**Overview**

Last week I began a series on compounding investments (click here for the article). I tried to provide an analogy that most of us are familiar with – the compounding of transistors in each new generation of memory chips. In the mid 80s, you could get a 4,000 transistor memory chip (known as a 4k chip). Today you can get over 4,000,000,000 transistors on a chip known as a 4 gig chip. Chips tend to double in the number of transistor between advancements at an exponential rate over time to where a 4k to 8k memory chip advancement only increased the number of transistors by 4,000 and today a 4 gig to 8 gig memory chip increases the number of transistors by 4,000,000,000, a million times more increase. This is the power of compounding over time.

As mentioned last week, visualize the transistors being dollars compounding over time. Eventually, you can make much more money from the compounding of your funds than from the amount you regularly contribute into the investment. However, the earlier you start a regular contributions into a compounding investment, the larger the compounding effect will be when you are ready to retire. Lets look closer at various examples of compounding to illustrate this point.

**Disclaimer**

All examples will assume investment in a tax free retirement account of some kind whether it is a IRA, , 401k, 403b, etc. These examples also assume interest is paid at the end of each month on the balance in the account. The amount shown on each line is balance at the end of each time frame (balance at the end of 5 years, 10 years, etc.). These assumptions allow us to focus on understanding the compounding affect alone with no other variables. In reality, other factors such as inflation and taxes when the funds are withdrawn will reduce the value of money over time and taxes when the funds are withdrawn will also reduce what you have for spending. Also, for simplicity, I assume the starting age of a new employee to be 25 years of age with retirement being planned at 65 years of age, which will show the effect of compounding over 40 years.

**Example for a single initial $1,000 contribution**

Assume a new employee at age 25 contributes $1,000 into a tax free account and never contributes any other funds. Lets now look at the effect of compounding interest over time 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 | 1,000 | 1,000 | 1,000 | 1,000 |

05 | 1,105 | 1,221 | 1,490 | 2,214 |

10 | 1,221 | 1,491 | 2,220 | 4,901 |

15 | 1,350 | 1,821 | 3,307 | 10,850 |

20 | 1,491 | 2,224 | 4,927 | 24,019 |

25 | 1,648 | 2,714 | 7,340 | 53,174 |

30 | 1,821 | 3,314 | 10,936 | 117,717 |

35 | 2,013 | 4.046 | 16,293 | 260,602 |

40 | 2,224 | 4,940 | 24,273 | 576,923 |

You may not think it is worth saving only $1,000 into an account without starting a ongoing contribution plan. However, this example clearly shows that $1,000 can grow into a much larger amount over 40 years without doing anything else by letting that money work for you (see last week’s article on having money be your best employee). Historically, most advisors say you can count on an 8% return from being invested in the stock market. Using 8%, your single $1,000 deposit would grow into $24,723 after 40 years. This says, for every $1,000 you deposit, each of those $1,000 will grow into $24,723. So, if you contribute $2,000 initially at age 25, then at age 65 it would grow to $49,446 (this is $24,723 x 2 since you contributed 2 x $1,000 or $2,000 initially). Similarly, if you had contributed $5,000 initially, then it would grow into $123,615 ($24,723 x 5).

**Understanding the effect of compounding**

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 initial $1,000 contribution:

At year 5, the account balance difference between all interest rates shown is not that much other than the fact that the 16% interest account has already doubled.

At year 10, the 8% balance has doubled and the 16% balance has almost increased five times over the initial $1,000 amount.

At year 15, the 8% balance has more than tripled while the 16% balance is now almost 11 times more than the initial $1,000.

At year 20, the 4% balance has finally doubled while the 8% balance is now almost 5 times more and the 16% account is 24 times more.

At year 25, the 8% balance has increased to seven times and the 16% account has increased to 53 times the initial contribution.

At year 30, the 4% balance has tripled, the 8% balance is now nearly 11 times more, and the 16% balance is now almost 118 times more than the initial contribution.

At year 35, the 2% balance has finally doubled. The 4% balance is now four times more, the 8% balance is now 16 times more, and the 16% balance is now nearly 261 times more than the initial contribution.

At year 40, the 2% balance is still just a little over double. The 4% balance is now nearly five times more, the 8% balance is over 24 times more, and the 16% balance is a tremendous 577 times more than the initial contribution.

**Further understanding the power of compounding**

Remember, all examples above started out with the same $1,000 initial 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 initial $1,000 contribution. You could have walked away and not done another thing (assuming you are able to get in an investment that consistently returns the rates I’ve illustrated each year without further management by you). Your money does all of the work.

**Portfolio management for consistent returns over time**

Many people leave their funds in CDs which are now paying very low returns. However, these funds are very secure. Higher rates of return usually mean you are investing in a higher risk investment where your funds are at more at risk of loss. Many accredited investors finds ways of diversifying risk over several investments that each vary in the level of risk and therefore in associated rates of return to try and generate a fairly consistent overall portfolio rate of return that performs in both good and bad times. This is called portfolio management. Some accredited investors become very proficient at this to the point of being able to generate high average returns over long periods of time. Consistently earning the higher returns provides the large multiplication factors you see above that the higher interest rates provide.

**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. Read the next article in the series "Part 3: Compounding interest – Compounding of contributions" to learn how a consistent monthly contribution to a tax free investment account can grow into significant amounts over 40 years of consistent investment.

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

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