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Einstein once said, “compound Interest is the eighth wonder of the world. He who understands it earns it; he who doesn’t … pays it.” So, understanding the basics of this powerful mathematical tool can play a valuable role in deciding how much risk to take when allocating investments.

What escapes many is the degree to which increasing percentages of annual investment earnings yield exponentially larger amounts of profit over time. Earning 10 percent per year instead of just 5 percent does not simply double the amount of earnings over, say, twenty years. That would be a linear relationship between the two earnings figures represented by a straight line going up diagonally across the chart. Instead the difference is “exponential” meaning that as the annual percentage increases, the line representing the return attains an ever-steeper upward slope. For example, a 5 percent return on a $10,000 annual contribution to a retirement plan would accumulate to $350,000 in twenty years. At an annual rate of 10 percent, the nest egg builds to $650,000. In both cases, the contributions total $200,000, but the interest earnings on the additional 5 percent are $300,000 greater.

To drive home the point, a one percent compounded return on a $1,000 annual investment over 20 years generates $2,150 in profit, but the 1% difference between 9 percent and 10 percent on the same annual contribution crates a difference of almost $8,000 in 20 years.

What this means for people who stay committed to stocks --- and the expectation of a 10 percent return --- is that they can afford to lose 20 percent of their account balance in a market downdraft and still be way ahead of what a safe 5 percent might have generated in some collection of conservative investments --- bonds exclusively or an equal balance of stocks and bonds.

It should also prompt people to look once again at what they are paying in fees and to assess carefully whether they are receiving comparable value-added performance to offset what might be 1 to 2 percent in advisor plus mutual fund costs. Fees, remember, are not the first 1 percent. Their long-term cost represents what we saw as the difference between 9 and 10 percent.

Starting with the rise of 27 percent in 2009, the average annual return in the S&P 500 since the crash has been 16 percent per year over a period that includes two flat years (including the current one to date) of just 2 percent. Talk about resilience. The difference between 16 percent and 15 percent (the missing 1 percent for either fees or performance reasons) amounts to $5,000 compounded --- it’s the difference between $129,000 versus $124,000 on a seven-year $10,000 per year contribution.

A user-friendly resource for playing with the math of compound interest can be found at www.thecalculatorsite.com.

“Nothing succeeds like success,” but the concept is especially true with regard to successful investing. Beyond a certain point, portfolios of assets take on a life of their own and their owners can envision having enough to support an eccentric personal lifestyle supported by these resources regardless of what happens in the way of temporary reversals of fortune. Considering that, over the past thirty nine years, we have had only two calendar years when the market posted a loss of more than 20 percent (including reinvested dividends.) Striving for higher returns and living with volatility is a reasonable bet for most long term investors. Those exponentially higher returns more than compensate for the few substantial, but rare, downdrafts.