Investments occur over time, and therefore the time element of interest rate “compounding” is extremely important. By compounding we mean interest that is paid on interest, which been reinvested; in other words, “interest on interest.” If this seems confusing, please stay with it until it becomes clear. To understand why, consider that Albert Einstein once said that, “Compound interest is the eighth wonder of the world. He who understands it, earns it… He who doesn’t, pays it.”
Significantly, you do not have to be as smart as Albert Einstein to appreciate the power of compound interest. One way to appreciate it is through the “Rule of 72.” I recently used this “rule” to explain compounding to a family friend. First, I asked him how many years it would take $1 to double at an annual interest rate of 50%.
He responded, “Two years.” When I then asked him to explain how he came up with his answer, he replied: “50% interest in year one plus 50% interest in year two equals $1, which when added to the $1 we started with equals $2. Double the investment.”
I replied, “Yes, but in the second year you are also earning interest on the interest received for the first year, which your answer excluded. Therefore, the actual amount of years it takes to double is approximately 1.5.” To understand why, you divide 72 by 50 (the interest rate), which equals 1.44 or approximately 1.5 years.
There are obviously limitations with “quick-and-dirty” calculations like the “Rule of 72,” which are beyond the scope of this article. A key benefit, though, is that such calculations can be useful for personal investment planning. To understand how, first consider the below table:
Note: “Years to Double” in the bottom row were calculated using the “Rule of 72,” and have been rounded.
Tables like the above beg a rather obvious investing question: How can higher returns be earned over time so that money will double at a faster rate?
One way to address such questions is to compare current investment options with the returns being earned in the market, which is fairly easy to do. For example, as of August 10, 2015 a popular investment website profiled the interest rates earned by four popular bond index funds. Those interest rates were 1.48%, 1.55%, 2.50%, and 3.38%. Given these rates, the “Years to Double” for these indices, per the first table above, range from approximately 48 to 21 years. This is a very long time, and as a result some people may be tempted to undertake riskier investments in the hopes of earning higher returns.
Many people who succumb to such temptations do not consider the compounding risks involved. To explain, if you lose money in a year (or in a number of years), it can take a long time to earn that money back, even with the power of compounding. Therefore, the first rule of personal investing is to not lose money, which is similar to the first rule of medicine: “first, do no harm.” Following this rule may not be exciting, but it will help to ensure that you do not lose the money you worked so hard to earn in the first place.