The Rule Of 72

Readers of my third money book will know that I use the very simple and quick "Rule Of 72" to work out in my head how long it will take debt and/or investment values to double.

Extract for people who haven't read Your Investment Property yet:
For an investment: divide 72, by the average inflation rate, and that's roughly how many years it will take for your investment to double in value. Eg. If inflation runs at around 3% per year every year over a long time, then a home that's worth $150,000, will be worth roughly $300,000 in 24 years. (72 / 3 = 24) If the inflation rate jumps to 12%, then the house will double in value in only 6 years. (72 / 12 = 6)

You can also use the 72 rule to see how long it will take for your cash to lose half of its buying power. E.G: If you have $1000 in your savings account now, and leave it sit there earning jack-squat year after year when inflation is running at 12%, then in 6 years that $1000 will only buy you the equivalent of what $500 will buy you now.

What else you can use the Rule of 72 for:

Your Investment Property then goes on to explain how it works with debt levels in the same way. But here's something I didn't have room for. Use this to see how important it is for your investments or term deposits to double as many times as possible (and for your debts like credit cards and store accounts etc to double as few times as possible).

First, work out how many years you want to keep your investment before cashing it in. Then divide that by how many years it will take to double each time using the rule of 72. Now look at what happens to your $$$ each time it doubles...

$1 ... $2 ... $4 ... $8 ... $16 ... $32 ... $64 ... $128 ...

Can you see now what a big difference there is? (Especially after your investment doubles for the fifth time!!!) Scarey to imagine what we've been missing out on by settling for poor returns, isn't it? But exciting to see where it can take you now…

Why it works:

Now for maths nuts who like to know why the rule works (and for which values it doesn't), here's a more thorough explanation which may interest you:

The rule of 72 applies to annually compounded interest, but it's easiest to understand by looking at the case of continuously compounded interest first. We'll write P for the starting principal and r for the return rate (as a decimal); we're looking for Y to double P:

2P = Pe^Yr

Solve for Y:

Y = ln(2) / r

The log of 2 is about equal to .69, so

Y = .69 / r

You can think of this as The Rule of 69. It's valid for all values of r.

Solving the formula for annually compounded interest is messier:

2P = P(1 + r)^Y

Y = ln(2) / ln(1 + r)

We want to approximate this as a neat fraction again,

Y = K / r

where K is some number that will make the approximation pretty good for some ranges of r (and pretty lousy for others). We'll choose K to make the approximation work for a return rate of ten percent:

ln(2) / ln(1 + r) = K / r

ln(2) / ln(1 + .1) = K / 0.1

K = [ln(2) / ln(1.1)] x 0.1

K = .72

And that's it!