Here's a shiny new penny, and it's just a "down payment." It's the first installment on a reward for becoming a teenager, and a bright one at that.
To celebrate your 13th birthday, I will send you 13 weekly payments, and each of the next 12 will be double the previous one: So next week, you'll receive two cents, then four cents the week after that, then eight cents the next week! And so on, over the next three months.
I know that at your age three months seems like a long time. So, if you'd like your reward sooner, just return this penny, and I'll immediately send you a crisp new five-dollar bill!
The proposed down payment.
Now, of course, adults wouldn't fall for such a cheap trick. They'd smell a rat right away. And they're no doubt aware of the old mathematical exercise, or could quickly do the math.
After the 12th week, the payments would total $40.95, and the 13th payment of $40.96 would bring the grand total to $81.91, a tidy sum for a new teenager and a whole lot better than $5. (Don't get carried away, though: The 28th payment would be $1,342,177.28, and the total would be nearly $2.7 million).
Such is the power of compounding, a financial tool that separates the really rich from the merely rich.
A young person could plunk a $100,000 inheritance into an investment yielding 8 percent, and after 40 years (compounded quarterly) it would grow to nearly $2.4 million.
Not a bad start on retirement.
But the miracle of compounding is just one of the amazing math tricks that make some folks rich and keep others poor.
For example, for those who think a little bit of inflation won't hurt, there's the "rule of 72," a neat old formula for determining how fast an investment, or prices, will double.
Just divide the rate into 72 to learn the approximate number of years in which the amount will double.
If an investment returns 6 percent a year, it should double its value in about 12 years. If inflation averages 3 percent, prices should double in 24 years.
But what if inflation hits 5 percent for an extended period? Prices would double in just over 14 years.
And if the unthinkable were to happen (again), and inflation hit double digits, woe to the person who hasn't prepared for it. At 10 percent inflation, prices would double in seven years or so.
And how about credit-card minimum-payment rules?
There's a trick that will keep millions of Americans paying credit-card balances down for many years.
We've all heard horror stories: Just paying the minimum on some cards would doom the consumer to 30-plus years of payments.
However, this year, under pressure from regulators, credit-card issuers are upping the ante. They're requiring larger minimum payments.
One popular choice: Pay interest and fees plus at least 1 percent of the outstanding balance every month.
Sounds like progress. Let's see, at that rate, the balance should be paid down in 100 months, or 8 years and change, right?
It's a matter of diminishing results. The first month, you're paying the full 1 percent of the balance, but the second month you're paying 1 percent of 99 percent, and the third month you're paying 1 percent of 98.01 percent of the original balance.
After 69 months, you will have paid your balance down to just under half the original amount. After 100 months, you will still owe nearly a third of the original balance.
You're a bit better off if the issuer wants 2 percent of the remaining balance paid each month.
In that scenario, your original balance is cut in half after about 35 months, but after 100 months you will still owe 13 percent of the original balance.
Even if you pay a net of 5 percent on the outstanding balance monthly, it will take nearly four years to get the balance down to 10 percent of the original.
The only answer is to start paying as much as you can and continue paying, ignoring the lower minimum payments.
Do some youngsters a favor.
Teach them a few amazing financial tricks: the wonders of compounding, the evils of credit-card debt, and the danger of not preparing for inflation.
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