There are two methods of calculation of Life Insurance Premium:

(i) Value of Service

(ii) Cost of Service

### (i) Value of Service

The value of service determines the rate of premium according to the utility of insurance to each proponent. Since, the value or utility to each person differs, the premium rate will also vary.

The value of service principle cannot be used in insurance because its utility to each individual cannot be determined. Moreover, the value is higher to the proper section of society and to the head of large family; but they cannot be charged higher premium than the premium charged by richer class of the society.

Moreover, the higher premium will not attract business from them. The value of service cannot be used to its impracticability.

### (ii) Cost of Service

In fact, the premium should be charged according to cost of the insurer. In insurance demand side does not play important role. Therefore, it is called that the insurer is not bought, but it is sold.

So, the insurer must fix the cost of premium to be charged on a particular risk or policy.

Insurance business may carry on only when the cost of insurance is met. The cost includes all expenses of the business plus small profit margin.

Above the profit margin, insurer is not expected to gain. This is the reason that insurance business is expected to run on ‘no loss, no gain’, basis.

The most important cost of insurer is cost of claim. Therefore, the insurer must charge at least so much of premium that can be used to pay the full amount of claim.

Technically, the premium charged to meet the amount of claim, is called ‘net premium’.

Another cost to insurer is cost of administration. It includes all expenses of management and other amount for provisions of contingency.

The cost of administration may be of two types:

(i) fixed cost, and

(ii) recurring cost.

The fixed cost is spread over the policy-life but the recurring expenses do not involve much problem of allocation.

The method of distribution of the expenses is called loading which. With the help of loading net premium is enhanced to charge a fixed amount regularly from the policy-holders, which is called gross premium or office premium.

So, the first problem before the insurer is to calculate the cost of claims.

#### Cost of Claims

The claims may arise at the death of the life assured or at that of the policy.

In annuity contract the payment shall continue to death therefore, the expectation of survival will be the basis of the cost. In life insurance, in most cases, payment of claims depends upon the death.

The death is certain but when it will take place is not certain.

Therefore, the main problem before the insurer is to decide when the death will take place. The forecasting of death is very important factor to decide the period and amount of claim.

If the period and amount of claims have been decided, the premium can be easily calculated.

The forecasting of death can be done on

(i) the experience of medical science, and

(ii) the experience of past records.

If the medical science of insurance has been sufficiently advanced and its knowledge could be perfectly used, the same, then, might have projected the time of death of each applicant.

The medical science can be useful to modify the past experience according to the present mortality prospects.

The insurer bases the calculating of time of death on the basis of experience of past death with certain modification in special cases.

The insurer has to rely upon the past experience which is treated as a basis for germinating future mortality.

It has been assumed that there is law of mortality on the basis of which deaths have been taking place in future.

Evidently, the death of one life cannot be forecasted; but the expectation of a number of deaths from a group of persons of the same age can be forecasted on the basis of

(i) Theory of probability and

(ii) The law of large numbers.

##### Theory of Probability

The theory of probability reveals the possibility of occurring a certain event or not occurring a certain event out of the given events.

Thus, in insurance, the theory of probability can be of three types:

(i) certainty,

(ii) simple probability and

(iii) compound probability

###### 1. Certainty

The probability of certainty is expressed as one. It means the chance of happening a certain event, say death, is 100 per cent.

It is sure that the death will occur in this expression. Naturally factor, i.e. certainty is taken as as the, basis of comparison.

In other words, the chance of death is related with the unity or one or certainty.

###### 2. Simple Probability

When the events are mutually exclusive or when only event is present, the probability will be known as simple probability.

For example; if the at the age of 40, 2 persons die out of 10,000 the probability of death of a person, who is of 40 years, can be expressed as:

2/10,000

= 0.02 per cent

or,

= 0.0002 of units.

Generally, the probability is expressed in terms of unity or one, i.e. the probability is related with one which can be expressed in the decimals.

Similarly, if there are more than one persons and the death rate of each person is to be calculated separately, the simple probability is applied.

For example, if there are two persons of ages 40 and 42 years the causes of death of one person only can be expressed as probability of death of first person plus probability of death of second person.

###### 3. Compound Probability

Multiplication is applied when the probability of the combined happening of two or more independent events, if the probabilities of their separate happening are known when two or more events occur together, their joints occurrence is called compound event.

For example, if the probability of death of A at the age of 40 is 0.0002 and the probability of death of B at the age of 42 is 0.0003, the compound probability shall be calculated when we are required to know the probability of death of any of the persons.

Thus, the probability of death of any of the, persons, will be .0002 x 0.0003 = 0.0000006.

In insurance, the simple probability is generally used to calculate death rate of one person.

##### Estimation of Probability

The probability can be estimated whether

(i) Priori basis or

(ii) Posteriori basis.

###### (i) Priori basis

In this case, the probability is estimated merely on the basis of knowledge.

It is not derived after experiment or practice. It is also deductive reasoning where estimation is based on from general to particular.

Although it is not tested, but it is useful to correct the defects of experimental probability where the probability not expected to give hundred per cent correct results.

It is well known fact that the death rate after 50 years, will not decline but it will go on increasing year after year.

If in any year there is fluctuation in mortality which has been calculated on the basis of experiment that is corrected with the help of interpolation or graphic method.

Thus, the apriori, probability is of much use in such circumstances.

###### (ii) Posteriori basis

The probability in this case is calculated on the basis of experiment. It is called as Inductive method because in this case, estimation is based from particular to general.

The posteriori probability can give correct result only when the experiment involves a large number of units and the data are correct.

In mortality estimation we cannot depend merely on the posteriori probability because cent per cent accuracy and universal experiment are not possible.

It is well known fact that the death after 30 years will not decline but it will go on increasing year after year. If in any year there is fluctuation in mortality which has been calculated on the basis of experiment that is correct.

##### Law of Large Numbers

The accuracy of probability depends on two factors:

(i) Accuracy of data;

(ii) The large number of units.

The important fact to be considered is that the probable experience should be nearest to the actual experience. If there is difference between the actual and probable experience, the probability will be of no use.

To avoid this deviation or difference, the date of estimation should be accurate enough and the experiment should base on a large number.

It has been observed that the larger the number, the lesser the deviation between actual and probable estimation.

So for calculating death rate or mortality rate, a large number of persons should be selected and their age should be correctly recorded.