The Rule of 72

[Bronte]

The Rule of 72

Divide the number 72 by the expected rate of return – the answer is the number of years it will take for a given sum to double at the expected compound rate of return.

Suppose your home is worth $400,000 today and you predict it will increase by 7% per annum. Divide 72/7% and the answer is close to 10.

If your prediction is correct, your house will be worth around $800,000 in 10 years time, and $1.6 million in 20 years time.

Any thoughts on this incredible rule?

 

[Buster]

Hey Bronte,

Errr No, not yet.. I vaguely recall the rule from some time ago..

Interesting stuff. Googling, will get back to you..

Regards,

Buster.

 

[Bronte]

Twenty years ago we read a book by Noel Whittaker
'Making Money Made Simple'

The Rule of 72 link:
http://www.thedaily.com.au/blogs/money-made-simple/2007/oct/26/rule/

 

[tech/a]

Its really just another observation with a statistic placed upon it.
Like an average.
Rule of Thumb.
80/20 rule
50/50/90 rule
90% of businesses fail in the first year.
95% of traders fail.
Technical analysis ultimately is a 50/50 proposition.

All observations which (someone--no one ever owns up) places a statistic on to quantify.

 

[Beej]

Rule of 72 breaks down on the boundaries - Eg, you need a 100% *annual* return to double in 1 year, but rule of 72 would say only 72% is required. (Although if you then break it down to a monthly compounded return of 6% per month then it actually does still work pretty well!).

So basically it's just a mathematical approximation (or rule of thumb) for a more complex mathematical formula, that works pretty well for the sort of time periods and sort of returns you tend to play with in investment/financial matters (ie, 5-20 year time horizons and 1-20% range average compounded returns.

Cheers,

Beej

 

[slackjaw]

Its actually quite accurate with that example, given an assumption of house value doubling every 10 years, then the interest earned is 7.17% per year, so divide 72 by 7.17 and you get 10.0418

Doing it the "hard" way ...

log(2)/log(1.0717) = 10.0099 ... so the error in this case was only 0.0319 years or 12 days

why does this work?

to calculate the true value, the formula is
log(F/C)/log(1+i)

F = future Value, C = Current Value, i = interest rate

since log(2) = 0.6931 and at low values of i, log(1+i) is very close to i itself (actually a little below), 100 times i is the way we generally express it as a percentage so se multiply the top by 100 to get 69.31, but since log(1+i) is actually a little bit smaller than i, then we get a closer value if we correct this by adding a couple to the numerator, making it 72.

The rule is optimised at an interest rate of 7.85% (completely accurate), using higher interest rates will make it less accurate, ie, at 15% there is a 2 month error, and if you managed a 72% interest rate, obviously the value would not double in that year.

It will work when broken down to a monthly rate of 5.95% for an annual rate of 100%pa, since the 5.95% youre now working with is close to the optimal 7.85%, remembering the number of periods is now in months, not years

 

[2020hindsight]

Its actually quite accurate

slackjaw - it's amazingly accurate yes?

Repost from Math Equation thread ...
btw, here's that table
and the difference between 2 and 2.0 is the fact that you are accurate to 2 significant figures in the second case. (note that the approxmation is evident when you take it to three significant figures. )

btw, that rule of 72 also works for trades obviously.

If you make a trade each week for 36 weeks that grows by 2% each (compounding), then you'll have doubled your money.

Equally if you trade each week for 24 weeks that grows by 3% each (compounding), then you'll have doubled your money.

.......... etc etc through that table

or each week for 6 weeks that grows by 12% each (compounding), then you'll have doubled your money. etc etc

 

[slackjaw]

Still I prefer to just use the formula, no need to concern with any inaccuracy and accommodates for working out the time for the investment to earn any multiple of its current value.

 

[chance]

you just divide 72 by inflation rate 72 divided by 3.25= 22 years