Why is Compounding Magic?

Over very long periods of time compounding will make you rich.  We find it to be one of the more amazing aspects. Investing intelligently at high rates of return and/or over long periods provides investors with substantial sums.  Even Albert Einstein said, “The most powerful force in the universe is compound interest.”  And this was the man that derived the Theory of Relatively!

This post should be a quick one as the concept of compound interest is easily explained.  Compound interest is interest on top of interest on top of interest and on and on.  For example, if you earn 10% every year and reinvest all earnings and you start with $1 then next year you will have $1.10 = (1*(1+10%)) and the following year you will have $1.21 = (1.10*(1+10%)).  The effect of your return in the second year is additive to your previous gain.  This boils down to an easy to equation.  For a lump sum invested at time zero the future value is that sum multiplied by one plus the interest raised to power of the time the money was invested.

Future Value = Present Value * (1 + Interest Rate) ^ Time

So, if you were to invest $10,000 at age twenty five and never touched this money until you retired at age sixty five and earned a reasonable 7% you would end with a value of roughly $150,000.  Most people, however, do not save just one lump sum.  They usually save little bits over long periods of time.  If this savings per year is constant it is known as an annuity.  The equation is generally the same but is edited for the effects of single payments made year after year.

Future Value of an Annuity = (Coupon / Interest Rate) * ((1 + Interest Rate) ^Time – 1)

So, what if you were to save $5,000 per year from age twenty five to age sixty five at the same 7% return you would end with a value of approximately $1,000,000.  You’d be a millionaire! The best part is at this savings rate, it is only 10% of the median wage of an American worker.  In other words it is highly achievable.  The key to achieving these amounts is having a long-term period to invest as well as having the patience and diligence to investment wisely.  The real problem is most people think they can wait and make it up later.  This is foolish.  A fifty year old deciding they need a $1,000,000 for retirement at age 65 would need to save about $40,000 per year to reach their goal.  This is almost 80% of the average person’s annual wages.  Needless to say, would you be willing to cut $40,000 per year out of your lifestyle and save it instead?  That is why it is important to start early!

To give you an idea of the power and magic of compounding and why using it your advantage over long periods can make you rich is an example from a book I recently read.  James Gipson in Winning the Investment Game: A Guide for all Seasons states: ‘If the Indians and their descendants who sold Manhattan for $24 had been successful in compounding their money at 7% after taxes for the last 350 years, they would have about $30 billion today.”  In conclusion, the more you save over long periods of time will generate huge sums of money.  It is important to put those powers to work in your favor.

Adam Wright

About Adam Wright

Ever since I switched into the Smeal College of Business at Penn State I have pursued intelligent analysis with all the vigor available to me. Joining Wright Associates in 2011 has provided me the opportunity to put years of education to work.