# A COMPOUNDING TALE: "HOW DOES COMPOUNDING INTEREST AFFECT MY ROI?"

Carlos M. Sera, MBA

August 25, 2015

If people were limited to understanding just one mathematical concept about money right at the top of the list would be the concept of compound interest. It’s essential that a person understand how compounding interest affect their ROI. If it were up to me it would be taught in every grade school from the time that children can perform simple percentages. This level of math is well within the level of most middle school students and once understood opens up endless possibilities for the imagination.

I remember how I was hooked. As a child in history class we were studying the tale of Peter Minuit and his purchase of Manhattan Island 400 years ago. As the tale goes he purchased this valuable real estate for $24. Since then there have been numerous sources that question the authenticity and validity of the purchase, but what struck me as curious was the concept of compounding and the idea that time was our greatest friend when it came to growing money. Our history teacher also happened to be our math teacher and he asked us a simple question. Did Peter Minuit overpay for his purchase of Manhattan? Of course everyone answered that he got the deal of a lifetime. Next the teacher asked us how we arrived at that conclusion. Soon thereafter he introduced the concept of compound interest and we all developed a different perspective.

It seems that the answer to our teacher’s question is that it depends on the interest rate that the seller were able to earn since the transaction took place. If we assume that the alleged $24 back then was worth what we consider to be $24 today and compounded it at 8% then the sellers got the better end of the deal. They would have taken that $24 and today it would be worth more money than all the value of all the world’s stock markets combined. This insight just knocked me off my feet. It also set in motion a series of insights that I use every day in my job as a financial advisor but those are for a later time. This tale is strictly about compounding.

## THE CONCEPT OF COMPOUND INTEREST

This is **A Compounding Tale** that stars Mr. Stock and Mr. Bond. I chose the names because over time stocks will outperform bonds and is a theme that you will see throughout these tales. These two fellows were childhood friends, went to the same college, studied the same subjects and upon graduation at age 22 they each received graduation gifts in the exact amount of $1,000 from an anonymous donor. The anonymous donor had only one stipulation to the money he gave them. The stipulation was that the money had to be invested in either stocks or bonds and it couldn’t be touched until they reached age 65. To make things easier for purposes of this illustration, this $1,000 was placed in a tax-favored account that would compound tax-free until they reached age 65. Lastly, they were only given two investment choices. The first choice was a low cost stock mutual fund that was correlated to the general movements of the US stock market. The other choice was a low cost bond mutual fund that was correlated to the general movements of the US bond market. For those that don’t understand what correlated means in this case it means that if stocks made 10% per year for the next 43 years the stock mutual fund would also earn 10% per year for the period. Similarly, if bonds made 5% per year for the next 43 years the bond mutual fund would also earn 5% per year for the period.

As their name implies, Mr. Stock chose to invest his money in the stock mutual fund and Mr. Bond chose to invest his money in the bond mutual fund. Lets see what happens to their money over their lifetime. For purposes of this example we will assume that stocks returned 10% per year for the 43-year period and that bonds returned 5%. I chose these returns for the individual mutual funds because they are fair approximations of what I believe are the long term returns one can expect to achieve from stocks (10%) and bonds (5%). Though some may argue the finer details of my assumption, everything I’ve learned about the differences between stocks and bonds is that stocks return between 10-12% annually and bonds return between 3-5% annually over long periods of time.

What happens to the money of these two over time? 15 years into the tale, Mr. Stock’s portfolio is worth $4,177 and Mr. Bond’s portfolio is worth $2,079. In only 15 years Mr. Stock has a little bit more than twice as much money as Mr. Bond. By year 25 Mr. Stock’s portfolio is worth $10,835 and Mr. Bond’s portfolio is worth $3,386. Mr. Stock’s portfolio is now worth more than three times Mr. Bond’s portfolio.

By year 30 Mr. Stock’s portfolio is worth four times Mr. Bond’s portfolio. By year 35 Mr. Stock’s portfolio is worth more than five times Mr. Bond’s portfolio. By year 40 Mr. Stock’s portfolio is worth more than six times Mr. Bond’s portfolio. Finally, in year 43 when they both reach the age of 65 Mr. Stock’s portfolio is worth more than seven times Mr. Bond’s portfolio. Mr. Stock’s portfolio has grown to $60,240 and Mr. Bond’s portfolio has grown to $8,150.

The magic of compounding is that even though Mr. Stock was only earning twice as much return as Mr. Bond, 10% vs. 5%, Mr. Stock was accumulating money at a much faster rate than Mr. Bond because he was making more money on his money than Mr. Bond. Another way of thinking about it is that Mr. Stock made more interest on his interest than Mr. Bond did.

## THE RATE OF RETURN TABLE

The table below shows actual numbers. Why the mathematical overkill in this tale? I believe that a complete understanding of this concept is crucial to any sound financial plan. I’ve met many financially successful people that don’t understand the magic of compounding. However, I believe they were able to overcome this deficiency. I don’t believe they succeeded because of their deficiency. As the saying goes, knowledge is power and a thorough understand of how money grows over time should be in everyone’s repertoire.

**Rate Of Return Table**

Results of $1,000 Invested

There are a few key observations to make from the table. The first and foremost is the cases of the 10% return as well as the 12.5% return. In both cases an investor made more money in the last 8 years, years 35 through 43, than they made from year 1 through 35. Though an investor would make a steady 10% per year in terms of return, they accumulate more money due to the fact that they earn interest on their interest over time.

The second key observation is that money does not grow in a linear fashion. If you look at the last column in the table it appears that money is growing at an increasing rate. Of course it isn’t growing at an increasing rate it is growing at a steady rate of 12.5%. However, in terms of absolute dollars, it is growing at an increasing rate—-this is the power of compounding over time.

I hope this tale conjures up more thoughts and questions on the topic of how money grows over time. In particular, I’d like to know why given such a simple concept and given such a relatively achievable threshold of 8% over time, which we learned from the sale of Manhattan, why everyone isn’t wealthy when they retire. Why can’t families transfer wealth successfully from one generation to the next? I would also like to know why given the knowledge that stocks outperform bonds over long periods of time why everyone doesn’t invest all of their money in stocks when they are building wealth. These questions and others will be answered throughout these tales.