# Investment Basics - Course 102 - The Magic of Compounding

By: Steve Bauer | Wed, Sep 8, 2010

This is the second course in a series of 38 called "Investment Basics" - created by Professor Steven Bauer, a retired university professor and still a proactive asset manager and consultant / mentor.

## Introduction:

When you were young, perhaps one of your friends asked you the following trick question: "Would you rather have \$10,000 per day for 30 days or a penny that doubled in value every day for 30 days?" Today, we know to choose the doubling penny, because at the end of 30 days, we'd have about \$5 million versus the \$300,000 we'd have if we chose \$10,000 per day.

Compound interest is often called the eighth wonder of the world, because it seems to possess magical powers, like turning a penny into \$5 million. The great part about compound interest is that it applies to money, and it helps us to achieve our financial goals, such as becoming wealthy, retiring comfortably, or being financially independent.

## The Components of Compound Interest

A dollar invested at a 10% return will be worth \$1.10 in a year. Invest that \$1.10 and get 10% again, and you'll end up with \$1.21 two years from your original investment. The first year earned you only \$0.10, but the second generated \$0.11. This is compounding at its most basic level: gains begetting more gains. Increase the amounts and the time involved, and the benefits of compounding become much more pronounced.

Compound interest can be calculated using the following formula:

FV = PV (1 + i)^N
FV = Future Value (the amount you will have in the future)
PV = Present Value (the amount you have today)
i = Interest (your rate of return or interest rate earned)
N = Number of Years (the length of time you invest)

Prof's. Guidance: Go to Google and find a Calculator that will do all of this for you.

## Who Wants to Be Wealthy?

As a fun way to learn about compound interest, let's examine a few different ways to become wealthy. First we'll look at a couple of investors and how they have chosen to accumulate \$1 million.

1. Jack saves \$25,000 per year for 40 years.
2. Jeff starts with \$1 and doubles his money each year for 20 years.

While most would love to be able to save \$25,000 every year like Jack, this is too difficult for most of us. If we earn an average of \$50,000 per year, we would have to save 50% of our salary - not very realistic!

In the second example, Jeff uses compound interest, invests only \$1, and earns 100% on his money for 20 consecutive years. The magic of compound interest has made it easy for Jeff to earn his \$1 million and to do it in only half the time as Jack. However, Jeff's example is also a little unrealistic since very few investments can earn 100% in any given year, much less for 20 consecutive years.

TIP: A simple way to know the time it takes for money to double is to use the rule of 72. For example, if you wanted to know how many years it would take for an investment earning 12% to double, simply divide 72 by 12, and the answer would be approximately six years. The reverse is also true. If you wanted to know what interest rate you would have to earn to double your money in five years, then divide 72 by five, and the answer is about 15%.

## Time Is on Your Side - or Is It?

Between the two extremes of Jeff and Jack, there are realistic situations in which compound interest helps the average individual. One of the key concepts about compounding is this: The earlier you start, the better off you'll be. So what are you waiting for?

Let's consider the case of two other investors, Luke and Walt, who'd also like to become wealthy. Say Luke put \$2,000 per year into the market between the ages of 24 and 30, that he earned a 12% after tax return, and that he continued to earn 12% per year until he retired at age 65. Walt also put in \$2,000 per year, earned the same return, but waited until he was 30 to start and continued to invest \$2,000 per year until he retired at age 65. In the end, both would end up with about \$1 million. However, Luke had to invest only \$12,000 (i.e., \$2,000 for six years), while Walt had to invest \$72,000 (\$2,000 for 36 years) or six times the amount that Walt invested, just for waiting only six years to start investing.

Clearly, investing early can be at least as important as the actual amount invested over a lifetime. Therefore, to truly benefit from the magic of compounding, it's important to start investing early. We can't stress this fact enough! After all, it's not just how much money you start with that counts, it's also how much time you allow that money to work for you.

In our first example, Jack had to save \$25,000 a year for 40 years to reach \$1 million without the benefit of compound interest. Luke and Walt, however, were each able to become millionaires by saving only \$12,000 and \$72,000, respectively, in relatively modest \$2,000 increments. Luke and Walt earned \$988,000 and \$928,000, respectively, due to compound interest. Gains beget gains, which beget even larger gains. This is again the magic of compound interest.

Ok, you say - I am retired and have reached an age where all this "compounding" stuff just isn't for me. Well, you are just plain wrong. Whether it's 5 years, 15 years, 25 years or 50 years - it always works the same.

Prof's. Guidance: It is important to dig a bit deeper with these calculations, to include taxes. Not to let air out of the balloon of compounding, but remember two things are for sure - death and taxes.

## Why Is Compound Interest Important to Stock Investing?

In addition to the amount you invest and an early start, the rate of return you earn from investing is also crucial. The higher the rate, the more money you'll have later. Is there any question about this past sentence?

Let's assume that Luke from our previous example had two sisters who, at age 24, also began saving \$2,000 a year for six years. But unlike Luke, who earned 12%, sister Charlotte earned only 8%, while sister Rose did not make good investment decisions and earned only 4%. When they all retired at age 65, Luke would have \$1,074,968, Charlotte would have \$253,025, and Rose would have only \$56,620. Even though Luke earned only 8 percentage points more per year on his investments, or \$160 per year more on the initial \$2,000 investment, he would end up with about 20 times more money than Rose.

Clearly, a few percentage points in investment returns or interest rates can mean a huge difference in your future wealth. Therefore, while stocks may be a higher risk investment in the short run, in the long run the rewards can clearly outweigh the risks.

## Wrap Up

Compound interest can help you attain your goals in life. In order to use it most effectively, you should start investing early, (and that means now) invest as much as possible, and attempt to earn a consistent and reasonable rate of return.

Quiz 102
There is only one correct answer to each question.

1. Using the rule of 72, an investment earning 10% per year would double in approximately how many years?
1. 10.
2. 7.2
3. 5.
1. Using the rule of 72, if you invested \$10,000 at 12% per year, in 12 years, you would have:
1. \$20,000
2. \$30,000
3. \$40,000
1. Which of the following is not a component of compound interest?
1. Time.
2. Interest rate.
3. Financial calculator.
1. If you had invested \$1 and doubled your investment 20 years in a row, you would have \$1 million. In the last year (year 20), you would have made how much money?
1. \$100,000
2. \$50,000.
3. \$500,000.
1. Which of the following is not true?
1. The earlier you invest, the more money you'll have in the future.
2. The lower the interest rate, the more money you'll have in the future.

Thanks for attending class this week - and - don't put off doing some extra homework (using Google - type "info" and the word or question) and sharing with or asking the Prof. questions and concerns.

Investment Basics (a 38 Week - Comprehensive Course)
By: Professor Steven Bauer

Text: Google has the answers to most all of your questions, after exploring Google if you still have thoughts or questions my Email is open 24/7.

Each week you will receive your Course Materials. There will be two kinds of highlights: a) Prof's Guidance, and b) Italic within the text material. You should consider printing the Course Materials and making notes of those areas of questions and perhaps the highlights and go to Google to see what is available to supplement those highlights. I'm here to help.

Freshman Year

Course 101 - Stock Versus Other Investments
Course 102 - The Magic of Compounding
Course 103 - Investing for the Long Run
Course 104 - What Matters & What Doesn't
Course 105 - The Purpose of a Company
Course 106 - Gathering Information
Course 107 - Introduction to Financial Statements
Course 108 - Learn the Lingo & Some Basic Ratios

Sophomore Year

Course 201 - Stocks & Taxes
Course 202 - Using Financial Services Wisely
Course 203 - Understanding the News xxx
Course 204 - Start Thinking Like an Analyst
Course 205 - Economic Moats
Course 206 - More on Competitive Positioning
Course 207 - Weighting Management Quality

Junor Year

Course 301 - The Income Statement
Course 302 - The Balance Sheet
Course 303 - The Statement of Cash Flows
Course 304 - Interpreting the Numbers
Course 305 - Quantifying Competitive Advantages

Senor Year

Course 401 - Understanding Value
Course 402 - Using Ratios and Multiples
Course 403 - Introduction to Discounted Cash Flow
Course 404 - Putting OCF into Action
Course 405 - The Fat-Pitch Strategy
Course 406 - Using Morningstar as a Reference
Course 407 - Psychology and Investing
Course 408 - The Case for Dividends
Course 409 - The Dividend Drill

Graduate School

Course 501 - Constructing a Portfolio
Course 502 - Introduction to Options
Course 503 - Unconventional Equities
Course 504 - Wise Analysts: Benjamin Graham
Course 505 - Wise Analysts: Philip Fisher
Course 506 - Wise Analysts: Warren Buffett
Course 507 - Wise Analysts: Peter Lynch
Course 508 - Wise Analysts: Others
Course 509 - 20 Stock & Investing Tips

This Completes the List of Courses.

Wishing you a wonderful learning experience and the continued desire to grow your knowledge. Education is an essential part of living wisely and the experiences of life, I hope you make it fun.

Learning how to consistently profit in the Stock Market, in good times and in not so good times requires time and unfortunately mistakes which are called losses. Why not be profitable while you are learning? Let me know if I can help.

## Author: Steve Bauer

Steven H. Bauer, Ph.D.

Steve has several degrees, i.e. post graduate degrees and doctorate and a great deal of (too much) continued education. For seven years, he did a stent as a University Professor of Finance and Economics.

He owned a privately held asset management firm and managed individual investor and corporate accounts as a Registered Investment Advisor - for over 40 years.

Professionally he is a financial analyst and private asset manager / consultant / mentor.

Steve can be reach at senorstevedrmx@yahoo.com

Copyright © 2010-2011 Steven H. Bauer, Ph.D.

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