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It's Magic!

Einstein in 1947Well okay, maybe not magic but it is pretty amazing in its effect.  Albert Einstein, a gentleman reputed to have known his way around numbers, called it the "eighth wonder" of the world.  He said that it was "the greatest mathematical discovery of all time."  He was talking about compound interest of course, that happy state where we earn interest on the interest that we previously earned.  One hundred dollars invested at 6% will earn 6$ in one year.  At the end of the second year, one hundred and six dollars invested at 6% will earn $6.36.  At the end of the third year, $112.36 invested at 6% will earn $6.74, and you will then have earned $1.10 in interest on the interest you were paid.  That is $1.10 that did not have to be saved in the usual way of taking it out of your regular income; it just appeared in your account due to the passage of time and the "magic" of compound interest.  Work that out to a couple of decades, and increase the dollar amounts by a bit and things get really interesting.  Someone else (whose name has been lost to me) said that "Those who understand compound interest are destined to collect it.  Those who don't are doomed to pay it." 


Those that understand compound interest also understand the role that time plays in increasing its effect.  Let's consider some examples of just what time can do when combined with compound interest.  Let's begin by assuming that an industrious 25 year old who wants to retire securely begins investing $200/month and continues this until his retirement at the age of 65.  Let's further assume that he invests that $200 in a good stock mutual fund like one of the funds I mentioned in my last missive, and he earns an average of 8% per year over those 40 years.  I realize that 8% is approximately 2% less than what US stocks averaged over the past 100 years, but let's be conservative with this estimate.  If our 25 year old sticks with his plan, at his retirement in 4o years he will have invested $96,000, but his mutual fund account will be worth $702,856.  This example also assumes that his investment was in a tax-deferred account like an IRA, so he has not had to worry with those pesky taxes.  Pretty nice, huh?  If he is lucky enough to earn the average return of the past, 10%, his account will be worth $1,275,356.  That 2% can turn out to be very significant, can it not?  Now let's assume that our industrious 25 year old has an older brother who takes a little longer to get started with with his investment plan.  This guy simply cannot get that extra $200 together until he reaches 35.  Maybe life gets in the way, he has school bills to pay, or he just cannot get focused on the future until he matures a little more.  These things happen!  But regardless of the cause of the delay, at 35 he gets cranked up and begins the same investment plan used by his younger brother.  By the age of 65 he will have invested $72,000, only $24,000 less than his energetic brother.  Alas though, his IRA account will contain only $300,059 if he earns 8%.  That 10 years of delay in his investing plan early in his life will cost him $402,797 by the time he reaches 65.  Not fair, you may say.  Such is the nature of compounding interest.  To further illustrate the need to begin saving and investing early in one's career, consider this example.  Let's say that our 25 year old got to be a spendthrift when he turned 35 and stopped saving and investing in his IRA.  He did not withdraw the money he had saved (at least he had the good sense to do that), but rather just left it with that mutual fund to collect dividends and capital gains, again earning 8%.  He only invested $24,000, but by his retirement at 65 his account will still be worth $370,638  Not bad for a slacker, huh?  Please note that this balance is nearly $70,000 more than his brother's balance, even though he made contributions to his account for only 10 years while his brother was making them for 30 years and actually invested a total of $48,000 more!  His account ended up worth more simply because it benefitted from 10 more years of growth!  It had 10 more years in which his earnings yielded earnings, which yielded earnings, which . . ., well, you get the picture. 

It has been my experience that many people do not begin to think seriously about retirement until they turn the "big Five-O."  This is a big mistake on a number of levels, especially as it relates to acquiring their retirement number.  Let me show you why.  Let's assume one of our brothers has just turned fifty and knows that he needs to get serious about saving for his retirement, since he has saved very little to this point.  He is making a good salary now and can afford to defer $1,500/month into his 401k plan where he works.  If he does this diligently until his retirement at 65, and again earns 8% with his 401k investments, he will have invested $270,000, and his account will be worth $522,518.  This is not an insignificant number, but it is still significantly less than what our 25 year old accomplished with but a $200/month investment over a much longer period of 40 years.  That forty year investment plan allows the power of compound interest to fully bloom and work its "magic."  If you would like to play around with your own numbers and assumptions, here is a link to a good calculator

All savers and investors should be familiar with the "Rule of 72."  This is simply a quick and easy way of determining how long it will take your money to double, given a particular rate of return.  Your money will double whenever the rate of return multiplied by a given number of years equals "72."  For example, if you earn 8% on your investment, you money will double in nine years (8% x 9 years = 72)  If you are savvy enough to find an investment earning 12%, your initial investment will double in 6 years.  If you settle for CD's rates of 3%, it will take 24 years for your investment to double.  This rule of thumb is amazingly accurate; I have checked it on a financial calculator and found it to work within a month in almost all cases.  It can help you do some quick, long-term calculations as you plan for your nest egg. 

Do you remember the song by Crosby, Stills, Nash, and Young, Teach Your Children?  That song came to mind as I was writing this.  I'm sure that C,S,N, & Y were not thinking of compound interest when they penned this song, (it was released in 1970 as a counter-culture anthem) but I think that we should ensure that our children are aware of the power of compound interest.  My parents were young adults as the Great Depression took hold in our country, and because of this were well acquainted with the need to save and have something set aside as an emergency fund.  Thus, the importance of thriftiness and saving were  always stressed as I was growing up.  Unfortunately, I do not remember either of my parents ever mentioning the effect compound interest can have on savings.  Nor do I remember it being explained in school to any degree.  I grew up thinking that thriftiness and saving were to be pursued simply because they were virtues, like honesty and courage.  Of course, I realized that if you saved something today, you would have it to spend tomorrow, but I never fully understood the power of compound interest until much later.  So parents, if the schools do not, Teach Your Children well the importance not only of saving, but also what compound interest can do to those savings over time.

Fly/Drive Safely

10 April 2008

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