please ignore this post...

GR, please see the "special characters" that in within and the automatic reptition...

i suspect it is to do with using the "colour" tab....i used this colour to "hide" the "......" at the formula...

i repeated the same post immediately succeeding this post but this time, i removed using the "colour" tab, and the problem seemed to be resolved

Continuously Compounding

this may seem to be a digression, but i assure you this small topic is an integral part of this series on prob and stats/ risks vs rewards

first, review this piece on time required to double your investment... viewtopic.php?f=16&t=1711&p=40377#p40377

now, 72 is that "special" number that can approximate the time needed for one to double the investment capital.

but how is the number 72 derived? surely, there must be a sound mathematical logic behind this. and it is indeed derived<textarea name="message" id="message" rows="15" cols="76" tabindex="3" onselect="storeCaret(this);" onclick="storeCaret(this);" onkeyup="storeCaret(this);" class="inputbox">this may seem to be a digression, but i assure you this small topic is an integral part of this series on prob and stats/ risks vs rewards

first, review this piece on time required to double your investment... viewtopic.php?f=16&t=1711&p=40377#p40377

now, 72 is that "special" number that can approximate the time needed for one to double the investment capital.

but how is the number 72 derived? surely, there must be a sound mathematical logic behind this. and it is indeed derived from what is known in mathematics (and surely, some what familiar to many FA practitioners), as continuously compounding

the formula is :

.....RT

e

Making continuously compounding = 2, means you want to achieve 2 times your investment capital and taking into account, "continuously compounding" of returns (R) over a period of time (T).

hence, using natural log, and applying to both sides of the equation, we arrive at this :

.....RT

e.......= 2

RT x ln e = ln 2

RT = 0.72 (0.72 is easily converted to 72, when you treat R in % terms,ie. eg 6%, instead of decimated figure or 0.06)

now, we know where that "special" 72 comes from...

it is derived from continuous compounding concept