The Rule of 72

 

I read an interesting article today on the growth being shown by various economies and it contained this quote:

Concern about Chinese debt is not unwarranted, but with GDP rising by 6% per annum, its economy will be 80% larger in a decade, whilst India’s, growing at 7%, will have doubled.

and this made me recall "The Rule Of 72".  The rule is a handy yardstick used by financiers to quickly estimate the time it will take to double or halve an amount based on an interest rate.  It's very simple, really.  It works like this:

Say you have $1000 and you invest it or bank it at a cyclic interest rate of 6%.  At the end of the first cycle, you will have $1,060. After the second, $1,123.60, with the increase accelerating each cycle due to compounding.  At the end of the 12th cycle, your balance will be $2,012.20, approximately double your original investment, and 6 x 12 = 72.  As to the quote above, the balance at the end of cycle-10 is $1,790.85, about an 80% increase.

Another example: the interest rate is 3%.  After cycle-1, your balance is $1,030, then $1,060.90 (almost 6%).  By the end of cycle-23, you're at $1,973.59, and after cycle-24, it's $2,032.79, so 23-1/2 cycles give or take — call it 24, and 3 x 24 = 72.

As you can see, it's not exactly exact, but it's pretty close for use as a first approximation.  So, someone offering you a 4% rate is offering to double your money in (72 / 4 =) 18 cycles.  India's growth rate (according to the quote) will double its present size in (72 / 7 =) 10.3 cycles.

'72' is a handy number.