The Real Free Money: Compounding Interest as Time Value

As discussed in The Real Free Money, free money is the money you get from nothing. It doesn't need any work or capital in advance to get it, but you have to work smart to get it.


The magic word is... the power of COMPOUNDING interest. This is one of the great principles of money management.¹ Compound interest, is defined as:

...interest which is added to the original principal. New interest is then calculated in subsequent periods, not only on the original principal, but also on the interest that has been added. The more frequently interest is compounded, the faster the principal grows.²

In simple words, Compounding earns us interest on the money we have invested and on any interest we have already earned on this investment.³⁴


Interest paid on interest.Well, it is not really pure Free Money, because the value of time element, but, the result of using this tips will have a great impact to our personal finance.⁵⁶


The risk is very low, but we have to work smart to gain it.We could see it works wonderfully in the savings with compounding interest. Even Einstein calls it the "8th wonder of the world."⁷ You see:

• After the first month you have your money in the savings, you gained interest on such savings, the calculation is: savings + (% interest x savings) = end of first month savings balance.

• After the second month of saving, the calculation is: (end of first month savings balance) + (% interest x end of first month savings balance) = end of second month savings balance.
  
• After the third month of saving, the calculation is: (end of second month savings balance) + (% interest x end of second month savings balance) = end of third month savings balance.
• And so on, and so on...

It took a bit longer of time to enjoy the significant impact of the compounding principle in our financial life. The earlier you act, the better.


The name of the game is to invest early and to invest often. To further gain an understanding of this concept, try doing your own experiments with this simple compounding calculator.⁸


Please note, that if we want to have the Compounding Interest magic works, we must make sure, and bear in mind:⁹

1. Start Early!The earlier we start investing, the more time we leave for the miracle of compound interest to take effect. Someone who invests £100 a month from age 20 to 29 and then lets their investments grow is likely to have more money at 60 than someone who invests £100 a month from age 30 to 59.
2. Do not take the interest! It needs to stay with and accumulated to the initial investment to make the compounding interest works.¹⁰
3. Small differences in return matter. A lot! Over long periods of time, the difference between investing at, say, 7% and 8% is enormous.
4. Never squander our inheritance on sex, drugs & rock'n'roll. (Unless we want to).Investing isn't everything. It is best to strike a balance. With investing it is the balance between enjoying ourself now and providing for our future.
5. Over time, regular saving of quite small amounts can build up an astonishing sum of money.If we save £100 a month for 40 years and your investments compound at 12% a year how much will we have? The answer is an astonishing £980,000!
6. Time and patience are the friends of compounding and, therefore, of investing.Time is the most powerful weapon in an investor's arsenal. Nothing comes close to it.¹¹ Saving for 40 years is obviously something we ca not do overnight. We have to exercise patience to feel the full benefit of compounding in the future.

The Rule of 72

The Rule 72 is the simple way to find out how many years it will take for our investment to double by dividing 72 by the percentage rate of growth.¹² So it will take 9 years for our investments to double if they grow at 8% a year (72/8=9).

It will only take 6 years if our investments grow at 12% and so on. The Rule of 72 only provides an approximate answer but it is sufficiently accurate for many calculations.

So, what do you think?

PS: Comments and corrections are very welcomely invited.
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References

¹Free Money Finance. How to Retire Rich: Use the Power of Compounding. Free Money Finance, 10 Oct. 2005. FreeMoneyFinance.com 31 Jan. 2007. http://www.freemoneyfinance.com/2005/10/how_to_retire_r.html

²"compound interest." Wikipedia, the free encyclopedia. Wikimedia, 2007. Wikipedia.org 29 Jan. 2007. http://en.wikipedia.org/wiki/Compound_interest

³"compounding calculator." The Mint, it makes cents. Northwestern Mutual, 2002. TheMint.org 31 Jan. 2007. http://www.themint.org/tryit/compoundingcalculator.php. See also: "compound interest." investorwords.com. WebFinance, Inc., 1997-2007. investorwords.com 31 Jan. 2007. http://www.investorwords.com/1013/compound_interest.html: "Interest which is calculated not only on the initial principal but also the accumulated interest of prior periods. Compound interest differs from simple interest in that simple interest is calculated solely as a percentage of the principal sum."

⁴"compound interest." The New Dictionary of Cultural Literacy, Third Edition. Houghton Mifflin Company, 2002. Answers.com 01 Feb. 2007. http://www.answers.com/topic/compound-interest: "Interest that is added not only to the principal of a loan or savings account but also to the interest already added to the loan or account; interest paid on interest."

⁵It is frequently mixed up with the term 'time value of money,' when it should be called the "money value of time," since what being valued here is not the money, but the time.

⁶It is because interest we must paid for a loan, or interest we gain for a savings is no more than a value of time in the amount of money, for the Borrower to use the money the Borrower actually don't have. See: "interest." Wikipedia, the free Encyclopedia. Wikimedia, 2007. Wikipedia.org 29 Jan. 2007. http://en.wikipedia.org/wiki/Interest: "Interest is the 'rent' paid to borrow money. The lender receives a compensation for foregoing other uses of their funds, including (for example) deferring their own consumption. The original amount lent is called the 'principal,' and the percentage of the principal which is paid/payable over a period of time is the 'interest rate.'"

⁷Woodard, Dustin. The Power of Compounding Interest. About, Inc., 2007. About.com 31 Jan. 2007. http://mutualfunds.about.com/cs/mutualfunds101/a/compounding.htm. See also:
Kirk Lindstrom. Compounding and Compound Interest Explained. Suite 101. Suite101.com 31 Jan. 2007. http://www.suite101.com/article.cfm/investing/25397: "Some believe it was Benjamin Franklin who said, 'Compound interest is the eighth wonder of the world,' while attributing 'Compound interest is the world's greatest discovery,' to Albert Einstein. Still others attribute the whole thing to John Maynard Keynes. Whoever said it first, all three of these great minds recognized the power of compounding. It doesn't take a 'genius' to see why."

⁸Woodard, Dustin. The Power of Compounding Interest.

⁹The Fool's School. The Miracle of Compound Returns. Fool, 1998-2007. Fool.co.uk 31 Jan. 2007. http://www.fool.co.uk/school/compound.htm

¹⁰See the definition of 'compounding interest' again. Compared to definitions in:
"compound interest." The American Heritage® Dictionary of the English Language, Fourth Edition. Houghton Mifflin Company, 2004. Answers.com 01 Feb. 2007. http://www.answers.com/topic/compound-interest

¹¹Glassman, James K. From Piggy Bank to Pension. Kiplinger's Personal Finance magazine, February 2006. Kiplinger.com 31 Jan. 2007. http://www.kiplinger.com/magazine/archives/2006/02/glassman2.html

¹²"What is the 'rule of 72'?." Invertopedia, Inc., 2007. Investopedia.com 31 Jan. 2007. http://www.investopedia.com/ask/answers/04/040104.asp: "The 'rule of 72' is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself."
There are also numerous articles about the 'rule of 72'. Just search it on Google.