The method of investment on the principle of annuities certain may be very profitable. Thus, on reference to the above-mentioned sinking fund, it will be.
found that the sum of £1087, 5s. 7d. has been provided for by an actual out-of pocket outlay of only £755, 16s. 3d. Again, to a debtor it is a most advantageous methocl of repayment of a loan. Whilst obliging him to lay by out of his income a small sum, it allows him to insensibly free himself from the debt, by spreading over a number of years the results of his work and thrift. But capitalists do not as a rule car for this method. It parcels out their funds and forces them to receive a succession of small payments, of which the immediate employment is difficult. And the same difficulty presents itself to any one who proposes obtain ing a certain ultimate sum by adopting the method of an annuity cgrtain—the difficulty of immediate reinvestment, in order to keep the compound interest constant. This difficulty would have to be carefully grappled with and overcome ; for annuity tables and calculations based thereon assume a constant and un varying yield of compound interest. The borrowing of money and its repayment by means of the annuity system is, however, becoming more and more general and popular, especially with regard to mortgages on house property. In this instance, building and similar societies have led the way for years. The result to-day is that owners of estates of small residential properties in course of development are generally in a position, and even anxious, to make arrangements with intending purchasers for payment of the greater part of the purchase-money on the principle of an annuity certain. Again, municipal and local government loans now often take the form of annuities. Life tenants of settled estates have also power under certain acts, for certain purposes, to raise money upon mortgage and charge the estates with the repayment thereof by annuities. Of annuities there are two principal sub-classes—deferred and reversionary. The former do not commence until after a certain number of years, the latter being such as depend upon the occurrence of some uncertain event, as the death of an individual, &c.
Life annuities present any application the theory of annuities. A life annuity is an annuity calculated upon the probable duration of the life of the person to whom it is payable. The principles on which tho calculation of the value of life annuities depends will be more fully explained in the articles PROBABILITY and MORTALITY TABLES. It is sufficient here to say that their value depends upon the manner in which it is presumed a large number of persons similarly situated with the intending annuitant would die off successively. Various tables of such expectations of life have at different times been con structed from observations made amongst different classes of lives in various districts. Some make the mortality greater than others ; and of course tables which give a largo mortality, give the value of an annuity as smaller than those which suppose men to live longer. Until recent years the insurance companies, whose business has always depended upon such considerations, have used various tables, some upon which annuitants would be rated according to a low expecta tion ; some upon which the expectation would be higher. At present, however, there are two tables in principal use — the II Table of the Institute of Actuaries, used by most of the insurance offices, and the Government Table. Wo
will now in Table III. give a selection from the 3 per Cont. Table prepared by the Institute of Actuaries—a table undoubtedly the most scientific and precise. The symbol " HM " stands for Healthy Males, denoting that the Table has been prepared from observations on such lives, which source of observation has made it by far the best existing criterion for testing the incidence of mortality. Other Tables, prepared by the Institute upon similar lines, are the II" (Healthy Females), II" (Healthy Males and Females), ,and D" (Diseased Males and Females), The value, therefore, of an annuity of £1 per annum on the survivor is Z22, 16s. 71d. It is, in principle, the same as if the annuity were payable to each *person on condition that one annuity should be returned during the duration of the joint lives. The value of an annuity not payable until one of two persons is dead, and then during the life of the survivor, is found by subtracting twice the value of the joint annuity, instead of the value itself, from the sum of the values as above.' This is so because the annuity is not payable during the joint lives. The value of an annuity payable to one person upon the previous death of another, is equivalent to the value of an annuity on thp life of the former less the value of an annuity on their joint lives. Let the ages and table be as before, the age of the former life being 25. We then have : Table III.—Annuity at age of 25 21.03 Table IV.—Joint annuity, 25 and 25 . 10.3 Difference 10.73 Whence the value of the required annuity of £1 is Z10, 14s. 71d.
As a suggestive guide to those intending to purchase annuities, we append in Table V. a characteristic selection of rates ruling in certain insurance offices for an annuity purchased at the price of £100. The top row of figures shows approximately the highest rates, and the bottom row represents approximately the lowest. Of course most insurance companies will give a quotation without reference to their published rates, and this table is subject thereto. It may be taken, however, that the rates of any company would vary between these two extremes—probably with a tendency towards the higher rates. The lower rates appear to be based upon the Actuaries Iia Table ; the higher to some extent on the Carlisle Table, which is distinctly favourable to an intending annuitant, and is consequently being gradually discarded by the companies.
In all the preceding tables and illustrations nothing more than a merely suggestive outline has been attempted. To attempt more would be to exceed the limits of this work, and even if possible, would be to some extent superfluous whilst complete tables of annuities are so easily available in handy form. To set out complete tables, with the object of general reference, would itself necessitate a small volume, and to do less would render them useless for that object. The only reasonable course has therefore been taken, viz. to introduce the subject to the reader, so that he may learn to appreciate its value and approach the complete tables with some knowledge as to their use. In addition to the articles mentioned in the text, reference should be made to APPORTIONMENT ; INSURANCE (LIFE); and INTEREST, •