## Forest fire

The current economical state, at least in India seems to me to be like a forest fire. A forest fire burns out all the dying vegetation that is blocking the sunlight and makes conditions suitable for new growth. It resets everything back to where it was. It’s a new beginning.

In times of growth and good earning, we settle down comfortably and over a period, our intrinsic cost increases. When I say intrinsic cost it also includes costs that are incurred by third parties, directly or indirectly for us. For example, if my office sponsors transport facility for me without charging me for it, it’s included in the intrinsic cost.

At times like this, each cost is re-thought about. “Do we really need it?” When the office cuts transport people think “Can I work closer to where I live?” or “Can I shift my residence closer to office?”. In good times there was never need to ask these questions, but now there is. Overall the cost goes down. People are doing something they should have done anyways, but did not just for comfort.

There is mass upheaval, but there is also rationalisation. If too many people have joined the IT industry (more than what is intrinsically needed), some will join the biotech sector for example, if that is an emerging sector. Again, it something that should have happened anyway.

So the point is, upheaval and rationlisation are good. While these move us out of our comfort zones at the moment, they are better for the long term.

## 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,

a=p*e^(rdash*t/100)

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
a=p*(1+r/100)^t

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

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