## Apr 22, 2009

### A useful rule of thumb

Recently someone was telling me about his savings that were in a guaranteed investment account, he was wondering how long it would take to double his money. I took him by surprise by giving him an answer after a couple seconds of thinking. Some of you might have guessed it, I do not have an integrated calculator in my brain, I just learned a trick from some specialists of the world of finance and, unfortunately, I do no know who the author is.

Usually, if you want to know how long it will take for your money to double, you need to use a pretty complicated formula, in a particular example, if one would ask how long it would take to double 1000\$ et would use n = ln(2000/1000)/ln(1+i). Here n is the number of years necessary to double your money, the time frame we are looking for. R is the interest rate the money is invested at. The expression ln(2000/1000) is the application of the natural logarithm. Using that formula on a financial calculator and using an hypothetical rate of 4%, this formula would give us 17.7 years. At 6%, it would give 11.9 years.

Now let me reassure you, i did not make that calculation to give an answer to that friend. That formula should be used if you want to get a very accurate answer. In the everyday life, we can use a shortcut. I did what very few people know about; it’s called the rule of 72. That simple rule has the following form: n = 72/r. That easier expression says that by dividing 72 in to r, that will give you the approximate number of years necessary to double the money. Coming back to the earlier example, 72 divided by 4% will give us 18 years. It is close enough to the earlier estimate of 17.7. With 6%, you get 12 years. It is still quite precise for everyday calculations.

So next time someone you know asks you how long it will take to double their capital, you will be able to surprise them by answering them in a couple of seconds, or almost, just by asking them their interest rate.

#### 1 comment:

1. now that's awesome. I had never heard about that before. And the nicest thing about it is that it's pretty accurate.