Compound Interest in the Seventeenth Century

BY C. G. LEWIN, F.I.A. RICHARD WITT’S Arithmeticall Questions, published in 1613, was a landmark in the history of compound interest. In a previous paper (J.I.A. 96, 121) I have described the book and attempted to show why it is so important. This article sets out some information about Witt’s life, which has come to light as a result of research done since the previous article (when very little was known about him). Then follows a discussion of some of the books on compound interest which were published later in the seventeenth century. These not only help to fill in the practical background but also show how the techniques came to be more widely known and how problems arose when interest rates were reduced. It is worth noting that there was an average inflation rate of around 1% p.a. during the first half of the century and an average inflation rate of nil, or even a slight deflation, during the second half (Birks & Morrell, 1976; Mitchell & Deane, 1962). Thus, to a very considerable extent, the interest rates used in calculations were real rates of interest. Witt’s book delved deeply into compound interest in a very practical way, with clarity of expression and accuracy in calculation. Tables of standard compound interest functions were given at 10%p.a. (the then legal maximum rate of interest) and 6¼% (which appears to have been the normal rate used for the purchase of freehold property, although Witt’s worked examples do suggest that 5% was sometimes used for this purpose). Although (1+i)n was also tabulated for 5%, 6%, 7%, 8% and 9%, the other standard functions were not printed for these rates of interest, which were therefore probably less commonly used in practice. Many worked examples were given, some with very elegant solutions, showing that of the subject, and thought processes like Witt had a considerable understanding those of modern actuaries. His book can perhaps be regarded as the first ever actuarial textbook. He came from a Northamptonshire...