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On the Rate of Interest in Loans repayable by Instalments
Published online by Cambridge University Press: 18 August 2016
Extract
There must at the present time be a vast amount of British capital embarked in loans. Foreign states are constantly holding out their lures with more or less of success to our monied men, and financial and other associations are always ready to take charge of the funds of such of them as prefer investing at home. In this state of matters it is somewhat remarkable that there is nothing to be found in our books on interest on the subject of loans. These are usually—and perhaps intentionally—so complicated with conditions in regard to premiums, discounts, times and modes of repayment, &c., as to render it almost always a matter of extreme nicety to determine the rate paid by the borrower for the accommodation, and that realized by the lenders on their investments. And yet, as I have just said, in no English work that I am aware of, is there anything to be found having special reference to the subject.
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- Copyright © Institute and Faculty of Actuaries 1869
References
page 91 note * These two rates will be the same in regard to a specified loan if the whole of the loan is held by a single individual; but by no means necessarily so if it is held by more than one. This will be seen hereafter.
page 92 note * Nouvelles Tables pour les Calculs d'Intéréts Simples et Composés, d'Amortissement, d'Annutés de Primes, etc. Far P.-A. Violeine. A Vaugirard, 1854. 4to. pp. 128 and 130. I may add that this work appears to be a recognised authority for the purposes of the Credit Fancier. A copy of it, I learn, has been recently added to the Library of the Institute of Actuaries.
page 92 note † Violeine, p. 124. M. V. has francs. I use pounds, as a measure of value with which we are more familiar.
page 93 note * The above is a very rude approximate process.
page 93 note † Assurance Magazine, vol. vi., p. 191. See also Introduction to the re-issue of Orchard's Assurance Premiums, pp. 12, 13.
page 93 note ‡ The above expression is simply the finite integral of bnvn. The general form is,
For C=b0, this gives the present value of the annuity to infinity when the first payment is made now; and for C = 0, it gives the like when the first payment is made a year hence. The form in the text is that which arises when the integral is taken between the limits 1 and n + 1. Multiplication of it by (1 +i)n converts it into
which is the amount of the annuity, first payment a year hence, in n years.
page 95 note * See Journal of the Institute, vol. xiii., p. 64.
page 98 note * Surely the first term of this numerator were better written {pr +af(1+t)}, and the last 