REVERSION. 



REVERSION. 



instance referred to ; in which p = 



= 10. 



x(29) 47783-19 

 N(39) 28225-55 



18557-64 

 x 11-6148 



227158-1 

 199014-0 



., A = 10001., x = 30, 



x(80) 932-6867 

 11(40) 733-67--'7 



199-0140 

 x 1000 



199014-0 



:i-l 



D(40) 1555-7S)28144-1(1S-09002 

 x 5075 



91806-84 



The answer U, that the reserve of premiums for each person of the 

 hen remaining is IS'09002/., which for the whole U 91806-841. 

 The rough answer in the scheme worked out at length is 91, Si)'.'/. 



Now, this 18-09/., or IS/. U 1M., is what is called the value of each 

 man's policy at the expiration of the ten years ; or the rrry titmott the 

 office could afford to give him to surrender all claim, and to keep hw 

 future premiums to himself. But what is the nature of his claim on 

 the office f Evidently this, that he has a right to make them give him 

 a guarantee for the next ten yean on payment of a premium of III. 

 Yii. 'A\d., which could not be done at so low a rate for a new comer. 

 Compute the premium for a person entering at 40, and insuring 1000/. 

 f.r 10 years; or divide 1000 times H(40)-M(60) by N(39)-N (49), 

 and the answer will be found to be 13-800A, or IS/. 16*. If then any 

 pet inn aged 40, having been in the office ten years, were to put 

 another penon of the same age in his place at his own premium, he 

 would obviously make that person a. present of the difference between 

 11-6148/. and 13-8001., at once (since a premium is to be paid imme- 

 diately), and for nine succeeding years, if the latter should live so long. 

 And 13-800-11-6148 is 2-1852, while an annuity of 2-1S52/. for niu.- 

 yean, at the age of 40, is worth N(40) N(49) divided by D(40) and 

 multiplied by 2-1852, or 15-903/. Add to this 2-185/. for the imme- 

 diate difference, and we get 18-088/., differing only a halfpenny from 

 18-OMU., the mm which the office has in reserve. If then the penon 

 who is to take the place of the insured at 40 yean of age, were to pay 

 him an equivalent, he must, besides taking on himself the future pre- 

 miums, pay the retiring member 18-090/, which is therefore the value 

 of the Utter 's policy. The last formula will always give the acnmtiia- 

 liom value of a policy, whether for the whole life or for a fixed term. 



The preceding contains the most material calculations which are 

 necessary in the management of an office, or rather, in forming an 

 opinion on the management of an office. It is to be remembered that 

 all which has hitherto been said supposes the rates of mortality and 

 Uiteiest to be absolutely known and invariable, the parties to enter on 

 their birthdays, and all claims to be adjusted at the terminations of 

 whole yean from the time of entry. We now proceed to the appli- 



An s sun Mil n company is a savings' bank, with a mutual under- 

 standing, presently to be noticed, between the contributors. To make 

 out this proposition, let us suppose that A borrows money, and insures 

 his life for the amount as a security to hi* creditor. For this be has 

 to pay a premium. If life were certain, the office of the company 

 would be to receive and invest these premium*, which would be calcu- 

 lated in such a manner as with their interest to amount to a ram suffi- 

 cient to discharge the loan in a settled time. At the end of this time 

 the creditor (who has been all this while receiving interest for lii* 

 money from A) calls upon A to make his claim upon the office, and 

 repay the loan with the money received. If such an office existed, 

 life being certain, the rationale of the proceeding would be that the 

 creditor, though tolerably confident of As power and willingness to 

 make any yearly payment, whether of interest or instalment, will not 

 trust him steadily to lay by and improve yearly instalments, but re- 

 quires that he should make his instalments payable to third parties, 

 who are engaged not to return them on demand until they amount to 

 a sum sufficient for the discharge of the debt. Such an office certainly 

 could not exist, on account of the uncertainty of individual life. So 

 soon however as it is known that the duration of masses of individuals 

 can be calculated with tolerable accuracy, there is a remedy for the 

 {dividual uncertainties. Let a Urge number of debtors, similarly 

 situated with A, agree to be guarantees for one another ; that U, let 

 each of them pay during his life not only his own instalments, but 

 snch additional sums as will provide the means of meeting the 

 nt those who die, and the savings' bank thus constructed will become 

 an assurance-office. Of course it matten nothing whether these debtors 

 pay their instalments to a person agreed on among themselves, or go 

 to a company which undertakes the management of such concerns. 

 And again, it makes no difference whether the instalments be fur liqui- 

 dation of debt, or to accumulate a provision for widows and children. 

 We have taken the case of debtor*, because in such a case an office 

 looks more like a mere indemnity-office than when iu contributors 

 enter for the benefit of their families; still however, in the former 

 ease, it is evident that the premiums are partly instalment*, of debt, 



partly sums intended to make good the deficiency of the life-instal- 

 ments of those who die. 



Let us now suppose a company to be formed for the simple purpose 

 of assuring lives. Their business is to invest the premiums of those 

 who assure with them ; their receipts will consist entirely of current 

 premiums and interest on the investments of the old ones ; and their 

 outgoings will contain expenses of management, payment of claims, 

 purchase of their own policies, and (possibly) losses by bad investment. 



There is one question which is generally settled at the very outset, 

 namely, whether the company is to be what is called mutual, proprie- 

 tary, or mixed. 



A mutual company is one in which the members stand bound to 

 each other, and constitute the company themselves. In such a com- 

 pany no capital is, generally speaking, raised at the outset, except a 

 small sum for necessary expenses at starting. This however is not 

 necessarily the feature of a mutual company ; for if its members choose 

 to constitute themselves an investment company as well as an assur- 

 ance company, they may, without losing their mutual character, re- 

 quire every assurer to be also a shareholder. In a mutual company 

 the profits of course are divided among the assured. 



A proprietary company is one in which a body of proprietors raise a 

 capital and pledge it for the payment of claims, in case the premiums 

 are not sufficient : for this security they receive, in addition to the 

 interest of their own capital, the profits of the assurance business. It 

 has long been proved that, with proper tables of premiums, and a fair 

 amount of business at starting, this capital is an unnecessary security ; 

 and the only reason which could now make such an office desirable, 

 would be the lownest; of its premiums. Of course it matters nothing 

 to the assured how claims are paid, as long as they are paid ; the 

 capital may be diminished, but the assurer fears nothing except its 

 exhaustion before his turn comes. This must be the sole considera- 

 tion with a person who is tempted by low premiums to a purely pro- 

 prietary office : the nominal capital signifies nothing ; it is upon the 

 amount of assurance to which it (with the premiums) is pledged that 

 the solvency of the office depends. Generally speaking however we 

 believe it will be found that the purely proprietary offices have not 

 allowed themselves to run much risk. 



A mixed office is one in which there is a proprietary company, which 

 does not take all the profits, but a share ; the rest being divided among 

 the assured. The only good effect of the capital upon the condition 

 of the assured in such a company is this ; that the directors, having 

 fixed capital as well as premiums, may justifiably seek for investments 

 which a mutual company must avoid. Having the capital to make 

 good purely commercial losses, they may perhaps attempt to get a 

 higher rate of interest, and of course take more risk of loss ; the 

 assured, who are sharers in the whole of the profits, since the profits 

 of premiums and profits of original capital are not distinguished, come 

 in for their share of the extra profits of the capital. But no such 

 attempt at gaining higher interest by secondary securities should be 

 made until a sum sufficient (with future premiums) to meet all claims 

 U invested in the very safest securities which the state of society 

 1 



There is much confusion in the ideas of many persons about interest, 

 arising from not distinguishing between interest and other returns. 

 The following remarks may serve to explain our meaning : 



Interest is the return which in made for the use of money, when the 

 owner entirely relinquishes its management, and believes he has un- 

 doubted security for its return. " Interest," says Mr. M'Cnlloch, " is 

 nothing more than the net profit on capital." The same author gees 

 on to say, " the rate of interest on each particular loan must of course 

 vary according to. the supposed solvency of the borrowers, nr the 

 degree of risk supposed to be incurred by the lender." But here the 

 acute writer from whom we quote, after setting out with the accurate 

 drliiiition of the political economist, proceeds to use the word in the 

 common sense, in which it is no longer the net profit of capital. For 

 this variation in the rate of interest (so called), this addition for pos- 

 sible insolvency, is or is meant to be only as much as will make every 

 debtor who does pay contribute towards the bad debts of those who 

 do not. Nothing then is n-tted by the increase for suspicion of in- 

 solvency, in the long run, and one debt with another ; so that, abiding 

 by Mr. H'Culloch's definition of interest as the correct one, we should 

 propose to call the additional sum debt-insurance. To this we must 

 add, that when a person employs his own money, as in trade or manu- 

 factures, he also gains that additional return which a borrower counts 

 upon reserving to himself after paying the interest (and debt- insurance, 

 if any) to his creditor. This U neither interest nor debt-insurance, but 

 is of the nature of salary, by which name it might be called. Perhaps 

 it woulfl be best to retain the term interest in its general loose signifi- 

 cation, and to subdivide it, for accuracy, into pure interest or net 

 profit, debt-insurance, and salary. 



In the construction of a table of premiums, three points must be left 

 to the judgment of the constructor, the rate of interest, the table 

 of mortality, and the addition to be made for expenses of management 

 and probable fluctuation, or discrepancy between the predictions of 

 the table and the events which actually arrive. The third point would 

 not arise if, as was once the case, the table of mortality made life 

 much worse than the actually prevailing state of things shows it to be. 

 Security against adverse fluctuation is thus taken iu the choice of the 



