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THE

ARITHMETIC OF ANNUITIES

AND

LIFE ASSURANCE,

OR

COMPOUND INTEREST SIMPLIFIED;

EXPLAINING

THE VALUE OF ANNUITIES CERTAIN, OR CONTINGENT ON ONE
OR TWO LIVES, AND THE VALUES OF ASSURANCES

IN SINGLE AND ANNUAL PAYMENTS,

AND COMPRERENDING

THE VALUES OF LEASES, PENSIONS, FREEHOLDS,
AND REVERSIONARY SUMS, IN POSSESSION OR
EXPECTATION, IMMEDIATE, DEFERRED

OR TEMPORARY,

Illustrated with practical and familiar Examples.

BY

EDWARD BAYLIS,

ACTUARY OF THE ANCHOR LIFE ASSURANCE COMPANY.

LONDON:

LONGMAN, BROWN, GREEN & LONGMANS.

1844.

LONDON: PRINTED BY JOHN WERTHEIMER AND CO.,

CIRCUS PLACE, FINSBURY.

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Bomes 1-21.3 3172

INTRODUCTION.

Many able mathematicians have written on the subject of annuities certain and contingent, the values of which they have analytically demonstrated in a manner the most scientific and conclusive. Price, Morgan, Bailey, Milne, Gompertz, and De Morgan, whose labours have largely contributed to extend this branch of knowledge, and whose works must not only be consulted, but studied, by those who desire to become proficients, are names pre-eminently distinguished.

The productions of those established authors, however, are for the most part too abstruse for the inere arithmetician; and the present work is intended as an introduction to their writings. It has, indeed, been expressly composed as a practical book for beginners, and as a treatise for the use of schools, by means of which he who is totally ignorant of algebra and of its symbols, may be enabled to determine the values, in single and annual payments, of annuities certain-of annuities contingent-of leases, pensions, and freeholds—of · legacies and reversions, however modified or combined, whether referring to the existence or failure of a single life, or of two joint lives, or on the last survivor of two lives; and whether such annuities and reversions be immediate, deferred, temporary, or perpetual, in the same manner, and with the same certainty and accuracy, as he would determine similar values when subject to no contingency of human life, but solely dependent for solution on a time certain, and a given rate of interest per cent., according to the ordinary principles of compound interest.

The student will find his labour vastly abridged, and his progress greatly accelerated, by having recourse to the aid of logarithms. Let him, if inexperienced in their use, devote but one or two weeks to the study of Babbage's Logarithms, and he will be astonished and pleased at the facility with which, by their assistance, he may accomplish the most lengthened and tedious calculation.

In conclusion, a hope is entertained that these pages may assist to diffuse a practical knowledge of a subject which is more or less beneficial and interesting to all. Anchor Life Office, Sackrille Street, Piccadilly,

19th April, 1844.

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