You have probably heard of compound interest before. At least you should have been as even Albert Einstein called it the eighth wonder of the world. He said:

Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it.

**What Is Compound Interest?**

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

In other words it is an “interest on interest” and its believed to have originated in 17th-century in Italy. It will make a sum grow faster than simple interest, which is calculated only on the principal amount.

Compounding multiplies money at an accelerated rate and the greater the number of compounding periods, the greater the compound interest will be.

The compound interest formula is:

A = P(1 + r/n)^(nt)

Where: A = the future value of the investment P = the principal amount r = the annual interest rate n = the number of times the interest is compounded per year t = the number of years the investment is held

For example, if you invest $1,000 in a savings account with an annual interest rate of 5%, compounded monthly, after one year, your investment would be worth:

A = 1000(1 + 0.05/12)^(12*1) = $1,051.16

Note that with compound interest, the interest earned in each period is added to the principal, resulting in a larger base on which future interest is calculated. This compounding effect can result in significant growth in the value of an investment over time.

What’s the difference between simple interest and compound interest you may ask?

So **simple interest** is calculated only on the principal, or original, amount of a loan.

**Compound interest** is calculated on the principal amount and the accumulated interest of previous periods, and that’s why it may be regarded as “interest on interest.”

Here’s an example for you guys.

For example there are two people who have $1M to invest for 30-years in something that generates 8% on average. Let’s say Karen chose not to reinvest the interest and just keep the initial principal invested. And another person let’s name him Thomas, chose to reinvest his interest (in other words he chose to compound his interest).

Karen would have generated $80,000 of interest per year for 30 years. So she received $2.4M in interest payments over the 30-year period plus she still has $1M she initially invested. So, her total capital is $3.4M.

While Thomas would have a total balance of $10,062,000. That’s almost triple the amount Karen has generated, only because Thomas chose to reinvest his interest.

## The Rule Of 72

Now here’s another rule which may help you to calculate how fast you can double your money with compound interest. It’s called the rule of 72.

The rule of 72 is a quick and simple way to estimate the time it will take for an investment to double in value based on a fixed annual interest rate. The rule states that the number 72 divided by the annual interest rate will give you the approximate number of years it will take for your investment to double in value.

It can only be used for annual compounding but can be very helpful in planning how much money you might expect to have in retirement.

You simply need to divide 72 by the return you are getting. For example, an investment that has a 6% annual rate of return will double in 12 years (72 ÷ 6%).

An investment with an 8% annual rate of return will double in nine years (72 ÷ 8%).

The rule of 72 is useful for estimating the time it will take for an investment to grow, but it is not an exact calculation. It assumes a constant rate of return, which is unlikely to be the case for most investments. Additionally, it does not take into account any fees or taxes that may affect the actual return on your investment.

Despite these limitations, the rule of 72 can be a useful tool for investors who want to quickly estimate the potential growth of an investment based on different interest rates.