Unit 3- Calculation of Premium

7/29/2019 Unit 3- Calculation of Premium

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Unit 3- Calculation of premium of

Life Insurance plans


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Basic Elements in Computation of

Premiums-Mortality

The rate at which a given of persons of a given

age are expected to die and survive is called

the rate of mortality. If the proportion of

persons actually dying in a in a given year are

less than what is assumed in premium

calculation there will be left a small surplus

and if the actual no of deaths is more thanwhat was assumed for premium calculation

the extra claim will have to be met from the

accumulated life fund.


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Since, the morality rate of the persons who

are living cannot be calculated, the Insurance

go about pricing their product on the basis of

the study of past experience of deaths among

a similar group of persons conducted either by

themselves or some other insurers or in some

cases some other outside the insurancebusiness. The study of the mortality of such

persons are summarized in the form of tables

called, mortality tables


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Mortality Tables

For pricing a product that a life insurance co.

would like to offer to its customers, first it

decides on a mortality table, which is

considered to be the closely matching that of

the largest customers. By using the mortality

table, it can go about the premium that has to

be charged for persons of a given age.


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Stages in Premium Computation

of Premiums

The three main components of Life Insurance

Premium are i) Mortality, ii) Interest and iii)

Loading for expenses, options, bonus etc.

The first step is to arrive at the Pure Premium

which can meet all the claims payout that are

expected within the first year.


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Q-

No. of persons insured for one year

10000

Age of the Assured 35 years

Sum Assured per policy Rs. 10,000/-

Mortality Rate at age 35 within one years is

0.0028


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This means out of 10000 person to whom the

policy is sold , 28 persons are likely to die

within one year term as per the Mortality

Table.


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Hence the total claim out go would be

10000x28

=Rs. 2,80,000/-


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Share of each person taking Insurance Cover

would be

Sum Assured x No. of death in one year

Total No. of Insured person

10000 X 28

10000

=Rs. 28/-


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Q

Age (x) No. of Person living at age x

and sharing the claims (lx)

No. of claims by death (dx)

prabability of Death (qx) x

(lx)

Pure or Natural Premium =

SA(dx)/(lx)

35 10,000 28 28.00

36 9,972 31 31.09

37 9,941 34 34.20

38 9,907 38 38.36

39 9,869 42 42.56


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Q.

No. of persons= 10000;

Age = 25 years;

Sum assured = Rs 10000;Mortality table = 0.0011 for 25 year aged

persons;

How much is the premium?


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11 persons will die out of 10000 persons;

11x10000=110000;

Premium = 110000/10000 = Rs.11

* This premium arrived after mortaility tablecalculation is called PURE premium or Natural premium


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Calculate

Age (x) No.of persons

living at age X and

share claims (Ix)

No. of claims by

death ( probability)

(Dx)1

Pure / Natural

premium = S.Ax

(Dx)/(Ix)

25 10000 11 ?

26 9989 15 ?

27 9974 20 ?

28 9954 25 ?

29 9929 29 ?


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Answer


living at age X and

share claims (Ix)

No. of claims by


(Dx)1

Pure / Natural

premium = S.Ax

(Dx)/(Ix)

25 10000 11 11.00

26 9989 15 15.02

27 9974 20 20.05

28 9954 25 25.11

29 9929 29 29.21


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Level Premium

The insurer can alternately apply method of

level premium by charging single rate of

premium uniformly through out the terrn of 5

years from the surviving policy holders thenbe would be able to meet all the claims


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Age (x) No. of Person living at age x

and sharing the claims (lx)

No. of claims by death (dx)

prability of Death (qx) x (lx)

Total claims out go.

35 10,000 28 2,80.000

36 9,972 31 3,10.000

37 9,941 34 3,40.000

38 9,907 38 3,80.000

39 9,869 42 4,20.000

Total 173 17,30.000


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If the uniform amount of premium that the

insurer wishes to collect from all the policy

holders every year is P there the same can be

found out by solving the following equation :-


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(10000 x P) + (9972 x P) + (9941 x P) + (9907 x

9) + (9869 x P) = 17,30.000

P x 49689 = 1730000

P = 34.82


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living at age X and

share claims (Ix)

No. of claims by


(Dx)1

Cost of benefit

payment

25 10000 11 110000

26 9989 15 150000

27 9974 20 200000

28 9954 25 250000

29 9929 29 290000

Total cost 1000000


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Level Premium:

(10000xP)+(9989xP)+(9974xP)+(9954xP)+(992

9xP) = 1000000

Px(10000+9989+9974+9954+9929)=1000000

Px49846 = 1000000

P = 20.06;


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Unit 3- Calculation of Premium

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