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INSTALMENT AND CONTINUOUS INSTALMENT INSURANCES "MONTHLY INCOME" POLICIES AND "INCOME" BONDS. Ordinary instalments. Another variation from the usual forms of life insurance, is to make the proceeds payable at death or on maturity as an endowment, or both, by instalments, payable annually, semi-annually, quarterly or even monthly, instead of by one lump sum. Thus there may be ten annual instalments of $roo each, 15 annual instalments of $66.67 each, 20 annual instalments of $50 each, 25 annual instalments of $4o each, etc.

When the benefits are to be paid in monthly instalments, such a policy is nowadays known as "Monthly Income." Of late, since so-called investment insurance on de ferred dividend plans is less in demand, and more atten tion is given to the virtues of life insurance, "Monthly Income" policies are becoming increasingly and deserv edly popular, providing, as they do, an income for the beneficiaries as needed for their support.

In order to compute the net premiums for such policies, it is first necessary to find the value of the instalments when discounted to the date of the insured's death.

When these annual sums are paid in equal monthly in stalments, the value is less, by approximately half a year's interest on the whole amount.

Then, to find the net premium, compute, in the proper manner for that form of policy, the net premium for an amount of insurance, payable in one lump sum, equal to this discounted or commuted value.

Sometimes it is provided that the beneficiary may with draw the commuted value instead of receiving the instal ments as they become due; but this is not usual, because the purpose in taking such an insurance is to provide the beneficiary an assured income. It is frequently provided, however, that in event of the death of the beneficiary be fore the death of the insured, the insurance becomes one for a lump sum equal to the commuted value, and also that in event of the death of the beneficiary before all the instalments have been paid, the remaining instalments may be commuted.

Reversionary Annuity: A much earlier form of instal ment insurance was the reversionary or survivorship an nuity, providing that if the insured die before the bene ficiary, a life annuity, first payment immediate, becomes payable during the subsequent life of the beneficiary. If

the beneficiary die first, the insurance is at an end and all premiums paid are fully earned.

The mode of computing the net single premium for this is not so complicated as might be thought. For, suppose the beneficiary now has a life annuity; this will pay her $i, for instance, as long as she and the insured both live, and then, if she survives him, through all her subsequent life time. It is composed, then, of an annuity payable for their joint lifetime and then of an annuity, beginning at the insured's death, and payable during her after lifetime. Therefore, if we compute the present value of a life an nuity for the beneficiary's life and deduct the present value of an annuity for the joint lives of the insured and the beneficiary, we shall have the present value of what remains of the life annuity, viz. : a reversionary life an nuity for the after-lifetime of the beneficiary.

How to compute the present value of a life annuity has already been explained. In short, it is to multiply the probability of living one year by the value of $i discounted one year, and so on to the end of the table, adding to gether the products.

The mode of computing the present value of a joint-life annuity is very similar. Multiply the probability of both living one year by the value of $i discounted one year and so on to the end of the table, remembering that the prob ability of both living is the product of the probabilities that each will live. Then add together the discounted products as before.

Theoretically, the first payment on the reversionary annuity will be due at the end of the policy year in which the insured dies, provided the beneficiary is then surviv ing. This is analogous to the usual assumption that death claims are payable at the end of the year. Practically it is always paid upon receipt and approval of proofs of death.