PREMIUM CALCULATION
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Transcript of PREMIUM CALCULATION
PREMIUM CALCULATION
Presented by:
Juhi Sharma
Rajat Gupta
Deepak Singh
Definition:
INSURANCE PREMIUM:
The periodic payment made on an insurance policy also called premium.
OR
Financial cost of obtaining an insurance cover, paid as a lump sum or in installments during the duration of the policy, called as Insurance Premium.
METHODS OF CALCULATION OF PREMIUM
METHODS
1). VALUE OF SERVICE: Premium according to the utility of insurance to each proponent. But cant be used due to impracticability.
2). COST OF SERVICE:
The premium should be charged according to the cost (include all expenses and profit margins) to the insurer.
TYPES OF PREMIUM
NET PREMIUM: The net premium makes provision for mortality losses only or the premium which is received to pay the amount of claim whenever it arises at death or at maturity or surrender. It does not provide for expenses of management.
GROSS PREMIUM:
The gross premium is that premium which is charged by the insurer to meet the amount of claims and expenses. Thus gross premium includes the net premium and loading.
PREMIUM SUB DEVIDED IN TO TWO PARTS
PREMIUM
1.SINGLE PREMIUM
2. LEVEL PREMIUM
Steps for Calculation of Premium
Determine what constitute a claim (a) death, (b) survival (c) Surrender
Determine when claim are paid
(a) at the beginning, (b) at the end, (c) during the year.
Determine the number of insured. Determine the duration of the policy. Determine the probable number of claims per year. Determine the value of claim per year. Determine the number of years of interest involved
and find the present value of a rupee. Determine the present value of the claim for each
year. Determine the present value of all future claims. Determine the net single premium (i.e., present
value of future claims) divided by number assumed for buying the policy.
Calculation of single premium
Term Insurance Whole life Premium Pure endowment Policy Ordinary endowment Policy
Net single Premium for 5-year Term PolicyYear of Insurance
Age attained
Number of Living
Number of Death
Amount of claims of Death
Present value of Re.1.0
Present value of claim4*5*6
1 2 3 4 5 6 7
1 40 96463 273 1000 0.971 2,65,083
2 41 96,190 302 1000 0.943 2,84,786
3 42 95,888 336 1000 .915 3,07,440
4 43 95,552 375 1000 0.888 3,33,000
5 44 95,177 418 1000 0.863 3,60,734
Net single Premium for Whole Life PlanAge Probability of
deathPolicy amount
Present value of Rs. 1 @ 2.5%
Present value of the claim
45 7340/852554 1000 0.975610 8.399441
46 7801/852554 1000 0.951814 9.039243
: : : : :
99 125/852554 1000 0.257151 0.037703
Total Single Premium:- Rs.551.372587
Net single premium in pure endowment policyProbability of survival
Policy amount
Present value of Rs. 1 for the endowment period
= Net single premium
0.981 1000 0.863 = 846.603
Net single premium in Ordinary endowment policyDescription Premium
Net single Premium on the basis of death for 5-years
Rs.16.18
Net single Premium on survival at the end of 5-years
Rs.846.60
Net single Premium on the basis of death and survival rate
Rs.862.78
Annuities
Net single premium in Annuities
Immediate annuity Life Annuity Term Annuity
Deferred Annuities
Minimum payment Annuity
Annuity due
Calculation of Net Single premium in life annuityAge Probability of
survivalAmount of annuity
Present value of Rs.1 @ 3%
Present value of annuity
95 97/249 1000 0.971 94187/249
96 30/249 1000 0.943 28290/249
97 6/249 1000 0.915 5490/249
98 1/249 1000 0.888 888/249
99 0/249 1000 0.863 0/249
Total Premium
Rs.517
Calculation of Net Single premium for term annuity
Age Probability of survival
Amount of annuity
Present value of Rs.1 @ 3%
Present value of annuity
71 553332/577445 1000 0.975610 934.87
72 528443/577445 1000 0.951814 871.04
73 502843/577445 1000 0.928599 808.63
74 476611/577445 1000 0.905951 747.75
75 449841/577445 1000 0.883854 688.54
Present value of total amount
Rs.4050.79
Deferred Annuity
Age Prob. of survival of 100,000 persons
Amount of Annuity
Present value of Rs. 1 @ 2.5%
Present value of Annuity
40 Year of contract
__ After 30 years __
70(deferred date
2000/100000 1000 0.477 9.540
71 1000/100000 1000 0.465 4.650
72 500/100000 1000 0.454 2.270
Total Rs. 16.46
Level Premium The single premium of a given policy can
be easily converted into level premium by establishing ratio between net level premium and net single premium
The ratio will differ according to the age at the beginning, nature and duration of the policy
Calculations of Level PremiumsYear of Insurance
Age No of persons living
No of premium received
Amount of premium received
Present value of re 1 @ 3%
Present value of premium received
1 40 96463 96463 96463 1000 96463
2 41 96190 96190 96190 0.971 93400
3 42 95880 95880 95880 0.943 90415
4 43 95552 95552 95552 0.915 87430
5 44 95177 95177 95177 0.888 84517
Total present value
4,52,225
Method of loading
Constant addition loading Percentage addition loading Modified percentage loading Constant and percentage addition method
What Is An Actuary
The actuary is an individual who will analyze important data such as mortality, sickness, injury and disability rates and use that information to aid those involved with insurance. An actuary is responsible for collecting the data to forecast future risks and see how these predictions will affect various aspects of insurance
Specific Duties of an Actuary
Review a variety of documents (Statistical) Insurance plans Annuity plansPension plansMortalityDisabilitySickness and AccidentsContracts and company policies
Traits Which All Actuaries Should Possess
Wonderful mathematical skills Good analytical skills Creativity Research skills good computer skills
THANK YOU…