Actuarial Society Examinations in 1905 Questions And Solutions Reprinted From R

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Actuarial Society Examinations in 1905 Questions And Solutions Reprinted From R
Robert Henderson
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Find the annual premium for whole life insurance, all premiums paid to be returned at death, assuming that the premium is loaded by a percentage and a constant. Let #! = office premium required and it = net premium where Then re N = M, + R^ \ (i + k) TT + c \ < ) x (* + ^ ^x f ~ ^x + c RX l~ + c R M- + c N^ - (i + k) R x ^ R^ (I + k) P x + c i - (i + k) - 6. Investigate the relation between the rates of mortality in two tables giving the same net premium reserves on ordinary life policies. What conclusion would you draw regarding the effect on such re- serves of an increase in the rate of interest ? We have for all values of n _ Suppose any other table of mortality gives the same terminal re- serve values and denote net premiums and rates of mortality according to this second table by accented letters then we have d +*')= V, +< ? i + M _ I (i - M V, ). Subtracting we get (P J- PJ (i + ) = (?i + M _, - q\ + n _ x ) 37 for all values of n so that (

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