Consider the following data extracted from 1980 mortality table.
Age....................... Number of living
50.......................... 896, 846
51.......................... 890, 828
52.......................... 884, 325
53.......................... 977, 286
54.......................... 869, 644
The number of people expected to die at age of 54 is 8,314
Assume that person at age of 50 purchased 5 year ordinary endowment life insurance for birr 25,000. Interest rate is 10%. Assume that the premium at paid at the begging and death claim are to be paid at end of the period in which death occur.
REQUIRED. A Determine the Net Single Premium(NSP)
B. Determine the Net Level Premium(NLP)
C. What is the amount of death claim that the insurer expects pay during the term policy?
A. To determine the Net Single Premium (NSP), we need to calculate the present value of the death benefit at age 54.
PV = Death Benefit / (1 + i)^n
PV = 8,314 / (1 + 0.1)^4
PV = 8,314 / 1.4641
PV ≈ 5,676.99
Therefore, the Net Single Premium (NSP) is approximately 5,676.99 birr.
B. To determine the Net Level Premium (NLP), we need to calculate the present value of the premium payments and the present value of the death benefits.
PV of Premiums = Premium Payment * (1 - (1 + i)^(-n)) / i
PV of Premiums = 25,000 * (1 - (1 + 0.1)^(-5)) / 0.1
PV of Premiums ≈ 142,366.04
PV of Death Benefits = NSP * Number of Living at Age 50
PV of Death Benefits = 5,676.99 * 896,846
PV of Death Benefits ≈ 5,090,150,810.54
Therefore, the Net Level Premium (NLP) is approximately 142,366.04 birr.
C. The amount of death claim that the insurer expects to pay during the term policy is equal to the present value of the death benefits.
Amount of Death Claim = PV of Death Benefits
Amount of Death Claim ≈ 5,090,150,810.54 birr.