this is the five chapter of finance and banking

this is the finance & banking chapter slideshow.

1. CALCULATION OF PREMIUM LECTURE – 5

2. What is Premium? Premium means an amount or money to be paid regularly for an insurance policy. – Oxford Advanced Learners Dictionary. Insurance premium means annual payment made by a person or a company to an insurance company.- P.H. Colin

3. Types of Premium Net Premium Net premium is the resultant amount after the gross premium is adjusted for the expenses related to the maintenance of insurance policies. The net premium of a policy does not consider future expenses associated with maintaining the insurance policy.

4. Net Premium It is sometimes called a benefits premium. Net premium also helps to determine the amount of state taxes owed by insurance companies. The net premium is based on the mortality and interest rates.

5. Gross Premium Gross premium is the amount expected to be received by the insurer over the life of the policy term. The gross premium is the amount the insured pays for an insurance policy that is not the amount the insurance company actually earns for writing the policy.

6. Gross Premium Gross premiums are typically adjusted upwards to account for commissions, selling expenses like discounts, and other insurer expenses. The gross premium depends upon the mortality rate, the assumed interest rate, the expenses and the bonus loading.

7. Single Premium: It is paid in one lump sum amount. Level premium: It is paid periodically in installments.

8. Net Single Premium 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. - M.N.Mishra PV of NCBs – PV of NCOs = 0

9. Steps for Calculation of Net Single Premium Determine the cause of claim – death , survival or both. Determine the time of claims payment – at the beginning of the year , at the end of the year or during the year . Determine the number of insured. Determine the duration of the policy Determine the probable number of claims per year.

10. Steps for Calculation of Net Single Premium 6. Determine the value of claims per year 7. Determine the number of years of interest involves and find the present value of a Taka. 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.

11. Assumptions underlying the Calculation of Net Single Premium 1 . As many policies of given type are being issued as are the number of persons. 2. Premiums are collected in advance or in the beginning of the period. 3. All collections are immediately invested and will remain invested until money is needed for the payment of claims.

12. Assumptions underlying the Calculation of Net Single Premium 4. The insurer will receive an assumed rate of interest. The assumed rate should be conservative to avoid future decline in interest rate. 5. The interest or dividend or any return of the invested funds is immediately invested for re-earning.

13. Assumptions underlying the Calculation of Net Single Premium 6. Mortality rate will be the same as given in the mortality table and will be uniformly distributed throughout the year. 7. All policies are of the same amount, say Rs. 1,000. 8. Claims will be paid only at the end of the period.

14. Calculation of Net Single Premium : Term Insurance Example Calculate the net single premium of a 5-year term insurance policy with the help of the following mortality table. Assume that the rate of return on investment is 3 percent and that each person dead will be paid Tk. 1000 claim.

15. Mortality Table Year of Insurance Age Number of Living Number of death 1 21 99,800 2,994 2 22 99,500 3,980 3 23 99,102 4,955 4 24 98,606 5,716 5 25 96,512 6,125

16. Mortality Table Year of Insurance Age Number of Living Number of death 1 21 99,800 2,994 2 22 99,500 3,980 3 23 99,102 4,955 4 24 98,606 5,716 5 25 96,512 6,125

17. Net Single Premium for 5-year Term Policy Year of Insurance Age Number of Living [Policy holders ] Number of death [Policy holders ] Amount of claims per death Present Value of Tk. 1 @ 3% PV Amount of Claim 4x5x6 1 2 3 4 5 6 7 1 21 99,800 2,994 1,000 0.971 29,07,174 2 22 99,500 3,980 1,000 0.943 37,53,140 3 23 99,102 4,955 1,000 0.915 45,33,825 4 24 98,606 5,716 1,000 0.888 50,75,808 5 25 96,512 6,125 1,000 0.863 52,85,875 Total 2,15,55,822

18. Total premium to be paid on all 99,800 living policy holders at the beginning of the year is Tk 2,15,55,822 Therefore, Premium per policy is Tk 2,15,55,822 / 99,800 = Tk. 215.9902

19. Net Single Premium for 5-year Term Policy Alternative Method Year of Insurance Age Probability of deaths in units Amount of claims per death Present Value of Tk. 1 PV Amount of Claim 4x5x6 1 2 4 5 6 7 1 21 2,994 /99,800 = 0.03000 1,000 0.971 29.1300 2 22 3,980/99,500 =0.04000 1,000 0.943 37.7200 3 23 4,955/99,102 =0.04999 1,000 0.915 45.7408 4 24 5,716/98,606 =0.05796 1,000 0.888 51.4684 5 25 6,125/96,512 = 0.06346 1,000 0.863 54.7659 Total 218.8251

20. Net Single Premium in Whole Life Policies The whole life policy continues for the whole of life and promise to pay the sum assured upon the death of the insured to his beneficiary. The general assumption of the most of the mortality table is that life will continue upto 100 years. Thus, the whole life policy assumes that the assured person may live 100 year.

21. Net Single Premium in Whole Life Policies Therefore, the calculation of premium will start from the date of commencement of risk to the 100 th year. If a person takes a policy at age 45, the calculation will continue until 100 th year.

22. Example Calculate net single premium for a whole life insurance policy with the following mortality table. Assume that the present value factor is 4% and the claim of each whole life insurance policy is Tk. 10,000.

23. Mortality Table Age Number of Death Claim per policy 55 830 10.000 65 975 10.000 75 290 10.000 85 1428 10.000 95 1346 10.000 96 1281 10.000 97 1157 10.000 98 1064 10.000 99 993 10.000 100 636 10.000

24. Calculation Method # 1 Age (1) No. of Living per year (2) No. of Death per year (3) Policy amount (4) Present value of Tk 1 @ 4% (5) Present Value of the claim (6) 3x4x5 55 10,000 830 10,000 0.962 79,84,600 65 9.170 975 10,000 0.676 45,63,000 75 8,195 290 10,000 0.377 10,93,300 85 7,905 1428 10,000 0.308 43,98,240 95 6,477 1346 10,000 0.206 27,72,760 96 5,131 1281 10,000 0.198 25,36,380 97 3,850 1157 10,000 0.190 21,98,300 98 2693 1064 10,000 0.183 19,47,120 99 1,629 993 10,000 0.176 17,47,680 100 636 636 10,000 0.169 10,74,840 Total PV of Total Claim of the Whole Life Policy Tk. 3,03,16,220

25. Net Single Premium of the Whole Life Policy =PV of Total Claim of the Whole Life Policy / Number of Policy holders at the beginning. = Tk. Tk. 3,03,16,220 / 10,000 = 3031.622

26. Calculation Method # 2 Age Probability of Death per policy Policy amount Present value of Tk 1 @ 4% Present Value of the claim 55 830/10000=.083 10,000 0.962 798.46 65 975/10000=.0975 10,000 0.676 659.10 75 290/10000=.029 10,000 0.377 109.33 85 1428/10000=.1428 10,000 0.308 439.824 95 1346/10000=.1346 10,000 0.206 277.276 96 1281/10000=.1281 10,000 0.198 253.638 97 1157/10000=.1157 10,000 0.190 219.83 98 1064/10000=.1064 10,000 0.183 194.712 99 993/10000=.0993 10,000 0.176 174.768 100 636/10000=.0636 10,000 0.169 107.484 Total Net Single Premium of the Whole Life Policy 3234.412 /3031.622

27. Calculation of Net Single Premium for 5 -year Pure Endowment Policy (PEP) Net Single Premium for PEP = Probability of survival X Policy Amount X Present Value of Taka 1 for the endowment in 5 th year @ 3% = (1.000-.083) x 10,000 x 0.863 = 0 .917 x 10,000 x 0.863 = Tk. 7,913.71

28. Calculation of Net Single Premium in Ordinary Endowment Policy (OEP) of 5 years OEP is the net single premium on the basis of death and survival rate of policy holders. Thus, Net Single Premium for OEP = Net single premium on the basis of death for 5 years / Net single premium for 5-year Term Policy + Net single premium on the basis of survival rate at the end of 5 years / Single premium for 5-year Pure Endowment Policy. NSP for OEP = 215. 9902 + Tk. 7,913.71 = Tk. 8,129.7002

29. Calculation of Net Single Premium in Double Endowment Policy (DEP) for 5 years Net Single Premium in Double Endowment Policy (DEP) for 5 years = Net Single Premium for OEP for 5years + Single premium for 5-year Pure Endowment policy. = Tk. 8,129.7002 + Tk. 7,913.71 = Tk. 16,043.4102

30. Calculation of Net Annual Premium for General Endowment Policy for 5 years Age Number of persons insured Number of annual deaths 41 24,847 2,428 42 22,419 3,157 43 19,262 3,739 44 15,523 3,286 45 12,237 4,235 Calculate the net annual premium for a Tk. 5,000 5-year general endowment policy with the help of the following mortality table at 5% rate of interest :

31. Calculation of PV of Claims of dead insured Year Age No. of living No. of annual death Clam amount Total death claim PV of Tk 1 @5% PV of death claims 1 2 3 4 5 6 =4x5 7 8 1 41 24847 2428 5000 1,21,40,000 0.9524 1,15,62,136 2 42 22419 6157 5000 3,07,85,000 0.9070 2,79,21,995 3 43 19262 3739 5000 1,86,95,000 0.8638 1,61,48,741 4 44 15523 3286 5000 1,64,30,000 0.8227 1,35,16,961 5 45 12237 4235 5000 2,11,75,000 0.7835 1,65,90,613 Total Tk. 8,57,40,446

32. Calculation of PV of Claims of living insured persons after maturity No. of insured persons living after maturity of the Policy : 12237 - 4235 = 8002 persons. Total value of claims of insured living persons : 8002 x 5000 = Tk. 4,00,10,000 PV of total claims (Dead and Living) = Tk. 8,57,40,446 + Tk. 4,00,10,000 = TK. 12,57,50,000

33. Calculation of PV of Total insurance claim taking Tk. 1 annual claim payable Year Age No. of living at the beginning of the year Receivable premium with Tk. 1 claim amount PV of Tk 1 @5% PV of death claims 1 2 3 4 7 8 1 41 24847 24847 0.9524 23664.2828 2 42 22419 22419 0.9070 20334.0330 3 43 19262 19262 0.8638 16638.5156 4 44 15523 15523 0.8227 12770.7721 5 45 12237 12237 0.7835 9587.6895 Tk. 82,995.293

34. Calculation of Net Annual Premium [NAP] for a 5 year General Endowment Policy @ 5% NAP = PV of total claims ( Dead and Living) / PV of Total insurance claim taking Tk. 1 annual claim payable = TK. 12,57,50,000 / Tk. 82,995.293 = Tk. 1,515.146

35. Calculation of Net Annual Premium[NAP] for a 5 year Pure Endowment Policy @ 5% Net Annual Premium [NAP] = PV of total claims of Living Policy holders / PV of Total insurance claim taking Tk. 1 annual claim payable = Tk. 4,00,10,000 / Tk. 82,995.293 = Tk. 482.0755 Note: Here only living policy holders at the end of the policy period will get the claim amount. Dead policy holders will not get.

36. Net Single Premium in Annuities An annuity is a contract whereby for a cash consideration (premium) one party (the insurer) agrees to pay the other ( the annuitant ) a stipulate sum ( the annuity) throughout life or during the life within a fixed term, annually, is to protect a hazard, the outliving of one’s income.

37. Example : A policy is to be issued for an immediate annuity of Tk. 1000 to be paid annually at the age of 70. The rate of interest would be 5% and the following mortality table would be used for calculating the net single premium to be paid.

38. Calculation of Net Single Premium for an Immediate Life Annuity. Year Age Probability of Survival Amount of annuity PV of Tk 1 @5% PV of death claims 1 2 3 4 7 8 1 70 520/ 847=0.6139 1000 0.9524 584.6784 2 71 320/ 847=0.3778 1000 0.9070 342.6646 3 72 120/ 847=0.1417 1000 0.8638 122.3802 4 73 2/ 847=0.0023 1000 0.8227 1.8922 5 74 0/ 847 = 0.00 1000 0.7835 0.0000 Net Single Premium for an Immediate Life Annuity = Tk. 1051.6154

39. Net Single Premium for Temporary (Term) Annuity The process of calculating the premium will consider a fixed period only. Example : A policy is to issued for an annuity of Tk. 1000 to be paid annually at the age of 65 and continues up to 5 years. The rate of interest would be 5% and the following mortality table would be used for calculating the net single premium to be paid.

40. Calculation of Net Single Premium for a Term Life Annuity. Year Age Probability of Survival Amount of annuity PV of Tk 1 @5% PV of death claims 1 2 3 4 7 8 1 65 520/ 847=0.6139 1000 0.9524 584.6784 2 66 320/ 847=0.3778 1000 0.9070 342.6646 3 67 220/ 847=0.2597 1000 0.8638 224.3288 4 68 185/ 847=0.2184 1000 0.8227 179.6777 5 69 120/ 847 = 0.1416 1000 0.7835 110.9436 Net Single Premium for a Term Life Annuity = Tk. 1442.2931

41. Assignments Any One Problems of Life Insurance Business in Bangladesh Perceptions of Students towards Insurance Business Insurance is a Risk Coverage Instrument. Submission date : 30 April, 2021