The formula for determining how long it takes to double your money is a bit tricky. Luckily, there is a simple shortcut that’s surprisingly accurate.
Let’s take a little trip back to high school and do some basic algebra. We’re going to assume a deposit of $1,000 and an annual growth rate of 5%. How long would it take to double our money?
$1,000 * 1.05x = $2,000. Where x = the amount of years, $1,000 is our initial deposit and $2,000 is our target of doubling our money.
Dividing both sides by $1,000, we simplify to 1.05x = 2. Great, we now require logarithms to solve this.
log 2 / log 1.05 = 14.2 years.
Certainly not the stuff you’d want to do on the top of your head.
Let’s introduce a simple guideline that will make your life a whole lot easier:
Divide 70 by the annual interest rate to get an approximation of how many years it would take to double your money
Let’s use our example: 70 divided by the 5% annual interest rate gives us:
70/5 = 14 years.
As you can see, the calculation is only 0.2 years off. Not bad for such a simple rule!
Testing our new rule
Below you’ll find a table of results in which we test the rule of 70 against the actual number. You’ll see that percentage-wise, the error margin increases as the interest rises. For quick and dirty off-the cuff calculations though, the rule of 70 should work just fine for interest rates at and below 10%.
|Interest rate||Actual time to double (years)||Rule of 70|
TLDR: if you want to have a rough estimate of how many years it will take to double your money with a given interest rate, divide 70 by that interest rate.