Part 3: Compounding interest – Compounding of contributions

Overview
This series is meant to help new investors understand the importance of having money work for you through the power of compounding. This is something most sophisticated accredited investors are keenly aware of and use as a key component of their investment strategy. This is the third article of the series. The first article gave an overview of compounding by considering the analogy of growth in memory chip transistors since the early 80s. The second article provided visualization of compounding over 40 years against a single $1,000 investment. This third article will provide visualization of compounding over 40 years against consistent investment.

Disclaimer
The same assumptions in the disclaimer provided in last week’s article will be used in this article as well.

Example of consistent contributions into a compounding investment
Assume, at age 25, a new employee starts contributing into a tax free account provided by his employer. In this case, the account begins with a zero balance, no initial contribution. This will allow us to focus solely on the effect of compounding interest against a consistent investment plan. In this example, the employee gets paid once a month. Also, this person will invest a total of $1,000 each year split over 12 months, or $83.33 monthly ( this is $1,000 divided by 12 months).

Lets now look at the effect of compounding interest over time against a monthly $83.33 investment at different interest rates. In the table below, I will show what the account balance will be at the end of each 5 year period for the different interest rates shown:

Year	2%	4%	8%	16%
00	0	0	0	0
05	5,254	5,525	6,123	7,586
10	11,060	12,271	15,246	24,381
15	17,476	20,508	28,837	61,561
20	24,566	30,565	49,085	143,870
25	32,402	42,844	79,252	326,087
30	41,060	57,837	124,197	729,480
35	50,629	76,144	191,157	1,622,514
40	61,203	98,497	290,917	3,599,519

You may not think it is worth saving only $83.33 monthly or about $2.75 daily into a retirement account. However, this example clearly shows that this $1,000 yearly investment into a tax free compounding account can grow into a very large amount over 40 years without doing anything else by letting that money work for you. Historically, most advisors say you can count on an 8% return from being invested in the stock market. Using 8%, your yearly $1,000 total investment would grow into $290,917 after 40 years. You can contribute any multiple of $1,000 and simply multiply the $290,917 40 year total by that multiple. So, if you contribute $2,000 annually over 40 years, it would grow to $581,834 (this is $290,917 x 2). Similarly, if you contribute a total of $5,000 each year, then it would grow into $1,454,585 ($290,917 x 5).

Understanding the effect of compounding against consistent investment
Now, look at the fact that each interest rate evaluated above is twice the previous interest rate: 4% is twice 2%, 8% is twice 4%, and 16% is twice 8%. I did this to illustrate the difference between compounding as interest rates double.

Notice the differences between the interest rates at each 5 year period described below in relation to the yearly $1,000 total contribution:

At year 5, the total contribution by the investor is $5,000. The account balance difference between all interest rates shown is not that much ranging from $5,254 to $7,586. However, the 16% interest balance is approximately 50% larger than the total contribution.

At year 10, the total contribution by the investor is $10,000. The account balance difference between all interest rates shown is more pronounced ranging from $11,060 to $24,381. The 16% interest balance is well over twice the total contribution.

At year 15, the total contribution by the investor is $15,000. The account balance difference between all interest rates shown is much more pronounced ranging from $17,476 to $61,561. The 8% interest balance is nearly twice the total contribution while the 16% balance is over four times the total contribution.

At year 20, the total contribution by the investor is $20,000. The account balance difference between all interest rates shown is very pronounced ranging from $24,566 to $143,870. The 8% interest balance is well over twice the total contribution while the 16% balance is over seven times the total contribution.

At year 25, the total contribution by the investor is $25,000. The account balance difference between all interest rates shown is extreme ranging from $32,402 to $326,087. The 8% interest balance is over three times the total contribution while the 16% balance is over thirteen times the total contribution.

At year 30, the total contribution by the investor is $30,000. The account balance difference between all interest rates shown is more extreme ranging from $41,060 to $729,480. The 4% interest balance is now nearly twice the total contribution. The 8% interest balance is over four times the total contribution while the 16% balance is over twenty four times the total contribution.

At year 35, the total contribution by the investor is $35,000. The account balance difference between all interest rates shown is even more extreme ranging from $50,629 to $1,622,514. The 4% interest balance is now over twice the total contribution. The 8% interest balance is over five times the total contribution while the 16% balance is over forty six times the total contribution.

At year 40, the total contribution by the investor is $40,000. The account balance difference between all interest rates shown is even more extreme ranging from $61,203 to $3,599,519. The 4% interest balance is well over two times the total contribution. The 8% interest balance is over seven times the total contribution while the 16% balance is nearly ninety times the total contribution.

Further understanding the power of compounding for consistent investment
Remember, all examples above relate to the same yearly $1,000 total contribution. Also, the interest rate was doubled from one column to the next. However, the effect of compounding after 40 years are drastically different. Intuitively, you might think that 16% interest would return twice as much as 8% over time or that 8% would return twice as much as 4%. In fact, we see that there is a HUGE difference in the returns between each double of interest rate over time. Initially we saw there was not that much difference after five years, but the power of compounding started kicking in over time to where you were earning interest upon interest already earned upon interest that money had earned. So, as your money gains new money from interest, that increased balance also started earning interest to where it then earned more interest, etc. That is what I meant by having money work for you. Let your money earn money for you. In this case, you didn’t need to do any more than provide the same yearly $1,000 total contribution.

Summary
Again, compounding is how to make money work for you as the ideal employee that never tires, never complains, always works, continues to get better, becomes self sufficient over time, and can end up paying you through your retirement years. Next week's article will provide strategies for investing in tax free accounts.

Copyright 2009 Ole Cram, President of Marcobe Investments, Inc.
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