2. LIFE INSURANCE
• Life insurance is a contract between an
insurance policy holder and an insurer
where the insurer promises to pay a
designated beneficiary a sum of money in
exchange for a premium, upon the death of
an insured person (often the policy holder).
3. Purpose of life Insurance
Financial protection
Financial compensation.
To support family income of the insured
To cover personal loans and other debts.
The family of the insured and the creditors
will then be protected from loss of money.
To accumulate an educational fund
It will be used to pay tuition fees for children
when they join higher education.
4. Considerations in life insurance covering
death of the insured
1.The benefit is determined in advance
2.The amount of money required to pay the
death benefits are to be collected in advance
3.Each insured in the group must be charged
an appropriate premium.
4.The probability of claim increases with the
passage of time
5.In some cases the insured & policy owner
may be different
5. BASIC TYPES OF
LIFE INSURANCE CONTRACTS
1. Whole Life Insurance
Straight Life
Limited –pay
Single- pay
2. Term Insurance
Level Term Insurance
- Convertible
- Nonconvertible
Renewable Term
Decreasing Term
3. Endowment Insurance
6. 1. WHOLE LIFE INSURANCE
It is a type of life insurance contract that provides
insurance coverage of the contract holder for his or
her entire life.
Provides for the payment of the face value upon
death of the insured, regardless of when it occurs.
When the policy holder dies, the face value of the
policy, known as a death benefit, is paid to the
person or persons named in the life insurance
policy (the beneficiary or beneficiaries).
Whole Life Insurance contracts are classified as:
1. Straight Life
2. Limited- pay & 3. Single-pay Policies
7. 1. Straight Life Insurance (Ordinary Life Insurance).
– Premiums are to be paid at regular interval until the
death of the insured or until the age of 100 year
– If the owner still alive at age 100, the face amount of
insurance is paid to the policy owner at that time
2. Limited-Pay Life Insurance
– Premiums are paid for a definite period of time,
which is determined in advance
– That is for 10, 15, 20, 25, 30 years or up to age 65.
– After the expiration of the specified time, the policy
is said to be paid-up
3. Single Payment Life Insurance
– Here premium payment is made in one lump- sum
at the time of purchase of the whole life insurance.
8. 2. TERM INSURANCE
Provides compensation (death benefit) to the
beneficiary if the insured person dies within the
stated period mentioned in the policy.
If the insured survives beyond the specified time
limit in the policy, the policy will expire and there
will not be any payment made by the insurer.
Term policy gives only temporary protection and
there is no saving element involved.
9. Term contracts can be classified as:
1) Level Term Policy
– Provides a constant sum assured throughout the term of
the policy.
– For example, under a 15-year term policy of Birr 30,000,
the amount of payment to the insured will be Birr 30,000
if the insured dies at any time during the policy period.
– It can be convertible or nonconvertible.
2) Renewable Term Policy
– It can be renewed upon expiration
3) Decreasing Term Policy
– The amount of claims to be paid to the insured decreases
periodically
– The amount of death benefit decreases because the
chance of death increase with the age
10. 3. ENDOWMENT INSURANCE
– Under this policy payment is made if the insured dies
within the specified period; and if he survives to the end
of endowment period the amount is paid to the policy
owner at that time.
– The period of this policy is shorter than that for Whole Life
Insurance, and hence the premiums are higher for the same
age level.
– The shorter the endowment period, the higher the
premium.
11. ENDOWMENT ANNUITY
– This is a policy that provides retirement income to
the holder.
– It also incorporates protection during the term of
the policy up to the age of retirement.
– Monthly income of Birr 10 for each Birr 1,000 of the
face amount for the remaining life of the holder,
after maturity, with the guarantee that 120
monthly payments be made even if the holder dies
within that period; or
– Instead of monthly payment, a single cash
payment equal to the maturity proceeds, or a
combination of paid-up Whole Life insurance and
cash payment.
12. Term Insurance Endowment Insurance
Only provide
protection for the term
specified in the policy
document.
• Provide protection
along with investment
opportunity.
They offer just the
death benefits.
• They offer death as well
as maturity benefits.
• The premium charged
by term insurance
plans is much less than
the endowment plans.
• The premiums payable
for endowment plans
are more expensive
than term plans
13. PREMIUM DETEMINATION
Types of premiums:
Net Premium
– This is a premium rate determined on the basis of
mortality rate and interest rate only.
– It does not include the operating costs charged by the
insurer.
– Net premium provides the insurer only with the amount
of money required to pay death claims.
Net Single Premium (NSP): It is PV of the future death benefit
– When the total net premiums of an insurance policy are
to be paid as a single sum at the beginning of the
contract, it is called the Net Single Premium.
Net Level Premium
– This is a premium charge that does not change from year
to year throughout the term of the policy.
14. Gross Premium
– When a portion of all the insurer’s costs of running the
business are added to the Net Premium, the resultant
premium is called the Gross Premium.
– The addition of the insurer’s costs of doing business to
the Net Premium is called Loading.
– These costs include operating expenses, commissions,
advertisement expenses etc.
15. Net Single Premium (NSP)
• The net single premium (NSP) is defined
as the present value of the future death
benefit
• The NSP is based on three assumptions:
– Premiums are paid at the beginning of the
policy year
– Death claims are paid at the end of the policy
year
– The death rate is uniform throughout the year
16. Net Single Premium Example:
•The following information is required to determine the net
single premium.
– Age and sex of insured’s.
– Mortality rate.
– Interest rate.
– Amount of insurance policy.
Example:
According to the 1980 CSO mortality table, out of an initial
population size of 1,000,000 male people 958,000 live at age 30.
The number of people expected to die at the age is 1,657. This
means that the probability that a person aged 30 will die
during that age will be
0.00173 = (1,657/958,000)
17. Assume that an Insurer issued one-year Term Insurance to
all these male individuals aged 30 (958,000 policies) for
death benefit of Birr 5,000 each.
Assume also that the premium is to be collected at the
beginning of the policy issue, and the death benefit
(policy amount) is to be paid at the end of the year.
Also assume that the interest rate is 10%. Each the insured
persons are assumed to bring the same level of risk to
the group.
Accordingly, expected amount of death benefits becomes Birr ,
1657*5000= 8,285,000
This is the amount that the insurer expects to pay for death
claims at the end of the year, i.e. upon maturity of the Term
Policy.
18. Steps to determine Net Single premium
1. Determine the PV of Birr 8,285,000
PV = FV/(1+i)n
PV = = 7,531,818.18
2.Divide the PV by the number of insured to arrive at the
NET SINGLE PREMIUM.
NSP = = Birr 7.862
Every Insured will have to pay NSP of Birr 7.862 at the
beginning of the Term policy. The Insurer will, then, collect a
total of Birr 7,531,818.18 which will grow to Birr 828,500 in one
year time at 10%
)
10
.
1
(
000
,
285
,
8
958,000
18
7,531,818.
19. TERM INSURANCE
With the above example as a background, let us try to
determine the Net Single Premium for a Term policy.
Consider the following information:
3- Year term policy for Birr 5,000 to be issued at the beginning of
the year.
Number of policy holders at age 30 is 958,000
Interest rate is 10%
Single premium payment at the beginning of the year.
Death claims to be paid at the end of the year in which the
incident occurred.
CSO, 1980 mortality rate.
20. Year Age Number
Living
Number
Dying
Probability of
Dying
1
2
3
30
31
32
958,000
956,343
954,640
1,657
1,702
1,747
0.00173
0.00178
0.00183
CSO MORTALITY RATE, MALE, 1980
Expected death claims
Year Age Number
Dying
Amount of
policy
Expected Death
Claim
1 30 1,657 5,000 8,285,000
2 31 1,702 5,000 8,510,000
3 32 1,747 5,000 8,735,000
Total Expected Death Claims = 25,530,000
21. Present value of Total claims
1
Yr
2
Death
Claims
3
PV
Factor at
10%
4 = (2*3)
PV of
Claims
5
No. of
Insured
6
(4/5)
Annual
Net Prem
1 8,285,000 0.9091 7,531,893.5 958,000 7.862
2 8,510,000 0.8264 7,032,664 958,000 7.341
3 8,735,000 0.7513 6,562,605.5 958,000 6.850
25,530,000 21,127,163 22.053
22. So each Insured must pay in advance the sum of Birr 22.053 for
three years protection. It helps the insurer to meet the expected
death claims that occur in each year
1
Yr
2
Beg Bal
3
Int 10%
4 = (2 + 3)
B.B + Interest
5
Death Claims
6= (4 – 5)
End Bal
1 21,126,774* 2,112,677.40 23,239,451.40 8,285,000 14,954,451.4
2 14,954,451.4 1,495,445.14 16,449,896.54 8,510,000 7,939,896.54
3 7,939,896.54 793,989.66 8,733,886.20 8,735,000 -1113.80*
23. ACTURIAL NOTATIONS: -
T = time (years)
X = age
Lx = number of people living during age x.
(Lx – Lx +1) = dx = number of people dying during age x.
(Dx/Lx) = px = probability of dying during age x.
(Lx+1/Lx) = qx = Probability that an individual at age x.
Survives age x.
Formula to determine Net Single Premium:
T
r
Lx
T
dx
s
r
Lx
dx
S
r
Lx
dx
S
NSP )
1
(
/
1
(
2
)
1
(
/
1
(
)
1
(
)
/
(
25. NET LEVEL PREMIUM
Instead of paying a single premium at the beginning of the
policy, the policyholders want to pay annual premiums of
equal size.
Here there are two points to consider.
1.Not all the policyholders will pay the annual level premiums
since some of them are expected to die before the end of the
term.
2.The insurer is now collecting limited amount of premiums to
invest at the beginning of the policy.
Accordingly, the total annual level premiums paid by a
policyholder will be greater than the single premium paid at
the beginning of the policy.
This equal annual premiums paid by a policy-holder is then
called NET LEVEL PREMIUM.
26. Yr Age
No. of insured
Paying premium
PV of $ 1 payable
Beginning of year
PV of $ 1
Premium
1 30 958,000 1 958,000
2 31 956,343 0.9091 869,411
3 32 954,640 0.8264 788,915
TOTAL PV 2,616,326
NLP- EXAMPLE
27. The following table shows the amount of Net Level Premiums to be
collected and the expected death claims to be paid each year.
1
Yr
2
Annual
LP
3
Total Prem
Collected
4 =(3 + 7)
Beg Bal
5
B.B Invested
at 10%
6
Death
Claims
7
Ending
Balance
1 8.075 7,735,850 7,735,850 8,509,435 8,285,000 224,435
2 8.075 7,722,470 7,946,905 8,741,596 8,510,000 231,596
3 8.075 7,708,718 7,940,314 8,734,345 8,735,000 -655*
28. Personal Accident Policy
It provides compensation for death or bodily
injuries caused by violent, accidental, external and
visible means.
The injuries shall be the direct cause of death, loss or
disablement.
In the event of death of the insured, the benefit is to
be given to his representative.
Death or disablement should occur within 12
calendar months from the date of the accident.
29. Worker’s Compensation Policy
This policy indemnifies the insured against all sums for
which he is to be liable to pay compensation for any worker
who sustains death or bodily injury by an accident or
occupational diseases arising from his work and during the
time of his work.
The worker should be employed by the insured, and the
category of work assigned to him and the place of work
should be specified in the Schedule.
The policy does not provide compensation for death or
disablement resulting from suicide attempted suicide or
intentional self-injury
