# Compound interest

## Example of compound interest

Suppose that one cent had been invested 2015 years ago at a constant annual interest rate of 2%. After the first year, this interest rate was applied to the initial principal of one cent and the capital grew to 1.02 cent. In the second year, the interest earned was again 2%. However, from that time onwards, it was not applied to the principal only but to the compound capital value (i.e., 1.02 cent). Thus, after the second year, the capital increased to 1.02×1.02 cent. After the third year, the capital grew to 1.023 cent. After 2015 years, the capital has eventually grown to 1.022015 cent, which is roughly equal to 2.13x1017 cent or, more precisely, 213,474,546,813,926,768.7 cent.

Compare this figure to a similar investment using simple interest rather than compound interest. Suppose again that 1 cent is invested for a period of 2015 years at a constant annual interest rate of 2%. In this case, after 2015 years, the final capital is only 41.3 cent. This comparison highlights the effect of compounding, especially for long-term investments.

## History

Compound interest was once regarded as the worst kind of usury and was severely condemned by Roman law and the common laws of many other countries.[2]

Richard Witt's book Arithmeticall Questions, published in 1613, was a landmark in the history of compound interest. It was wholly devoted to the subject (previously called anatocism), whereas previous writers had usually treated compound interest briefly in just one chapter in a mathematical textbook. Witt's book gave tables based on 10% (the then maximum rate of interest allowable on loans) and on other rates for different purposes, such as the valuation of property leases. Witt was a London mathematical practitioner and his book is notable for its clarity of expression, depth of insight and accuracy of calculation, with 124 worked examples.[3][4]