APPENDIX

In Chapter XIV of The Rate of Interest “virtual,” or “real,”rates of interest were computed from “nominal,” or “money,”rates of interest by making adjustments for appreciation in thevalue of money calculated from index numbers of prices. Int his book, the money rates of interest are adjusted directly tothe rates of change in the general price level. These twomethods, of course, yield identical results, since the one is theobverse of the other.

The average annual percentage changes in the general pricelevel, given in the Tables VII to XI inclusive, are computedfrom the wholesale price indexes of the several countries. Theindex numbers for two dates, as 1825 and 1834, give us ameasure of the price level at those two dates, and from theseit is easy to calculate the average annual percentage change.The method is the same as that employed for finding the rate ofinterest by which $1, by compounding, will amount to a givensum in a given time. Theoretically, since the loans here in-cluded run usually perhaps thirty to ninety days, the quotationsof rates of interest averaged should begin at the first of the twodates, and cease, say, sixty days before the second. But theindex numbers are not always for definite points of time, norcan the interest quotations be subjected to such minute correc-tions without an immense expenditure of labor. Hence, themethod adopted has been to average the rates for all the yearsof a period, e.g., for the ten years, 1824-1834. The annualpercentage change in the price level is reckoned between thosedates. If the index numbers present the price levels at themiddle of 1825 and 1834, then the average interest rates oughtin theory to include only the last six months of 1825 and thefirst four months of 1834. But it seems better to include toomuch at both ends than to omit the averages for 1825 and 1834altogether, for the reason that an average is the more valuablethe greater the number of terms included.

The real interest rates are obtained by subtracting from themoney rate for any period the rate of annual change in theprice level for the same period.

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