If you’re one of the many who don’t understand the meaning of “percent” or what decimals are, don’t be embarrassed, just read on …
It’s a fact that a large proportion of the population doesn’t understand the meaning of “per cent” (frequently spelled as one word, “percent,” or indicated by the symbol %). This is not a reflection of their intelligence or knowledge. I’ve met extremely intelligent and knowledgeable people who simply don’t know what percent means. It’s an important concept in financial planning, so I’m going to explain it here, just in case you need it.
“Per” means “for each.” You’ve encountered this in many forms.
For example, “mph” means “miles per hour”; it tells you your speed, how many miles you will travel for each hour you travel, if you maintain that speed. Or “kph” for kilometers per hour.
It’s used for quoting prices. For example, flowers may cost $5 per dozen. If you want a dozen flowers, that’ll be $5. If you want two dozen, $10. If you want half a dozen, $2.50. And so on.
“Cent” is short for “a hundred.” It is derived from the same Latin source (“centum”) as “century.” Divide a dollar or a euro into 100 pieces, and each is one cent.
So “per cent” means “for each hundred.”
For example, if you are charged interest at 6% a year, it means you have to pay $6 of interest each year for every $100 you borrow. Borrow $200 and you pay $12 in interest. Borrow $50 and you pay $3 in interest. In both borrowing examples, whether you’re borrowing $200 or $50, the interest is $6 for each $100, or 6%.
Similarly if your bank credits you with 4% interest a year and you have $250 on deposit, you’ll get $4 on the first $100, another $4 on the second $100 and $2 on the remaining $50, for a total interest payment of $10, in that year.
OK, let’s try another example.
Here’s the first question in a financial literacy quiz offered by the FINRA Investor Education Foundation. (FINRA stands for the Financial Industry Regulatory Authority, in the US.)
“Suppose you have $100 in a savings account earning 2 percent interest a year. After five years, how much would you have? (A) More than $102 (B) Exactly $102 (C) Less than $102 (D) Don’t know.”
Well, 2 percent a year (as you now know) implies that you’ll get 2 for each 100, every year. So in the first year your $100 will get $2 interest added to it. And that’ll keep happening for five years. So you’ll clearly have more than $102 after five years. Easy, right?
Yet it’s unfortunate how many people can’t get it. To them 2 percent is like 2 units of currency on some foreign planet. Who knows how to translate that into dollars?
You can stop there, and that’s all you’ll need. Skip to decimals.
Or, if you’re enthusiastic and eager, you can take a step further along this path and explore a couple of unusual applications of percentages.
What is 0%? Well, it means zero for each 100. Aha, then it doesn’t matter how many hundreds are involved, the answer has to be zero! Kind of a trick question, going to this extreme.
What about 100%? OK, that’s 100 for each 100 — so it’s the whole thing. 100% of 72 is 72. 100% of 365 is 365. That’s another extreme.
Wait a minute, how about someone who “gives 110% effort” (as we often hear). Well, if you give your all, that’s 100%. So it’s impossible to give 110% effort! 110% effort is just an exaggerated way to say “Wow, what a huge effort!” But it may not be a good idea to correct someone who says they’re giving 110% effort, if you want to keep a friend.
Can you have a negative percentage? Sure. If you invest money and lose 5% of it, it means you have lost 5 of each original 100. So if you started with 300, you’ve lost 15 and you’re now left with 285. That’s often expressed as “earning a return of -5%,” even if it’s not the result you want!
One more notion: decimals.
You may not have heard the expression “place value,” but it’s an important concept that you already understand. If I were to say to you, “Write down the number five thousand and sixteen,” you’d write “5016” (with or without a comma after the 5, it doesn’t matter). The 5 indicates the value 5000 because it’s in the place for thousands; the 0 indicates that there are no hundreds; the 1 indicates that there’s 1 ten; and the 6 indicates that there are 6 ones. You have to put in the zero, even though there are no hundreds, because that place is reserved for hundreds. You put a value in each place. If you left out the zero and just wrote “516” that would be “five hundred and sixteen” rather than “five thousand and sixteen.” So the place in which a number is written signifies what value that number has.
OK, on to decimals. What would be the value of a number written to the right of the ones? Numbers that have one-tenth of the value. We indicate that by inserting a stop (called a “decimal point”) after the place for the ones. (In France they use a comma to indicate a decimal, instead of a stop: it has the same meaning.) And then to the right of that would be the place for numbers with one-hundredth of the value. You come across this all the time, without realizing it. With dollars, the first place after the decimal point indicates dimes and the second place indicates cents. So $1.06 means one whole dollar plus no dimes and 6 cents.
You can indicate percentages in exactly the same way. An interest rate of 1.06% simply means $1.06 for each $100. An interest rate of 0.06% means 6 cents for each $100.
Percentages and decimals are just ways of expressing fractions of something bigger.
I have written about retirement planning before and some of that material also relates to topics or issues that are being discussed here. Where relevant I draw on material from three sources: The Retirement Plan Solution (co-authored with Bob Collie and Matt Smith, published by John Wiley & Sons, Inc., 2009), my foreword to Someday Rich (by Timothy Noonan and Matt Smith, also published by Wiley, 2012), and my occasional column The Art of Investment in the FT Money supplement of The Financial Times, published in the UK. I am grateful to the other authors and to The Financial Times for permission to use the material here.