Rule of Seventy??

Question

A rule of thumb for fiding how long it takes an investment earning continuously compounded interest to double is called the RULE OF SEVENTY.

To apple the rule, divide 70 by the interest rate written as a percent. At 5%, doubling requires 70/5(shows as a fraction)= 14 years to double an investment. At 7 %, it takes 70/7 (shows as a fraction)= 10 years. Explain why this formula works.

Phew.... that was a lot... I searched the internet and I am still having problems...LOL don't know why... Can someone help me understand... if you could show me step by step that would be great... I have 5 more just like this one...

Thanks.!!!

Answer 1

the formula works because it's just one of those number oddities.  however, the rule only works at less extreme rates of return - for instance if you double your money in a year, it's a 100% return even though 72/1 isn't even close to 100.

but it's a good quick and dirty estimate if you don't have a calculator handy.

Answer 2

it has to do with the compound formulas and the way they are derived.  Together with the formula of 69.3 and 72 these rules of thumb are close approximations when you solve the compound for 2 (meaning when your principal doubles) I can try to derive it for you here but it would take too long.  Instead look at the wikipedia article I found that touches on this point...

Answer 3

The rule of 70 is one of multiple rules that allow quick approximations of the number of years it takes to double your capital. A more commonly used rule is often called the rule of 72 (divide 72 by interest rate to figure out years to double).

Why does it work?

Let us assume a 10% interest rate. If the interest was simple interest (no interest on the interest), how long will it take for your money to double? Fairly easy to figure out, it would take 10 years. Based on this you know that a 10% interest when compounded should take less than 10 years (since you get interest on the interest).

If you calculated it out it takes 7.27 years to double your money with a 10% rate of return. The formula is CI = P + (1+r)^t. CI = compound interest. P = principal. R=rate and t = time.

With the rule of 70, you would divide 70 by the rate of interest (10) and come up with 7 years. This is a very close approximation. With the rule of 72 you would divide 72 by 10 and come up with 7.2 years which is even closer.

The rules of 70 and 72 do not give you exact answers. They are useful because they let you figure out the time it takes to double your investment when you are away from a calculator. These rules are also popular because they tend to be easily divisible by commonly used investment numbers (3, 4, 8, 10, 12).

Why does it work? Well two factors impact the period to double your capital. One is interest rate and the other is time period. Financial analysts (or mathematicians) figured out that a number around 70 can give an approximation of the time period for doubling.

Can it be mathematically demonstrated? Sure can. In fact I have seen it, but since I am no longer in school and use computer programs for most of my financial analysis, I would be hard pressed to work out the numbers.