# Witness the Power of Compounded Returns using the following Compound Interest Example

A simple compound interest example can go a long way in explaining the power of this fundamental financial concept.

Some people have even claimed that when asked to name the greatest invention in human history, Albert Einstein simply replied "compound interest". [Hartgill, 1997]

Use the "Rule of 72" to estimate how long it will take to double your money

Divide 72 by your yearly interest rate, and you get the number of years it will take you to double your money (assuming no change to the interest rate, which is unlikely).

The rule of 72 ONLY works when your interest rate remains constant (unlikely) and your interest/dividends are reinvested. The rule does not factor in taxes.

### What is Compound Interest?

First, lets start with the concept of "simple" interest. Simple interest refers to the calculation of interest based on the "principle" or initial value.

For example, if you have \$10,000 and earn 10% interest, the simple interest calculation would be:

\$10,000 x 0.10 = \$1,000

Compound interest is the calculation of interest based on the principle AND accrued (i.e. accumulated, earned, etc.) interest. Let's take the simple interest equation above and turn it into a compound interest example.

If you have \$10,000 and earn 10% interest per year, how would you calculate the interest in the second year using compound interest?

Year 1 = \$10,000 x 0.10 = \$1,000

Year 2 = (\$10,000 + \$1,000) x 0.10 = \$1,100

Compounding allows you to earn interest on your interest, so to speak.

### The Positive Benefits of Compound Interest

The chart below illustrates the power of compounding, using an initial account balance of \$10,000. Each colored line represents a different annual interest rate.

Compound Interest Example - Yearly Compounding of \$10,000
(Click for the full size image)

For each interest rate (see the legend along the bottom of the graph), you can trace how much your balance will rise over a given period of time. If you achieved a constant return of 7%, your account would grow as follows:

Year 1 = \$10,000 + (\$10,000 x 7%) = \$10,700

Year 2 = \$10,700 + (\$10,700 x 7%) = \$11,449

Year 3 = \$11,449 + (\$11,449 x 7%) = \$12,250

Year 4 = ...

The reason everyone talks about investing for the "long term" is due to compounding returns. You can see how quickly your balance can grow in this compound interest example.

The real magic happens after your money has been earning a particular interest rate for 20+ years!

### The Negative Side of Compounding

Unfortunately, compound interest can also work against you. The chart below shows how long it takes to recover from a 7% loss to a starting account size of \$10,000.

Time Required to reach \$10,000 after a One Year Loss of 7%
(Click for the full size image)

For example, if you lost 7% in Year 1, and then gained 7% in Years' 2 and 3, the calculations are as follows:

Year 1 = \$10,000 + (\$10,000 x -7%) = \$9,300

Year 2 = \$9,300 + (\$9,300 x 7%) = \$9,951

Year 3 = \$9,951 + (\$9,951 x 7%) = \$10,648

Assume that you have all your money in one investment that loses 7% in one year (or that your overall portfolio lost 7%). How would you regain what you lost?

Would the investments you currently hold give you the returns needed to get back to where you started in a year or less?

Hold that thought...lets take this "negative" compound interest example one step further.

### The Real Break-Even Point

Technically speaking, the chart above shows you how to get back to your original balance. In other words, if you lost 7% the first year (\$700 based on the \$10,000 compound interest example graphed above), it would take at least 1 year to get back that loss and have an account balance of \$10,000 again (sometime in Year's 2 through 9).

But is that really break-even?

As you can seen in the first example, if you avoided a loss in years 1 and 2, you would have more than \$10,000 at the end of year 2, regardless of the rate of return.

This means that your break-even point is NOT \$10,000...it is actually something higher, depending on the original rate of return.

Returning to our 7% loss example, lets take a look at the real break-even point.

Time Required to "Catch-Up" after a One Year Loss of 7%
(Click for the full size image)

You would need to achieve a 23% return in Year 2 in order to get to that higher break-even point!

From the first set of calculations, we know that we need \$11,449 at the end of year 2. And we know that our balance at the end of year 1 is \$9,300, due to the 7% loss.

Year 2 = \$9,300 + (\$9,300 x ?%)

Year 2 = \$11,449

Combine the two equations:

\$9,300 + (\$9,300 x ?%) = \$11,449

(\$9,300 x ?%) = \$11,449 - \$9,300

?% = (\$11,449 - \$9,300)/\$9,300

?% = 0.23 = 23%

Think about this: Many financial advisors and retirement calculators use 6%-8% as the "average" return for the stock market over the "long term".

Using the first chart, you can estimate the dollar amount you need to see in your account balance, at the end of each year, in order to make those 6%-8% projections come true 20 or 30 years down the road.

This is why it is EXTREMELY important to focus on finding and minimizing your losses (The 2nd Principle of Safe Investing).

**Please note that these are very basic compound interest examples. The data assumes a constant interest rate, annual compounding, and no adjustment for taxes, fees, commissions, etc.

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