Table Of ContentCOMPOUND
INTEREST SIMPLIFIED
BY
GUY E. CHURCHILL
B.Sc. (London), F.C.I.I., F.I.Arb.
Senior Lecturer on Insurance, Holborn College
Formerly Examiner to the Chartered Insurance Institute
P E R G A M ON P R E SS
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Copyright © 1969 Pergamon Press Ltd.
First Edition 1969
Library of Congress Catalog Card No. 68-18893
Printed in Great Britain by Hazell Watson & Viney Ltd., Aylesbury, Bucks
This book is sold subject to the condition
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08 013300 2 (hard cover)
Foreword
by SIR ERIC RICHARDSON, C.B.E., PH.D., B.ENG., C.ENG., F.I.E.E., A.M.I.MECH.E.,
F.B.H.I., F.P.S., F.R.S.A.
Director of Education, The Polytechnic, Regent Street, London, W,l.
IN writing this foreword to Guy Churchill's book on Compound
Interest Simplified two points should be made clear at the outset.
First, I am a layman on the intricacies of insurance but as a lay-
man I do have an interest in the subject even though that interest
must remain simple and may not be compounded. Secondly, I
have a professional interest in the author since it is anticipated
that the Holborn College of Law, Languages and Commerce
where he is Senior Lecturer in Insurance will have been "com-
pounded" with my own institution to form a new polytechnic by
the time this book is published.
There is no shortage of books on Compound Interest but most
of those known to me are produced more as narrowly specialized
works in arithmetic and algebra. This book, while primarily
written for the student preparing himself for insurance examina-
tions, is so written as to become interesting reading matter for the
non-specialist. The text is made all the more attractive by a few
cartoon drawings and occasional quotations from Alice in Wonder-
land and other works. For the serious student there^are many
reminders of the good teacher in the background. After the
Preface there is a plan of study with its absolute minimum
recommendations and its advice on examination procedures,
together with a whole chapter on preparing for examinations.
There is a liberal use of worked examples in the text with the
examples to be worked at the end of each appropriate chapter.
Appendix 6 contains a summary of equations. Clearly the book
vii
VÜi FOREWORD
will be very valuable for students studying privately or by corre-
spondence since it conveys the feeling of the teacher sitting along-
side prodding and reminding as the study proceeds.
While it is true that "of the making of many books there is no
end" this one is justified by its new and refreshing approach. A
book which helped me as a student engineer was Calculus made
Easy and this prompts me to say that an alternative title for this
book might well have been "Compound Interest made Readable".
The publication merits great success.
ERIC RICHARDSON
Preface
COMPOUND INTEREST is almost as old as money itself—in fact it
started its existence just about a year after the first loan ever was
not repaid on the promised date. The lender then felt quite
intuitively that if only he had been repaid with interest in full he
could have re-lent the whole amount on the same terms to some-
one else. So why not treat the first borrower as he would a
second ? That is, why not charge interest on the interest itself as
well as on the original loan? The lender would certainly have
felt it justified, for in those days the law did not smile kindly
upon debtors and they could expect little protection from it. Thus
there developed the business of money lending, often at quite
exorbitant terms.
Through the ages, the popular outlook on money lending and
borrowing has fluctuated between the extremes of disapproval
and encouragement, until today, far from being associated with
"usury", one who grants credit to another is accepted as an
essential link in the national economy. It is not often realized
just how essential this link is. Without it, there would be no
banks, no building societies, no hire purchase, no houses "bought
on mortgage", no debentures, hardly any stocks or shares, no
government borrowing (and consequently frequent and violent
changes in taxation rates), and—perhaps worst of all—no life
offices as we know them today.
The type of mathematics with which we are particularly con-
cerned here is that applicable to the transactions of this latter
type of organization. A life office in its daily routine receives
premiums ("borrows") from its policyholders, invests ("lends")
them, and ultimately has to meet the claims ("repay") to those
who live or die, according to which "event" was covered
("assured") at the outset.
CT.S.—1* ix
X PREFACE
It is not, of course, the sole prerogative of life offices to lend
and borrow money, and much of what follows is applicable to
bankers, accountants, estate agents, economists, stockbrokers and
jobbers, and, indeed, to all who are professionally or privately
concerned with how money increases with the passing of time.
It is primarily for insurance students that this book is written,
and a thorough grasp of Chapters 1-22 and 24-28 will enable the
average student to pass the Part C examination paper called
Fundamentals of Compound Interest for the Associateship of the
Chartered Insurance Institute. By "a thorough grasp" is meant
not only reading and knowing the bookwork, but also doing
enough of the many examples to become really fluent in the
language and methods, so that before the examination the candi-
date is properly prepared and already accustomed to getting
answers down on paper in a pleasantly readable form.
The student aiming for a distinction should also cover the
ground in Chapters 23 and 29-34, and the budding actuary will
find the remaining chapters interesting apart from their taking in
some of the syllabus of another Part C subject, Mortality and
Elements of Valuation.
I am especially grateful to the Chartered Insurance Institute
for permission to reproduce many previous examination questions
and the table on p. 378 which sets out the factors hitherto "given"
on the examination paper itself. There is no guarantee, of course,
that the Institute will continue to set its papers in precisely the
same form, but all the questions reproduced here are intended to
be answered from those tables only.
I would also like to acknowledge the kind consent of the Editors
of The Times, The Sunday Telegraph, and The Amateur Winemaker
to reproductions from their respective papers on pp. 7—9, 42, and
310. For the illustrations, I am happy to thank the Institute of
Bankers, the British Insurance Association, Macdonald & Co.
(Publishers) Ltd., Heinemann Educational Books Ltd., and—
last but by no means least—"Rookie" (R. F. Rooke, M.B.E.),
whose lively interpretations and misinterpretations do so much to
add spice to what is usually thought to be a rather dull subject.
PREFACE XI
Finally, I must express my sincere appreciation to Mr. M. E.
Lewis, M.A. (Cantab.), F.I.A., F.S.S., for his many constructive
suggestions and his untiring assistance in the otherwise thankless
tasks of checking the table on p. 376 and the original manuscript.
Now good luck with your adventure into the unknown; remem-
ber, as you go, the R.A.F. Parachute Training School's motto,
Knowledge dispels fear. You will soon become familiar with the
fearsome-looking symbols by getting to know them verbally, and
if your colleagues catch you mumbling to yourself that "immedi-
ate is not immediate, it's in arrears" you will be one up on them,
because by then you will know what you mean, and they won't.
Holborn College G.E.C
Plan of Study
COMPOUND INTEREST is a subject which is ideally suited to study-
ing with pencil and scrap paper. As you read through the steps
developing each numbered equation, note them down in your own
abbreviated way. Then in the train to the office, or over coffee, or
at any other uncommitted moments of your day, go through your
rough notes and check whether you have fully grasped the subject-
matter which they represent. Compound interest can be exciting—
and dangerous—when studied in this way. One recalls the sad
fate of the gallant actuarial student who was run over by a bus
while reviewing a paid-up sum assured formula in the middle of
the road
So keep your feet on the ground! As you feel you have grasped
each numbered equation, and each sentence printed in bold type,
transfer the best of your scrap-paper notes into a little pocket-
sized book which you can carry around with you and refer to
frequently—and do so progressively more often as the date in
April gets closer. Make these notes in ink.
If you find you cannot grasp a particular point after, say, three
attempts, write it down (either an equation or a brief sentence
summarizing the idea which is eluding you) into your notebook in
pencil and press on, but come back to this point as often as you can
during the next few weeks. You will probably find, as with most
mathematical studies, that many things which seem obscure and
difficult at first suddenly become clear later on with usage and
practice. The difficulty never lasts for ever, but do not waste time
while it does last. By pressing on you will be acquiring fresh
knowledge as well as developing (by use) whatever has been
causing the trouble, and when eventually it does "click" it will
xiii
XIV PLAN OF STUDY
be seen in a much wider context than was possible when it was
introduced.
If the difficulty persists, at least memorize the formula which
emerged from the troublesome paragraph, but recognize that this
is only a second best, and it can never be as good as remembering
how that result was produced. The ideal, of course, is to grasp
each point before passing on to the next, but if the ideal cannot
be attained without spending hours reading and re-reading a
certain part of the text over and over again, it is the lesser of two
evils to utilize those hours forging ahead covering more ground
and regaining any lost self-confidence.
The mathematically inclined will find little difficulty in master-
ing the essentials (indeed, they may even be somewhat critical
of the lack of mathematical rigour in the earlier parts), and they
will doubtless find themselves comfortably completing the C.I.I,
syllabus (Chapters 1-22 and 24-27) well within the customary
September-April session.
It is primarily for those without the doubtful blessing of a
mathematical bent, however, that this book has been written, and
for those in particular the opening advice about note-making is
known to produce successful results.
Whatever the student's level of attainment or ambition, planned
regular study is essential to master this subject as much as any
other. This particular subject, too, lends itself to grading, and two
grades which are immediately and easily discernible are those with
and without G.C.E. O-level (or equivalent) in mathematics.
Included in the "with" category are those who comfortably passed
the algebra part of the Institute's preliminary examination. In-
cluded in the "without" category are those who qualified in the
preliminary examination by taking the arithmetic and geometry
options in mathematics, and those who took G.C.E. more than
10 years ago and have not used their algebra since.
Another classification is into those who just wish to acquire the
barest minimum necessary to pass the examination (whereupon
it is all forgotten), and those who really want a broader and
deeper insight into life assurance in general (which could hardly
PLAN OF STUDY XV
exist in its present forms without the effects of investment and
compound interest); who take examinations in their stride, and
who prefer "the big picture".
Both are catered for in the pages that follow, but however you
classify yourself, there are three more tips (as well as the note-
making one) which do bear dividends for all students.
(1) HAVE A TIME-TABLE, AND STICK TO IT. Only planned and
regular study produces successful results. There are specimen
study plans on pages xvii and xviii, but whether you stick rigidly to
one of those or not it is essential to have a set of targets throughout
the studying period, and reach them. If you find yourself behind
schedule, do not alter the schedule', alter instead your own alloca-
tion of your available time. Otherwise you are ignoring a most
useful red light, and you will have only yourself to blame when
the inevitable crash comes.
(2) Do THE EXAMPLES at the end of each chapter. They provide
invaluable experience not only on the course itself, but also on
recognition of the questions actually being asked in "exam-style"
English. Without this experience, you will have to spend many
valuable minutes in the examination just reading questions over
and over again to find out what the examiners want. There is no
substitute for such experience, and there is only one way to get
it. So don't wait until April. Make a point, after reading each
chapter, of doing at least one of the examples on it formally;
write out a self-contained answer as you would in the examina-
tion, making every effort to get a correct answer onto paper within
10 or 15 minutes.
Then—and follow this routine in the examination proper too—
ALWAYS CHECK BACK TWO THINGS:
First: HAVE I ANSWERED THE QUESTION WHICH
WAS ASKED?
Secondly: IS MY ANSWER REASONABLE?
Getting this habit right from the start will obviate the two main
causes of loss of marks in examinations—not answering the
question, and giving obviously impossible answers.
