Calculation of Premium in Life Insurance

1. Dr. Amitabh Mishra

2.  An insurance premium is the money charged by
insurance companies for coverage.
 Premium is the consideration money that a
policyholder has to pay in lieu of the benefit that the
insurer promises to confer on the happening of the
scheduled eventuality.
 Insurance is a contract and the policyholder /insured.
Premium forms the obligation on the part of the
insured.
Dr. Amitabh Mishra

3.  Insurance premiums differ from company to company, so it
is advisable that individuals shop around for insurance
premiums.
 It is important to note that, sometimes, insurance premiums
quoted are slightly different from the premiums charged.
 The amount of insurance premiums charged by the
insurance companies is determined by statistics and
mathematical calculations done by
the underwriting department of the insurance company.
Dr. Amitabh Mishra

4. Dr. Amitabh Mishra

5. Premiums
Net/Pure
premiums
Net Single
premiums
Net level
premiums
Gross/Office
premiums
Gross Single
premiums
Gross level
premiums
Dr. Amitabh Mishra

6.  Net premium: Net premium is based on
◦ Mortality &
◦ Interest rate
 Gross premium: Gross premium is based on
◦ Mortality
◦ Interest rate
◦ Expenses &
◦ bonus loading
Dr. Amitabh Mishra

7.  Single premium: The premium can be paid at one time, when it is
called a single premium.
 Level premium: Premium can also be paid in instalments i.e.
◦ Yearly,
◦ half–yearly,
◦ quarterly or
◦ monthly.
 Single premiums are rare except in pension plans. Tabular premiums are given in
yearly mode. Half–yearly, quarterly and monthly mode instalment is obtained by
dividing the tabular premium by 2 or 4 or 12. However before going for this division,
one has to allow for certain rebates which are allowed at different rates for different
modes under different plans.
Insurers allow some rebate on the premium for yearly and half–yearly mode. However
this rebate varies from plan to plan.
Dr. Amitabh Mishra

8. Dr. Amitabh Mishra

9.  There are three important elements in the
computation of premium. They are
Dr. Amitabh Mishra
Important
elements in the
computation of
premium
Mortality,
Expenses of
management,
Expected yield on
its investment.

10.  The mortality tables are prepared by the insurers on
the basis of their experience over a number of years.
 Though the rate of mortality increases with the increase
in age, all insurers charge a level premium which
remains constant over the entire duration of the policy
term.
 It is the actuarial science which provides the method to
assess such increasing risk and convert it into a level
premium.
Dr. Amitabh Mishra

11.  Any insurer has to incur expenses for conducting the insurance business.
 These expenses are not of constant nature. They keep on increasing due to
inflationary market conditions.
 Huge expenses are incurred for
◦ Procurement of new business,
◦ Payment of commission to the agent and
◦ Incidental expenses like preparation of policy document etc.
◦ Servicing of the policies, e.g.
 Collection of renewal premium,
 valuation to determine bonus payable,
◦ Payment of Survival Benefit and Death claim and Maturity Benefit etc.
Dr. Amitabh Mishra

12.  As the above two elements go to increase the
premium rate, the expected yield on investment of
the collected endowment component of premium
goes to reduce the premium rate.
 However, as the future yield cannot be determined
exactly, it is necessary for a prudent insurer to keep
a reserve to take care of unexpected fall in the rate
of yield.
Dr. Amitabh Mishra

13. Calculation of
Dr. Amitabh Mishra

14.  Net single premium is that premium which is
received by the insurer in a lump sum and is
exactly adequate, along with the return earned
thereon, to pay the amount of claim wherever it
arises whether at death or at maturity or even at
surrender.
 It does not provide for expenses of management
and for contingencies.
Dr. Amitabh Mishra

15. 1. Determine what constitutes a claim
(a) death, (b) survival or (c) both.
2. Determine when claims are paid
(a) at the beginning, (b) at the end, or (c) during the
year.
3. Determine the number of insured.
4. Determine the duration of the policy.
5. Determine the probable number of claims per
year.
Dr. Amitabh Mishra

16. Dr. Amitabh Mishra
6. Determine the value of claims per year.
7. Determine the number of years of interest
involved and find the present value of a rupee.
8. Determine the present value of the claim for
each year.
9. Determine the present value of all future
claims.
10. Determine the net single premium, (i.e.,
present value of future claims) divided by
number assumed for buying policy.

17.  The following factors are assumed while
calculating the net single premium.
◦ As many policy of a given type is issued as are the no. of person”
◦ Premiums are collected in advance or in the beginning of the
period.
◦ All collections are immediately invested and will remain
invested until money is needed for the payment of claims.
Dr. Amitabh Mishra

18. ◦ The insurer will receive an assumed rate of interest.
◦ The interest or dividend or any return of the invested
funds is immediately invested for re- earning.
◦ Mortality rate will be the same as given in the
mortality table and will he uniformly distributed
throughout the year.
◦ All policies are of the same amount, say, Rs. 5,000.
◦ Claims will be paid only at the end of the period.
Dr. Amitabh Mishra

19. Calculation of net single premium is different in
different types of policies
Dr. Amitabh Mishra

20.  This is the simplest type of insurance contract
whereby, payment is made only when the life
assured dies within the term specified.
 Nothing will be paid if death does not occur
during the designated term. This is also called
temporary insurance.
 The premium is received in advance and it will not
be returned if life assured survives.
Dr. Amitabh Mishra

21.  The premium is paid only once in a single sum at the
inception of the policy.
 Death claims will be paid at the end of the year in
which they occur and not at the end of the term.
 Thus the probability of death in each year along with
the present value, of the claim for each year will be
calculated because the death may occur at any moment
and the insurer may be required to pay.
The term may be
one, two, five or seven years.
Dr. Amitabh Mishra

22.  A person wants a term insurance is for a period of
5 years.
◦ Rate of return on investment is 3 per cent and the
mortality experience is like the one shown in the oriental
1953-54 Experience Life Table.
◦ The person is proposing at the age of 40 for the period of 5
years.
◦ Each person dead will be paid Rs. 1,000. The number of
details can be known from the table.
Dr. Amitabh Mishra

23. Dr. Amitabh Mishra
Age No. of person
living
No. of
death
Mortality rate per 1000
(No. of deathx1000)/
No. of person living
40 96463 273 (273x1000)/96463 = 2.83
41 96190 302 =3.14
42 95888 336 =3.50
43 95552 375 =3.92
44 95177 418 =4.39
45 94759 467 =4.03
Oriental 1953-54 Experience Life Table

24.  The insurer will earn a fixed return on the investment,
therefore, only the present value of the claim should be taken
as a premium. Thus, the net single premium for each year
will be calculated:
Dr. Amitabh Mishra
(Number of deaths x Amount of claims x Present value of Re. 1)
=
Present value of claims

25.  Where,
◦ P= The present value,
◦ S= The amount of which present value is to be calculated
◦ i = The rate of interest and
◦ n = The number of years for which present value is to be
calculated.
Dr. Amitabh Mishra

26.  The present value of the first year,
◦ S= Rs. 1, n = 1, & i = .03
 Present value for the 1st year of insurance P=
 The present value of the 2nd year,
◦ S= Rs. 1, n = 2, & i = .03
 Present value for the 2nd year of insurance P=
Dr. Amitabh Mishra

27.  The present value of the 3rd year,
◦ S= Rs. 1, n = 3, & i = .03
 Present value for the 3rd year of insurance P=
 The present value of the 4th year,
◦ S= Rs. 1, n = 4, & i = .03
 Present value for the 4th year of insurance P=
Dr. Amitabh Mishra

28.  The present value of the 5th year,
◦ S= Rs. 1, n = 5, & i = .03
 Present value for the 5th year of insurance P=
Dr. Amitabh Mishra

29. Dr. Amitabh Mishra
Year of
insura
nce
Age
Attain
ed
No. of
person living
No.
of death
Amount
claimed per
death
Present
value of
Rs1.0
Present Value of claims
4x5x6
1 2 3 4 5 6 7
1 40 96463 273 1000 .971
(273x 1000x .971)=
265083
2 41 96190 302 1000 .943
(302x 1000x .943)=
284786
3 42 95888 336 1000 .915
(336x 1000x .915)=
307440
4 43 95552 375 1000 .888
(375x 1000x .888)=
333000
5 44 95177 418 1000 .863
(418x 1000x .863)=
360734
Present value of all claims 1551043

30.  Present value of all claims = 15,51,043
 Total premium charged on all 96,463 policies (no. of living
person) = 15,51,043
◦ It was assumed that “as many policy of a given type is issued as are the no. of
person”
 Therefore, premium per policy= 1551043/96463
= Rs. 16.18/
Dr. Amitabh Mishra

31.  Thus, the present value of claim for the first year will be
273 x 100 x 0.971 = 265083 because the number of deaths
are 273 and the total amount of claim, so, would be
2,73,000. If multiplied by factor of present value it gives
present value of claim.
 Thus the net single premium will be the same whether
it has to be calculated on the basis of group policy or on
the basis of single policy; the probability method is
generally used for calculation of premium.
Dr. Amitabh Mishra