I'm sorry. I find this sort of thing annoying... and overstated. No, you can't make your descendants rich by depositing a dollar in a bank account and leaving it there for a few centuries. Money compounds, yes. But so does inflation, and so does risk.
Yes, you should start saving early, but the comparison between Sarah and Roger is misleading, because due to inflation it was almost certainly a heavier burden on Sarah to save $1000 a month for those first ten years than later. In my personal case, I earned between $2,500 and $4,000 a year from in my twenties (I was a grad student), and my first real-life job came with a salary of $14,000. Even if I'd had that real job all those years instead of a grad student stipend, it would not have been so easy to save $1,000 a month.
There's a great old science fiction story by Mack Reynolds, entitled "Compounded Interest," that's worth digging up. But it's silly. The concept is that a time traveler shows up in middle-ages Venice with a proposal to a banker. The concept, which is telegraphed clearly enough that I don't think this is much of a spoiler, is that he wants to invest the money really early so that it will compound enough to make him wealthy enough to build and power the time machine.
Anyway, he shows the banker ten gold coins and says he wants to invest them. In the story, the banker scoffs, and says it would hardly be worth his while, until the time traveler says "Wait... you don't understand. I would not ask for an accounting for a hundred years." The banker pauses for a moment, presumably working the Rule of 72 in his head, and his eyes light up as he realizes what a big account this will be.
That's in the story. (The compounding of risk is dealt with, by the way. The time traveler shows up every century to renew the contract, and each time he comes equipped with a few investment tips for the bankers).
In real life, try walking into a private bank today. When they tell you the minimum to open an account is $250,000, show them ten gold one-ounce coins. When they explain that that's not enough, say, "Wait... you don't understand. I would not ask for an accounting for a hundred years." Do you think they will say, "Ah. Let's see. $20,000 at 3% interest, oh, OK, you'll meet our minimum in just 85 years. Welcome! Just fill out these forms?"
Last edited by nisiprius
on Tue Jan 08, 2013 9:13 am, edited 2 times in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.