## Observations on Reversionary Payments: On Schemes for Providing Annuities for Widows, and for Persons in Old Age; on the Method of Calculating the Values of Assurances on Lives; and on the National Debt. Also Essays on Different Subjects in the Doctrine of Life-annuities and Political Arithmetic ... |

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according amount annual payments Annuities lapsed annuity payable yearly annum assurance babilities calculations complement compound interest computed consequence continue decrements deduced denote difference divided Doctrine of Chances edition entitled equal established find the value five guineas former four per cents give given sum given term half Halley's Table joint lives less life-annuities Logarithms London marriages married mean age ment millions Moivre Moivre's hypothesis multiplied Northampton Table Note nuity number of annuitants number of persons number of widows oldest payable half-yearly perpetuity present value probability public debts quarterly Question rate of interest reckoning interest redeemed remainder reversionary rixdollars rule scheme Scholium shew Simpson's Simpson's rule single lives single payment sinking fund Society SOLUTION subtracted supposing surplus survivorship Table of Observations taxes theorem three lives three per cents tion Treatise values of single volume whole

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Page 183 - They are all founded on a table of the probabilities of the duration of human life at Northampton, which will be inserted among the other tables in the second volume of this work. This table made a part of all the former editions of this work ; but it is in the present edition much improved, and gives, I believe, more correctly than any other, the mean probabilities of the duration of human life, and therefore seems to be more proper than any other for general use".

Page 143 - But this is too gentle a censure. There is reason to believe that worse principles have contributed to their rise and support. The present members, consisting chiefly of persons in the more advanced ages, who have been admitted on the easiest terms, believe that the schemes they are supporting will last their time, and that they will be gainers. And as to the injury that may be done to their successors, or to younger members, it is at a distance, and they care little about it. Agreeably to this principle,...

Page 297 - All these taxes were appropriated to the discharge of the interest of ^7,808,o8/, (originally .§£10,000,000,) capital stock of SouthSea annuities, together with charges of management. All that remained of the produce of the taxes thus digested into these three funds, after satisfying the charges upon them, was in the same year (or 1716) carried into a fourth fund^ to which was given the name of the Sinking Fund, because appropriated to to the purpose of sinking the public debts. The words of the...

Page 97 - April 1 780, ^3,850. — —Its income, consisting of the interest of ^4Q,ogo three per cent, stock, and the subscriptions of 550 members at five guineas each, amounted at the same time to <^4,36o, leaving a favourable balance of only ^480. Supposing the Society to preserve its present number of members, and the number of annuitants to increase for six years to come only at the rate of ten annually, its expence at the end of the present year, or the beginning of the next, will be equal to its income;...

Page 109 - Act for the better raising and securing a Fund for a Provision for the Widows and Children of the Ministers of the Free Church, and for the Widows and Children of the Professors holding Professors' Offices in any College connected with the said Church.

Page 276 - It is an observation that deserves particular attention here, that on this plan, it will be of c . .. of less importance to a state what interest it is obliged to give for money : For the higher the interest, the sooner will such a fund pay off the principal. Thus...

Page 158 - It might, however, certainly have been much more useful, had it gone from tho first on a different plan. It is obvious that regulating the dividends among the nominees by the number of members who die every year is not equitable ; because it makes the benefit which a member is to receive to depend not on the value of his contribution, but on a contingency ; that is, the number of members that shall happen to die the same year with him. This regulation must also have been disadvantageous to th

Page 272 - No resources can be sufficient to support a kingdom long in such a course. 'Tis obvious, that the consequence of accumulating debts so rapidly ; and of mortgaging posterity, and funding for eternity, in order to pay the interest of them ; must in the end prove destructive. Rather than go on in this way, it is absolutely necessary, that no money should be borrowed, except on annuities, which are to termi* Reversionary Payments, 1783, 1.

Page 293 - But to proceed to some further observations. What has been said, has all along supposed a sacred and inviolable application of the fund I have described, and of all its earnings, to the purpose of sinking the national debt. The whole effect of it depends on its being allowed to operate, WITHOUT INTERRUPTION, a proper time.

Page xlix - ... mating interest at 4 per cent?" ANSWER. It is evident, that the value of such an expectation is different, according to the different ages of the purchasers, and the proportion of the age of the wife to that of the husband. Let us then suppose, that every person in such a...