Math for life Insurance.doc Daffodil International University BBA FIN-401

Problem-1: Calculate the net single premium (NSP) and Net Annual Premium (NAP) for 5 years Term and
Endowment policy of TK 50000 at the age of 36 from the following information:

Age Number of insured person Number of death person PV of TK 1@3%
36 9480 25 0.971
37 9455 26 0.943
38 9429 28 0.915
39 9401 30 0.888
40 9371 31 0.863


Solution (Term Policy): We know that,

NSP= PV of Total Death Claim/No. of Policy holder at the beginning of the year

NAP= PV of Total Death Claim/PV of Total Premium Receipt at Tk.1 @ 3%

Age Number Number PV of TK Amount of PV of Death Claim
of of death 1@3% Insurance
insured person
PV of Premium
person
Receipt at Tk.1 @ 3%
36 9480 25 0.971 50000 1213750 9205.08
37 9455 26 0.943 50000 1225900 8916.065
38 9429 28 0.915 50000 1281000 8627.535
39 9401 30 0.888 50000 1332000 8348.088
40 9371 31 0.863 50000 1337650 8087.173
PV of Total Premium
PV of Total Receipt at Tk.1 @ 3%
Death Claim= 6390300 =43183.941


NSP=6390300/9480

= 674.0823

NAP= 6390300/43183.941

=147.9786


Solution (Endowment Policy): We know that,

NSP= PV of Total Claim/No. of Policy holder at the beginning of the year

NAP= PV of Total Claim/PV of Total Premium Receipt at Tk.1 @ 3%




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, Ag Numbe Numbe PV of Amount PV of Death Claim
e r of r of TK of
insured death 1@3 Insuranc
PV of Premium
person person % e
Receipt at Tk.1 @ 3%
36 9480 25 0.971 50000 1213750 9205.08
37 9455 26 0.943 50000 1225900 8916.065
38 9429 28 0.915 50000 1281000 8627.535
39 9401 30 0.888 50000 1332000 8348.088
40 9371 31 0.863 50000 1337650 8087.173
PV of Total Premium
PV of Total Receipt at Tk.1 @ 3%
Death Claim= 6390300 =43183.941


The no. of living Person= (Number of insured person in last year- Number of death person in last year)

The no. of living Person= (9371-31) =9340

The PV of Living Person’s Claim= the no. of living Person × PV of TK 1@3% in last year× Amount of
Insurance

The PV of total Living Person’s Claim= 9340×0.863×50000=404358650

The PV of Total Claim= The PV of Living Person’s Claim+ PV of Total Death Claim
= 404358650+6390300

= 410748950


NSP=410748950/9480

=43327.95

NAP= 410748950/43183.941

=9511.613


Problem-2: calculate net single premium for 5 years term policy.

Age Number of insured person Number of death person PV of TK 1@3%

31 61350 1350 0.971
32 60000 2000 0.943
33 58000 2970 0.915
34 55030 2450 0.888
35 51580 4200 0.863



This study source was downloaded by 100000853497421 from CourseHero.com on 07-18-2023 06:03:39 GMT -05:00


https://www.coursehero.com/file/71871959/Math-for-life-Insurancedoc/