What Is The Rule of 72 Investing and How to Double Your Investment

If you ever want to double your money according to a certain interest rate, then you should follow the “Rule of 72”. It is the rule at which money will double every 7.2 years at 10%.

Just divide your yearly interest into 72. Let us take an example: if your interest for an investment is a constant 6%, then your money will double in 12 years (72 divided by 6). You can use the same rule the other way round, for example, you can calculate your interest rate based on the knowledge of how many years are required to double your money. Thus, to double your money in 2 years, you will need 36% rate (72 divided by 2).

Of course, and like any rule of thumb, these are approximate results, for to calculate the exact result in the case of a 10% rate, we have to follow the following equation, where “P” is the given principal, “r” is the interest rate in percent per year, “n” is the number of years:

P * (1 + r/100) ^ n = 2P

Please notice that the symbol ‘^’ is used to denote exponentiation (2 ^ 3 = 8).

Since r = 10%, therefore:

P * (1 + 10/100) ^ n = 2P

We cancel the P’s to get: (1 + r/100) ^ n = 2

Continuing:

(1 + 10/100) ^ n = 2
1.1 ^ n = 2

Since in calculus the natural logarithm (”ln”) has the following property:

ln (a ^ b) = b * ln ( a )

 

Thus:

n * ln(1.1) = ln(2)
n * (0.09531) = 0.693147

Finally:

n = 7.2725527

Which means that at 10%, your money will double in nearly 7.3 years, and that is extremely close to the 72% rule.

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