Compound Interest

“Compound interest is the eighth wonder of the world. He who understands it earns it. He who doesn’t pays it.”

 

– Albert Einstein –

There are people that argue that Albert Einstein was not the one that first called compound interest “the eighth wonder of the world”. Does it really matter? The real point is to drive home the fact that compound interest is likely the most powerful tool we have for wealth accumulation. It is used in every aspect of your financial life – banking, credit cards, investing, loans and mortgages, overdue bills, and is a critical component in retirement planning. Understanding how it works, and how it can work against you, is absolutely necessary in order to be financially successful.

Compound interest plays a critical role in saving enough money for retirement.
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Compound Interest – How it works

When you receive regular (simple) interest on an investment, you are paid an amount that is continuously based on the original balance (principal). For example, if you have a 10 year, $1,000 bond that pays 10% simple interest, you would receive an interest payment of $100 every year for 10 years.

$1,000 (bond value) x 10% (interest rate) = $100 (interest payment)
$100 (interest payment) x 10 years = $1,000 (interest earned over 10 years)
$1,000 (bond value) + $1,000 (interest earned over 10 years) = $2,000 – Value of investment after 10 years of simple (regular) interest

When interest compounds on an investment, instead of being paid out to you, it is added to the investment. Every year interest will be calculated on a higher amount because the value of the investment is growing. Using the $1,000 bond above, the example below is color coded to show how compounding increases each year’s interest payment (in green), and how the balance grows each year (in purple) with the added interest.

Note:The value of the bond at the end of each year after interest is added to it, becomes next year’s ‘starting’ value.

Interest Earned = Bond value beginning of the year x  10% interest
#2 – Bond value beginning of the year + Interest earned = Bond value end of year

Interest earned each year                  Bond value end of year
Year 1   – $1,000 x 10% = $100    *    $1,000 + $100 = $1,100
Year 2   – $1,100 x 10% = $110    *    $1,100 + $110 = $1,210
Year 3   – $1,210 x 10% = $121    *    $1,210 + $121 = $1,331
Year 4   – $1,331 x 10% = $133    *    $1,331 + $133 = $1,464
Year 5   – $1,464 x 10% = $146    *    $1,464 + $146 = $1,610
Year 6   – $1,610 x 10% = $161    *    $1,610 + $161 = $1,771
Year 7   – $1,771 x 10% = $177    *    $1,771 + $177 = $1,948
Year 8   – $1,948 x 10% = $195    *    $1,948 + $195 = $2,143
Year 9   – $2,143 x 10% = $214    *    $2,143 + $214 = $2,357
Year 10 – $2,357 x 10% = $236    *    $2,357 + $236 = $2,593

Interest earned after 10 years of simple (regular) interest: $100 (interest payment per year) x 10 years = $1,000
Interest earned after 10 years of compound interest: $2,593 (bond value after 10 years) – $1,000 (original value of bond) = $1,593
You earn $593 more with compound interest over 10 years, than you do with simple (regular) interest. $1,593 – $1,000 = $593
Over 10 years, compound interest gives you 59% more growth than simple (regular) interest.

A Penny a Day…

This example has been around for decades, and is a great way to teach kids about compounding interest. The sole purpose of this chart is to drive home the impact of compound interest, because the chance of an investment doubling every day for 30 days is about as likely as winning the lottery every week for 30 weeks. You could even add (on top of your lottery winnings) being struck by lightning (twice), and walking away without a scratch. The question is:
Would you rather have $1 million dollars now or a penny a day, doubled every day for one month?

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