The rule of 70 explained

PaulW63

What Is the Rule of 70?

The Rule of 70 is a simple formula used to estimate the time it takes for an investment to double in size based on its growth rate, taking into account compounding interest over the years. By dividing 70 by the growth rate percentage, you can quickly determine the doubling time.

How Do You Calculate the Rule of 70?

To calculate the Rule of 70, divide 70 by the annual growth rate percentage. For example, if an investment grows at 7% per year, the doubling time is approximately 10 years (70 ÷ 7 = 10). 

Why Is the Rule of 70 Useful?

The Rule of 70 provides a quick way to understand the impact of compounding growth rates. It’s commonly used in finance and economics to estimate the doubling time of investments, economies, or populations.

El_Torro

Not something I've encountered before. Seems simple and useful enough. 

Have a Thanks

Brie

I was taught the 8 and 10 rule.  Money at 8% compounded annually would double in 10 years.  Money at 10% compounded annually would double in 8 years. 

This was based on a savings bonds that were available in my youth.  Granted one rarely sees those sort of rates on savings these days.

clairec666

Brie said:

I was taught the 8 and 10 rule.  Money at 8% compounded annually would double in 10 years.  Money at 10% compounded annually would double in 8 years. 

This was based on a savings bonds that were available in my youth.  Granted one rarely sees those sort of rates on savings these days.

My quick calculation suggests that compounding at 8% should double in about 9 years. 1.08^9 = 1.99. And 10% would double in 7.25 years.
But as you say, we don't see those kind of rates any more!

clairec666

For those who are interest in the maths behind the "rule of 70", I've just spent a fun 5 minutes playing around with a graphing calculator.
If you want an exact formula relating the interest rate (x) and the time taken to double (y) you get:
y = log 2 / log (1 + x/100)
A good approximation to this is y = 70 / x (i.e. the rule of 70)
If you plot the two graphs alongside each other, you see how good an approximation it is
(the red line is the "exact" function, the blue line is the "rule of 70")

InvesterJones

More like a statement than explanation The actual formula for doubling is ln(2)/growth rate, but that can be approximated to 0.69 so using 70/growth% is close enough. Though I like to use 72 just because it has more factors so is easier to do in my head

clairec666

InvesterJones said:

More like a statement than explanation The actual formula for doubling is ln(2)/growth rate, but that can be approximated to 0.69 so using 70/growth% is close enough. Though I like to use 72 just because it has more factors so is easier to do in my head

Actually 72 looks like a slightly better approximation overall...


Although for rates of around 5% then 70 is more accurate than 72
71 is even more accurate!

masonic

clairec666 said:

Brie said:

I was taught the 8 and 10 rule.  Money at 8% compounded annually would double in 10 years.  Money at 10% compounded annually would double in 8 years. 

This was based on a savings bonds that were available in my youth.  Granted one rarely sees those sort of rates on savings these days.

My quick calculation suggests that compounding at 8% should double in about 9 years. 1.08^9 = 1.99. And 10% would double in 7.25 years.
But as you say, we don't see those kind of rates any more!

Still quite useful for investment returns.

EthicsGradient

The rule of 70 is pretty accurate, and it gets more accurate with lower interest rates. For instance, 1% doubles in 69.661 years, because 1.01 to the power of 69.661 is 2. 2% doubles in 35.003 years. 3% doubles in 23.45 years (23.45*3=70.35), etc.

I think the true number to use with very low interest rates and long periods is rather than "70" is 100 times the natural log of 2, which is 69.315, but "70" is obviously easier to work with (and almost exactly right for 2%, anyway). As the interest rate gets smaller and smaller, the product of the rate and the years gets closer and closer to that. And it works with other ratios - eg to triple your money it would be a rule of 100*ln(3)=110, more or less.

I think once upon a time I could have proved this, but not now.

20122013

interesting post, I envy you all, as you seem to understand this  and have a discussion..Would anyone mind sharing  how do you get to know what you know about the calculations? is it from being taught and/ or keep reading and learning? I ask as I would like to be able to follow posts,  usually they may seem basic to most but I find it quiet advance (one example is 'EthicsGradient' reply even though gave a breakdown of their calculations, I am still not always understand and do not know what to look up to teach myself, as it will be helpful for me to do my financial planning etc. thanks