Continuous Compounding

I feel there is something mathematically wrong with the way compound interest is defined today. We say “5% per annum, semi-annually compounded”. If I have money invested, mathematically speaking, it should get compounded all the time, not just in fixed intervals.

I would like to define the term “absolute percentage” – the annual interest rate at which the money must grow all the time in order to reach the same amount as it does using normal interest rate calculation. Let me explain what that means.

If I invest amount ‘p’ for period ‘t’ years, at an ‘absolute’ interest rate of ‘rdash’, then,


where ‘e’ is a mathematical constant having value approximately 2.71828182845904.

This means, that amount ‘p’ will grow to amount ‘a’ in ‘t’ years if it compounds continuously.

Here, rdash is the absolute equivalent of rate r if

Here is a table that explains it. Try and understand, ok?