Thomas Harriot on continuous compounding

Abstract

In the unpublished papers of Thomas Harriot (BL Add Ms 6782 f. 67) there is a remarkable calculation. It concerns what is now known as the continuous compounding of interest, and was probably written before 1620. This article describes the background to Harriot's calculation, and its significance. The general solution of Harriot's problem depended on some of the important mathematical developments in seventeenth century, such as logarithms and infinite series. By 1727 John Arbuthnot was able to give a recognizably modern account of it, but the final step was the work of Leonhard Euler.

Acknowledgements

I am very grateful to Jacqueline Stedall for deploying her extensive knowledge of seventeenth century mathematics (and Harriot in particular) in order to comment on an early version of this article. The transcript of Harriot's manuscript is published by permission of the British Library Board.