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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
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 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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Age (x) No.of persons
living at age X and
share claims (Ix)
No. of claims by
death ( probability)
(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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