, I would choose it. Obviously, I am talking about pension or savings contracts. The insurance company collects, keeps and wagers the customers' money for twenty to thirty years and returns an equal amount of money plus the agreed interest minus the agreed (and random, not always agreed) "costs".

 Just like a bank and a casino, an insurance company can be considered as "The House" too. And The House always wins. They receive money from car insurance, health insurance, fire, death, etc. Do they return all of this money back to the clients? Absolutely not. But this is the way this system has always been functioning. In other words, we pay for services that we do not always use. Legally, it is acceptable. Ethically, I cannot say. It depends on one's background and culture.

 The savings or pension programme works like this: the client deposits every year an increasing amount of money. After the agreed number of years passes, the insurance company returns an amount of money greater than the sum of all yearly installments the client has deposited.

 1st year: Client deposits C

 2nd year: Client deposits C + C×i = C×(1 + i)

 3rd year: Client deposits C×(1 + i) + C×(1 + i)×i = C×(1 + i)×(1 + i)

 4th year: Client deposits C×(1 + i)×(1 + i)×(1 + i)

 Obviously, this is C×(1 + i)^3

 5th year: Client deposits C×(1 + i)^4

 .......

 20th year: Client deposits C×(1 + i)^19

 i stands for inflation and usually varies between 1% and 5%. It is supposed to cover the expenses of the insurance company due to yearly inflation of money. In other words, if the client signs a contract for twenty years, the insurance company supposes that after twenty years the first installment of C will have a very low value. So, the client pays for that every year. But this is fair enough, the company will return every single cent of it.

 Now, the insurance company sums all the yearly installments. It is boring enough(and time consuming) to make all calculations for the sum but since it is a sum of the first twenty terms of a geometric sequence, then the result is C×(1/i)×(1 + i)^19.

 Well, I have made a typographical error above. Most insurance companies prefer to start the inflation from the 1st year, which means that the 20th installment is C×(1 + i)^20 and thus the above sum of all twenty installments is C×(1/i)×(1 + i)^20. In both cases the sum is considered to be a lovely amount of money for every average human being. The client will take it back in either of the cases, it is just that the second case is more expensive. Additionally, the client will receive an interest around 40%.

 Usually, this amount is tax free too. Theoretically. Practically, the government does not apply any direct tax on the final yield but very tiny ones, paid per installment which are not refundable and varying between 0.05% and 2% of the installment. Unfortunately, these "costs" occur randomly and at will by all governments across the globe. It seems that all governments have at least this in common.

Moderator: Gauss, Overseers.