The reversionary annuity has always been favored by experts in life insurance, but never by the public, because of the uncertainty whether the beneficiary will survive to realize much, and also because of the possibility that noth ing at all would be realized by reason of the beneficiary dying before the insured.
To remedy the latter disadvantage an increasing insur ance on the life of the beneficiary in favor of the insured, promising in event of the death of the beneficiary before the death of the insured, a return of all premiums paid, has been combined with the promise of a reversionary an nuity. The mode of computing the extra premium for such a return premium insurance is the same as that de 66 scribed in an earlier chapter. The addition so consider ably increases the premiums as to prevent the plan from becoming popular.
Among the distinguished life insurance men who long ago showed a preference for this plan in selecting insur ance for themselves was the late Sheppard Homans. When he left the service of the Mutual Life Insurance Company of New York, more than forty years ago, it was disclosed that his only insurance was a large policy of this character. At the present time the most distin guished American actuary, Emory McClintock, shows his preference for this form of protection in a like manner.
No small part of the neglect of survivorship annuities in former years was due, no doubt, to the over-emphasis upon life insurance as an investment. They have recently become more popular.
Continuous Instalment Insurance : The objection to or dinary instalment insurance is that the beneficiary may outlive the instalment period and be left without the in come in old age when it is most needed; the objection to the reversionary annuity that the beneficiary might die so soon after the insured as to realize very little. The "con tinuous instalment" plan, invented by Emory McClintock, obviates both. It provides for the payment of instalments for a fixed period in any event usually for twenty years and as much longer as the beneficiary may survive.
The policy promises a fixed amount yearly for a definite period of years after the death of the insured and there after during the lifetime of the beneficiary. The net single premium is the sum of the net single premium for an insurance of the commuted value of the 20 instalments and the net single premium for a reversionary annuity for the after-lifetime of the beneficiary, the first payment 20 years after the death of the insured.
The mode of computing the net single premium for a 67 life insurance payable in annual instalments has already been explained.
To ascertain the net single premium for the contin gent benefit, let us first compute its value twenty years from now. If twenty-one years from now the beneficiary were living and in receipt of an annuity for her lifetime, its then present value would be that of a life annuity for an age twenty-one years older than the beneficiary's pres ent age.
But the beneficiary will not then be in receipt of this first payment of the contingent annuity unless the insured shall have died the first year, nor the next year after that, i. e., the twenty-second, unless the insured shall have died the second year; and so on. That is to say, an instalment of this contingent annuity will not be paid the first, second, etc., year after the expiration of twenty years from now if the insured survives the first, second, etc., year after the policy is issued.
We must, therefore, deduct the value of payments due in one year, two years, etc., conditioned upon the benefi ciary living one year (after surviving twenty years al ready), two years, etc., and the insured living one year, two years, etc., from his original age. But this is a joint life annuity, based upon the joint lives of the beneficiary at an age twenty years older and the insured at his orig inal age.
The value, then, twenty years from now if the benefi ciary then survives, of the benefit beyond the twenty in stalments certain is the present value of a life annuity for the life of the beneficiary at the attained age less the pres ent value of an annuity for the joint lives of the benefi ciary at the attained age and of the insured at the age of entry. This is the value twenty years from now and on the condition that the beneficiary then survives; its present value, which is the net single premium for the contingent 68 benefit, is the net single premium for a pure endowment for twenty years, for the amount of the present value twenty years from now, such endowment being based on the life of the beneficiary at age at entry.