As if it weren't hard enough to be a voter in 2012, what with negative advertising screaming in our ears while we try to sort through claims and counter claims and counter-counter claims. And now, what? Math! You gotta be kidding me!
You can't look at a newspaper, change the channel or even check your Twitter without having to grapple with numbers, numbers and more numbers. If 47% of Americans don't pay federal income taxes, then 53% do, but what's the ratio between income taxes and payroll taxes or the percentage of non-payers who are in combat zones, and just what's fair, anyway? The numbers just keep coming. It's enough to make your head hurt.
There are plenty of folks -- well-intentioned and otherwise -- trying to analyze, explain and put the perfect spin on Mitt Romney's controversial comments at that fundraiser in Florida. We'd like to offer some help on a related issue by dusting off a piece on math anxiety that we published back in 1990, a time at which fully 45.9% of Americans living today had not yet been born. One telling line from the story: "You can use data to prove almost anything, partly because people too readily believe 'facts' presented with numbers." (By the way, we just made up that statistic about the percentage of people born since the story was originally published.)
The story holds up extremely well after more than two decades, but some of the numbers might seem startling. Just remember that back in 1990, 30-year home mortgages were averaging over 10%, money market mutual funds were yielding over 7.5%, the annual inflation rate was 5.4% and the Dow Jones Industrial Average closed the year at 2634.
From Kiplinger's Personal Finance magazine, August 1990:
When Numbers Make You Numb
Does the term "math anxiety" barely begin to describe your fear of numbers? You're nodding your head, but don't turn the page – there's only one formula in this article, and you can avert your eyes when you come to it. You won't emerge a math whiz, but you will sharpen what Temple University math professor John Allen Paulos calls the "rough, numerical horse sense" needed to get along in today's world.
Solomon Garfunkel, executive director of the Consortium for Mathematics and Its Applicators, worries that people too often benignly accept what they're told when math is involved because they don't trust themselves to know better. "That can get very scary," he says. It makes people susceptible to inferior investments and questionable proposals. Protecting yourself doesn't mean carrying a loaded calculator. More often than not, you need know only what questions to ask, not how to decipher the answers.
1. Compound versus simple
People simply don't comprehend the power of compounding, laments Garfunkel. "As much as it is the basis of all financial computation, people still don't understand the effects of compounding on both savings and debt."
On the savings side, the easiest way to think of compounding is that you earn interest on interest as well as on your original investment. Invest $100 at 10% compounded annually and at the end of the first year you have $110 ($100 plus $10). That $110 earns interest the second year, so you end the year with $121 ($110 plus $11). And so on. By contrast, with simple interest you earn only on your original investment. Thus, you end year one with $110, year two with $120 and so forth, adding just $10 each year.
It's also easy to underestimate the power of compounding. At low interest rates and over short periods of time, the effect is modest. Then it snowballs. The longer the earnings compound, the faster the growth accelerates.
Imagine two checkerboards, with the squares representing 64 years. Put 2 cents on the lower left-hand square of each board and assume you'll earn 100% interest each year, with larger and larger piles of money accumulating on each square as you go along.
On one checkerboard, you earn simple interest, adding 2 cents to your booty on each successive square: 2 cents, 4 cents, 6 cents, 8 cents and so on. At the 64th square you have $1.28. On the other board, your 100% interest compounds annually: 2 cents, 4 cents, 8 cents, 16 cents, etc. How much do you have by the time you reach the 64th square? Would you believe $184 quadrillion? That's $184 followed by 15 zeros. In just the final year, the interest amounts to $92,000,000,000,000,000. Such is the power of compounding.
You don't have to know how to calculate that phenomenal figure to realize that compounding is a key to investment performance. Consider this real-world example: An investment is ballyhooed for having generated an average annual return of 20% a year for ten years. In other words, it increased in value by 200% over the decade. Or, put another way, it returned a simple noncompounded annual yield of 20%.
But a 200% return over ten years translates to an 11.6% compounded annual return. That's not bad, but it's anemic beside the 20% "average" return being hyped. With a financial calculator, you can make quick work of translating average returns to annual yields.
Even without a calculator, you can protect yourself from being bamboozled by asking that all rates be translated to effective annual yields and that multiyear returns reflect annual compounding.