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…