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Life Insurance Reserves and Cash Values.docx

3 Pages

Mathematics Electives
Course Code
David Kohler

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Life Insurance Reserves and Cash Values Saturday, October 12, 2013 11:29 AM Reserves Policy Reserves  Liabilities that represent the amount that, with future premiums and interest earned, is expected to be needed to pay future benefits under those policies  Formula statutory policy reserve: the amount sufficient amount to pay future claims  Statutory reserve has no relationship with the insurer's actual past experience  Retrospective reserve considered as the difference between the accumulation at interest and benefit of survivorship of the net premiums received in the past and the accumulation at interest with benefit of survivorship of the claims paid Methods of Calculation  Retrospective Method o Group  Arises from the payment of a level net premium in excess of that needed to meet current mortality costs  Usually in the early years, the reserve is in excess and is therefore able to satisfy the spike in claims in later years o Individual  Add net premiums for current year to the terminal reserve of the preceding year, increasing the combined sum ( called the initial reserve)  Increases by one year's interest at the assumed rate, and deducting cost of insurance  Prospective Method o Reserve is the difference between the present value of expected future benefits and the present value of expected future net premiums o Present value of expected benefits increases towards maturity and present value of expected future net premiums decreases since fewer premiums remain to be paid o Terminal reserve = net single premium - net level premiums*present value of a life annuity due of 1 for the remaining premium paying period o On a paid-up policy, no further premiums are due so the reserve must equal the present value of future benefits, measured by the net single premium of the policy at the attained age of valuation Terminal, Initial, and Mean Reserves  Terminal reserve: the reserve at the end of any given policy year o Mortality savings allocated on the basis of the net amount at risk o Used to determine nonforfeiture values  Initial reserve: the reserve at the beginning of the year, equal to the terminal reserve of the preceding year plus the net level annual premium of the current year o Used to determine dividends under par-policies  Mean reserve: average of the initial and terminal o Used in connection with the annual statements of life insurance  Significance of Actuarial Assumptions o Under the net level premium method, the effect of a change in mortality is spread out over the premium-paying period o May result in an increase or decrease since the impact of a change in mortality is not uniform from age to age and duration to duration o Calculate and compare to analyze the effect of a change in mortality o Impact on reserves of a change in the interest assumption is a negative relationship o Smaller anticipated earnings must be offset by a larger reserve at any point in time o Statutory policy reserves are based on the assumption that no policies will lapse and thus makes the present value of future benefits considerably greater than the insurer's actual present value of future benefits Modified Reserves  First policy year expenses greatly exceed subsequent year expenses an
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