The famous "Rule of 72" states that roughly speaking money will double in (72 / r) years when the money is invested at an annual compounded interest rate of r%.
Notice that according to the rule, we are not interested in the amount of money that you will have in your bank account when the money is doubled.
We are interested in knowing when the money will be doubled.
For example, suppose you invest money at an 6% compounded annual interest rate, how long will it take for the money to double?
The money will double in 72 / 6 years or 12 years.
Suppose instead you invest money at an 9% compounded annual interest rate, how long will it take for the money to double?
The money will double in 72 / 9 years = 8 years
Finally, notice that it will take the same amount of time for the money to double regardless of the amount you invest as long as the interest rate is the same.
For example, 1 million dollars will take 8 years to double at an 9% compounded annual interest rate.
By the same token, 100 dollars will take 8 years to double at an 9% compounded annual interest rate.
Therefore, the higher the interest rate, the faster the money will double.
On the other hand, the lower the interest rate, the more time it will take for the money to double.
For example, a rate of 1% interest will take 72 / 1 or 72 years to double. Imagine that!
Imagine you have a 100 dollars in a saving account at a local bank. If they offer 1% compounded annual interest, you will have to wait 72 years to see 200 dollars in the bank.
Yet most banks do not even offer 1%!
Feb 17, 19 12:04 PM
There is no rational number whose square is 2. An easy to follow proof by contraction.