‫كلية التجارة‬
‫جامعة طنطا‬
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Name: Rana Moustafa Ibrahem Elgamal
BIS Level II.2020
Course: Insurance
Course number: COM210
Student ID: 2172
Dr: Ahmed Abd Elfatah & 
DR :sayed Matwally
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Research title Topic 1 : If you are the Risk manager in faculty
of commerce- Tanta University prepare the steps number 1&2 of
Risk management program. (b) Contracts that cover survival risk:
Type of contracts and basic formulas for computing net single
premiums (NSP), with illustrated examples.
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Identifying potenial losses 
The first step within the risk management losses is to spot all
major and minor loss exposures :
1. Property loss exposures
 Building plants, other structures .
 Fumiture equipment, supplies .
 Company planesboats ,mobile equipment .
 Computers ,computer software and data .
 Accounts receivable ,valuable papers and records .
2. ILiability loss exposures :
 Defective products
 Liability arising from company vehicles.
 Sexual harassment of employees, discrimination
 Environmental pollution (land ,water air, noise
 against employees ,wrongful termination
 Premises and general liability loss exposures
 Misuse of the web and e-mail transmissions , tranomissions of
pomographic material
 Directors 'and officers' liability suits .
3. Human resources loss exposures :
 Death or disability of key employees
 Job- related injuries or disease experienced by workes
 Retirement or unemployment
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4. Business income loss exposures :
 Loss income from a covered loss
 Contingent l business income loss
 Continuing expenses after a loss Extra expenses .
5. Crime loss exposures :
 Employee theft and dishonesty
 Holdups robberies ,burgiaries
 Fraud and embezzlement
6. Foreign loss exposures :
 Foreign currency risks
 Kidnapping key personnel
 Political risks
 Plants, business property, inventory
 Acts of terrorism
7. employee henefit loss exposures:
 Group life and health and pension plan expore
 Violation al of fiduciary responsibilitie
 Failure to ccomply with government regulations
 Failure to pay promised benefits
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8. Reputation eue and public image of the corporate
Sources of data which will be wont to identify loss exposens Several
sources of data are often wont to identify potential they're as follows:
 Physical inspection :
A Physical inspection of company plants and operations can major and
minor loss exposures .
 Financial statements loss of income exposures, and key customers
and be protected, suppliers. analysis of monetary statements can
identify the main assets
 Risk analysis questionnaires questionnaires require that the danger
manager to anowg questions that identify major and minor loss
exposures .
 Flowcharts:
Flowcharts which will show the flow of production and delivery can
production bottlenecks where a loss can have severe financial
consequences for the firm .
 Historical loss data identifying major loss exposures. historical and
departmental loss data over time are often invaluable In additional,
risk managers must know industry trends and market changes that
can creates new loss exposures and cause Analyze the loss exposures
. This step involves an estimation of frequency and severity of loss.
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 Loss frequency refers to the probable number of losses which will occur
during some given period of time.
 Loss severity refers to the probable size of the losses which will occur .
 Once the danger manager estimates the frequency and severity of loss
exposures, the various loss exposures can be ranked according to their
relative importance .
Example:
A loss exposure with potential for bankrupting the firm is much more important
than an exposure with a small loss potential , In addition the relative frequency
and severity of each loss exposure must be estimated so that the risk manager
can select the most appropriate technique , or combination of techniques for
handling each exposure
Basie sorts of life assurance :
Life insurance companies have made available many sorts of life assurance
contmcts (policies) to satisfy individual needs. However, there are only four basic
sorts of life assurance contracts:
 Pure endowment contracts.
 Whole life assurance
 insurance
 life insurance Every life assurance contract is one among these four kinds
or may be a combination of them.
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The protection offered by any sort of life assurance contract can also be deferred
la to a future date.
 Pure endowment contracts :
A pure endowment contract provides that the face value of the contract are going to
be paid if the purchaser of the pure endowment survives to the top of the contract
term. However, no payment is formed to him or her if the purchaser dies during the
amount .
Example:
A person is 30 years of age and wishes to purchase a pure endowment policy
that will pay 10.000 dollar when age 65 is reached . Find the net single premium
of the policy ?
The present value ( at age 30 ) is divided among the group of 9480358 persons
A simpler way to compute the net single premium of a pure endowment policy is
to apply following formula
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nEx =
𝑫𝒙+𝒏
𝑫𝒙
- let nEx = the net single premium of a 1 $ , N year , puer endowment contract
for each annuitant at age X
- The contract will pay 1 $ to each annuitant at the end of n years or at age
X + N If the annuitant is still living .
Dx and Dx+n are symbols whose values are listed in table
Proof – Formula : Pure endowment Contract
Let Ix represent the number of persons at age x . Each of them wants to buy
a pure endowment policy of 1 $ payable at age x + n if he or she is then alive
The diagram . which is similar to that of example 1 , may be arranged
symbolically as follows :
let nEx = the net single premium of a 1 $ , N year , puer endowment contract for
each annuitant at age X . The contract will pay 1 $ to each annuitant at the end of
n years or at age X + N If the annuitant is still living .
Then
nEx =
𝐿𝑥+𝑛( 1+𝑖 )−𝑛
𝐿𝑥
Let v = (1 + 𝑖)−1
VR= (1 + 𝑖)−𝑛
Then
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nEx =
nEx =
nEx =
𝑉𝑅𝐿𝑥+𝑛
𝐿𝑋
, multiply both the numerator and the denominator by V
𝑉𝑅+𝑛𝐿𝑥+𝑛
𝑉𝑅 𝐿𝑋
𝐷𝑋+𝑁
𝐷𝑋
DX represent the value of VXIX for convenience in writing .
Example:
Refer to example 1 solve using formula :
nEx =
𝑫𝒙+𝒏
𝑫𝒙
X=30 . N = 35
The net single premium for a 1 $ payment to each annuitant at age 65 is :
E = E = 𝑫𝒙+𝒏 = 𝑫𝟑𝟎+𝟑𝟓 = 𝑫𝟔𝟓 𝟏𝟑𝟑𝟔𝟏𝟐𝟖.𝟓𝟒𝟔𝟐 = 0.302261
=
n x 35 30
𝑫𝒙
𝑫𝟑𝟎
𝑫𝟑𝟎
𝟒𝟓𝟏𝟗𝟔𝟗𝟎.𝟑𝟕𝟓𝟏
For a 10.000 $ payment , the net single premium is :
0.302261 * 10000 = 3022.61 $
I. WHOLE LIFE ANNUITIES a A Glads
Life annuities are generally classified into two major groups Whole life annuities
Temporary life annuities.
A: whole life annuity is: a contract under which an insurance company will pay
annuitant a given sum periodically for life, ceasing y with the last payment
preceding the annuitant's death.
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X
The purchase price of a whole life annuity depends on the age of the annuitant and the time of the first payment made
to the annuitant.
• When the first annual payment is made one year after the date of purchase, the
annuity is called : an ordinary whole life annuity slo, or an immediate whole life
annuity.
• When the first annual payment is made at the time of purchase, it is called a:
whole life annuity due .
• If the first payment begins after a period of more than one year has elapsed , it
is called: a deferred a whole life annuity.
Ordinary Whole Life Annuity :
net single premium of an ordinary whole life annuity dinary whole life annuity of
$1 payable at the end of each year.
let a = the net single premium. or the present value, of an for a person whose age
now is x years .
ax =
then
𝑁𝑋+1
𝐷𝑋
Example:
Find the net single premium of an ordinary whole life annuity of $1 payable at the
end of each year for a person aged 95 years. The first payment will be made one
year later (or when the age of 96 is reached).
Assume that the 1958 CSO Table is used interest rate is 2.5%
A=
9
𝑁96
𝐷95
=
11610.1087
= 1.24765 or 1.25 $
9305.5630
Example:
A person aged 35 wishes to purchase an ordinal whole life annuity that will pay,
$1000 at the age of 36 and the same Amount at the end of each year thereafter for life.
Find the net single premium of the annuity. purchase, the contract interest rate is
assumed to be 2.5% Since the first payment is to be made one year after the date of
is an ordinary whole life annuity.
x = 35, R $1,000 Substituting the above values in formula
A=𝑅
𝑁𝑋+1
𝐷𝑋
=𝑅
𝑁35+1
𝐷35
= 1000 ∗
𝑁36
= 1000 ∗
89956987.56
𝐷35
= 22.774 $
3949851.09
The payments thus form a whole life annuity due with
1. It is the period from the date of purchase to the date of the first the term
beginning on the date of the first payment. The period of deferment may be
expressed in two ways: purchase period of more than one year has elapsed from
the date of The first payment of a deferred whole life annuity begins after a
Deferred whole Life Annuity due with the term beginning on the date of the first
payment
2 - is the period from the date of purchase to the date that is one prior to the date
of the first payment. the payments thus form ordinary whole life annuity. For
convenience. the period of deferment is expressed from the of purchase to the
date of the first payment (item 1 above).
For example, if a person aged 60 buys a whole life annuity with first payment to be
made at 65 years of age, the period of deferment is considered to be five years. The
annuity is a deferred whole life annuity due. with the term beginning at age 65.
Let k= the period of deferment in years
K ӓX = the net single premium, or the present value. of a deferred annuity of $1 per
year for life, with the first payment at the end of the deferment period. k years, for
a person now aged x yearsThen
K ӓX =
10
𝑁𝑋+𝐾
𝐷𝑋
Let A(defer) the net single premium, or the present value, of a whole life annuity
that will pay R per year after k years Then
A(defer) = R * K ӓX = R *
𝑁𝑋+𝐾
𝐷𝑋
Example 6 :
A person aged 25 wishes to purchase a whole life annuity that will pay 3000 $ a
year for life . the first payment is due at age 65 . find the net single premium of the
annuity .
The period of deferment k = 65 -25 = 40 year and x = 25 and R = 3000 $ substituting
the values in formula : R . K ӓX
A(defer) = 3000 *
𝑁65
𝐷25
= 3000 *
15077832.60
= 8757.68 $
5165077.95
TEMPORARY LIFE ANNUITIES :
When the payments of a life annuity cease at the end of a certain number of years, even though
the annuitant is still living, the annuity is called a temporary life annuity Like whole life annuities,
temporary life annuities may be classified depending upon the date of the first payment as:
* Ordinary.
* Due.
* deferred.
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Ordinary Temporary Life Annuity :
The first annual payment of an ordinary temporary life annuity is made one year after the date
of purchase. Thus, if a person now aged 47 purchases an ordinary temporary life annuity, The
first annual payment of an ordinary temporary life annuity is annual payment will be made to
him at +1 years of age.
Let n = the number of payments
the net single premium, or present value, at age x of an ordinary temporary life annuity of $1
payable each year for n annual payments .
ax n =
𝑁𝑋+1−𝑁𝑋+𝑁+1
𝐷𝑋
Let A(tem.) net single premium, or present value, of an ordinanry temporary life
annuity that will pay R Per year Then
A (tem.) = R ax n = R *
𝑁𝑋+1−𝑁𝑋+𝑁+1
𝐷𝑋
Example:
What is the net single premium of a five-year ordinary temporary life
annuity of $2,000 per year for a person aged 20 if the first payment is to
be made at age 21 ?
X = 20 , n = 5 , R = 2000 $
A (tem.) = R ax n = 2000 *
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𝑁20+1−𝑁20+5+1
𝐷20
= 2000 *
𝑁21−𝑁26
𝐷20
= 2000 *
161928780.91−134674488.96
5898264.97
= 9241.46 $
REFERNCE :
 https://www.negotiations.com/definition/
 https://economictimes.indiatimes.com/what-is-anendowment-policy-and-when-should-you-go-forit/tomorrowmakersshow/48465113.cms
 YouTube lecture.
 Principles of risk and insurance for Dr Ahmed
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