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What Is Compound Interest – Definition, Formulas & Obstacles

Humanity’s first experience with compounding – the accumulation of vast numbers through the systematic addition of small sums over a period of time – came from nature, not mathematics.

Thousands of years ago in the Fertile Crescent of the Middle East, ancient humans abandoned their nomadic ways, formed the world’s first communities, and began to till the ground, raising wheat, barley, and other grains. Growing seasons concluded with reaping and storing grain, which was used during months when agriculture was not possible and other food sources were scarce.

But because the large amounts of grain were stored in roofed buildings (silos), they provided an irresistible food source to Mus musculus – the common house mouse – which would feast protected from their natural enemies by the shelter of the silos. As a result, mice became extremely prolific, eventually leading to the spread of mice around the world as they followed migrating agriculturalists. In fact, a single pair of mice can produce 70 offspring during their two-year life, with an average litter of seven pups, five times a year.

SOURCE: M.R. Lewis, November 8, 2013
SOURCE: M.R. Lewis, November 8, 2013

The addition of 70 mice over a two-year span would be bothersome, but not catastrophic. A single mouse eats about one gram of food per day; 70 mice would eat about 70 grams, or less than a single bushel of wheat each year. However, when considering the effect of “compounding,” the mice pose a serious threat.

Each pair of mice is going to produce another 70 pups who, in turn, are going to have their own litters, and so on through the following generations. By the end of two years, the original pair of mice can produce a population of more than six million hungry creatures, collectively consuming more than 223 bushels of stored wheat per day.

Ancient granaries stored between 60 and 80 tons of wheat, or around 2,500 bushels. A single pair of mice, left unchecked, could grow – or “compound” – into a mass of creatures capable of eating an entire village’s stored food supply in less than two weeks. Indirectly, the effect of compounding led to the domestication of feral cats, the control of burgeoning rodent populations, and perhaps the survival of towns and communities as we know them today.

Compounding and Wealth

Just as mice produce generations of offspring, each of which produces its own progeny, wealth begets more wealth in the form of interest which, in turn, produces more wealth and more interest. Jack London, the early 20th century author, referred to “compound interest” in a 1906 essay, calling it “a remarkable invention of man.” London concluded that “if I began immediately and worked and saved until I was 50 years of age, I could then stop working and enter into participation in a fair portion of the delights and goodness that would then be open to me higher up in society.”

The compounding of wealth (or mice, as in the above example) is directly impacted by the following:

  • Incremental Increase Each Cycle (Interest Rate). In the case of mice, the increase would be the average litter size. When concerning money, it would be the amount of earnings on the underlying principle, commonly referred to as “interest” – a higher interest rate consistently earned over a certain period produces a greater ending sum than a lower interest rate over the same period.
  • Length of Each Cycle. In our mouse population, a key factor is the length of gestation and infant care required before producing the next generation. In the financial world, the length of each cycle is the period for which interest is earned and paid. For example, interest might be paid every six months, or it might be paid annually. Receiving interest payments for a shorter cycle has a greater impact on total accumulation of wealth. Earning 5% per year on a principal of $1,000 would create a balance in 10 years of $1,629. If you were paid 5% every six months, rather than annually, your balance would be almost 60% greater, accumulating to $2,653 in the 10-year period.
  • Number of Cycles Within the Period of Compounding. The importance of time is often overlooked when considering the impact of compounding. As years pass and the number of cycles increases, total accumulation accelerates. For example, the mouse population at the end of a year beginning with a single pair would number 3,285. If their offspring reproduced at the same rate, an incredible six million would be added in the second year alone. An investment of $10,000 earning 5% per annum would increase $500 at the end of the first year, but that gain each year would increase by more than 50% to $775 in the 10th year. As the earnings rate increases, the benefit from a longer holding period accelerates.

Obstacles to Compounding

Animal populations face natural obstacles – predators, disease, uncertain food supplies – which limit their population growth and the effect of compounding. Investors seeking the advantage of compounding in the financial world face similar obstacles, including the following:

  • Human Nature. The urge to consume, rather than save, is powerful and escalated by the plethora of products available and adroitly marketed by psychologists and advertising mavens. It takes considerable discipline to forgo immediate gratification in favor of amassing significant wealth over time. As a consequence, the willingness to let investments grow unimpeded is rare.
  • Theft. Left unprotected, capital is subject to predation from thieves by way of fraud and burglary. As a consequence, it is lost, earning rates are reduced, and holding periods are shortened.
  • Competition. Investors compete for a limited number of investment opportunities with maximum return and minimal risk. This results in depressed earning rates as more capital (supply) chases the same investments (demand).
  • Risk. Some investors, seeking higher returns, invest in assets that are subject to greater perils, thus exposing their capital to significant loss. Inappropriate assumption of risk without compensating higher returns – or failure to manage it – is likely to result in capital loss.
  • Taxes. While many obstacles to wealth-building are sporadic and capricious, government taxes are constant, reducing annual net rates of return up to 39.6% and drastically reducing total accumulation. For example, the tax rate for a family with taxable income between $72,500 and $146,400 is 25%, effectively reducing an annual return of 6% to 4.5%. Fortunately Congress, recognizing the societal benefits of savings, provides legal methods to defer or eliminate taxes through tax-advantaged accounts such as individual retirement accounts (IRAs) and 401k plans.

Being willing to accept a lower return for assurance of a longer, more consistent, and safer earnings rate is the key to compounding success, as are regular contributions into tax-sheltered vehicles such as IRAs and 401ks. An investment of $10,000 per year at 5% per annum return is going to grow to $948,363 in 35 years. Investing the same amount at the same rate, but paying a 25% annual tax on the growth each year, would reduce the principal to $726,887. The difference of more than $220,000 between the two values is solely the consequence of using a tax-advantaged account.

Super Growth Formula

A Super Growth Formula

Saving regularly and leaving income in the account where it can compound is the key to building large sums of wealth. Consider the following example:

Saving Regularly

Andy opened a tax-sheltered IRA in 1974 at the beginning of his career as a salesman of HVAC equipment. He began contributing $125 per month to the IRA, the maximum amount he could contribute at that time. He continued his contributions even though he married, bought a home, changed jobs several times, and paid for two kids to go through the local college.

Over the next 39 years, the law was changed several times to allow greater annual amounts to be put into the tax-sheltered IRA – in 2013, for example, the maximum contribution for people over the age of 50 was $5,500. Always contributing the maximum allowed, Andy’s total contributions for the 40-year period have been $180,000. The value of his account today, however, is considerably greater as a result of compounding interest.

Compounding Interest

Being a practical man, Andy’s investments have always been conservative, heavily weighted toward government and corporate bonds with less than one-third of the total invested in a no-load mutual fund recommended by his neighbor. As a consequence, his average annual return of 6% has been considerably less than he would have earned had he invested entirely in an equity fund with an average return during that same period of more than 9%.

Nevertheless, the balance in Andy’s account had grown to $502,000 by mid-2013, a fund large enough to provide a monthly income of $2,082 without invading his principal. This income, plus the estimated $3,200 a month he and his wife receive from the Social Security program, ensures that both are going to be secure in their retirement. While older than Jack London’s “50 years of age,” Andy should be able to quit working and “enjoy a fair portion of the delights and goodness” of life in his remaining years.

If you haven’t started investing, today is the day. You can open an account with M1 Finance and receive free trades with no commissions. You can set your investments to be automatic and enjoy the benefits of compound interest.

Final Word

Compounding can be a difficult concept to grasp initially, but once learned and appreciated, can pay dividends for years. Beginning to save early and regularly, carefully selecting your investments, and resisting the impulse to spend the accumulating sums can provide comfort and stability when you are no longer able or have the desire to work. It is the foundation of wealth, and like any solid foundation it supports and encourages unlimited growth.

Have you seen evidence of compounding interest in your savings?

Michael Lewis
Michael R. Lewis is a retired corporate executive and entrepreneur. During his 40+ year career, Lewis created and sold ten different companies ranging from oil exploration to healthcare software. He has also been a Registered Investment Adviser with the SEC, a Principal of one of the larger management consulting firms in the country, and a Senior Vice President of the largest not-for-profit health insurer in the United States. Mike's articles on personal investments, business management, and the economy are available on several online publications. He's a father and grandfather, who also writes non-fiction and biographical pieces about growing up in the plains of West Texas - including The Storm.

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