My high school Trigonometry teacher was the first person I knew to correlate mathematical theory to experiences in life. She loved to draw parallels between equations and philosophy. At the time, much of what she said was over my head, but I remember her kind smile and light-hearted references between math and life. It seemed like she was about 80 years old, and I wish now I had paid more attention to what this wise woman was really trying to teach us teenagers. 

These days, the mathematical equation of compound interest resonates with me. Perhaps it’s because we’ve had several years of mostly favorable markets. (We will forget about 2022 for a moment.)

For an investor, compound interest works like magic to help build a portfolio over time. I have often heard the analogy of compound interest being like a snowball rolling down a hill. It starts small, but as it gathers more momentum it picks up more snow, making the snowball become larger and larger. Even the famous investor Warren Buffet used this analogy. 

Now, for a debtor, such as anyone with a mortgage, a car loan, or credit card debt that is carried each month, compound interest is seen as not as something magical, but quite the opposite. We will save further discussion on that for another day. For today, I thought you might enjoy a primer on the concept of compound interest for an investor, and how it may correlate with certain non-financial aspects of life.

The four main components for compound interest include: 

• Principal amount
• Growth rate 
• Length of time funds are invested and
• How often interest is compounded (daily, monthly, or annually.) 

Let’s define first the difference between simple interest and compound. If you have $10,000 invested for 1 year, and you receive a distribution each month for the interest earned, that is considered simple interest. You don’t reinvest the earnings, but you do keep the original amount invested and receive your return. So, $10,000 invested at 4% with simple interest will yield you $400 at the end of a year. If you keep going, you will end up at the end of 10 years with your original $10,000, plus $4,000 that you earned over time and spent on various things. 

Compound interest is different in that in lieu of taking that distribution, you instead reinvest it. Therefore, each month you earn money on your interest as well as your original principal. The more you can earn, the faster the earnings multiply. For that same $10,000 over one year at 4%, your earnings would have been slightly more at $407.42.

At this point, you may be thinking, “that’s not that big of a difference”, but hang with me a little longer. Over 10 years, the accumulated earnings are $4,908.33, because month after month, you earned the 4% on your original amount invested plus all the monthly earnings after each month, plus all the earnings on those earnings. That means over $900 more is earned in this example.

Now, instead of a 4% return, assume the return is 8%. So, for simple interest at 10 years, that would be $8,000, but for compound interest, you are now at $12,196. Are you starting to see the gap widen?  

For an investor, it is difficult to control the rate of return (which are determined by market forces), other than you can raise or lower your rate of risk. However, you can control the amount of principal you invest. In addition to your original investment, plus a little higher risk, you could add $200 per month. That would spice things up a bit, and after 10 years at 8%, you would now have about $59,000. For someone saving for a first home, that math may be encouraging.

What I like about compound interest theory is that it applies to so much more than financial investments and savings. If you look carefully, you can see the concept of compound interest applied to almost any endeavor. Think about how this concept could apply to an exercise program, starting a business, improving your eating habits, spiritual growth, and almost any hobby you can think of.

For example, a student who is learning a musical instrument and practices every day will experience his abilities improving exponentially. You can think of the purchase of the instrument as the initial deposit, the amount of time spent each day as the interest earned. As time passes, the student gains proficiency as he masters the instrument and gains knowledge in the music being played. The student’s overall skills progress—much like the power of compound interest. That is a very different approach to just showing up at a music lesson one day a week, which is more like the simple interest concept.

Even students trying to learn a new life skill or profession will find the compound interest philosophy important. It is no longer good enough to “just pass the test” each week at a course in school. For any real progress to be made, a subject needs to be studied for the knowledge to stick—much like the snowball rolling downhill in my opening analogy. So, there it is: a little bit of math philosophy to kick off your weekend. No wonder Albert Einstein referred to compound interest as the 8^th Wonder of the World. When you realize its power, it becomes a strong motivational force. One of the best gifts you can give to a youngster is to help them to understand it.

Kristina Bolhouse, CPA/PFS, CFP®

Vice President/Shareholder

© 2024 Kristina Bolhouse and The Arkansas Financial Group, Inc., All rights reserved.

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