The Million-Dollar Challenge

Your decision is whether to accept the $1,000,000 offered, or hold out for a penny, doubled every day for a month. The illustration shows a penny doubled for a week. How many days will it take to get $1.00?

The first time I heard this challenge, Robert said, "Picture putting a penny in a drawer. Every day when you go back and open the drawer, the penny has doubled. There are twice as many pennies in the drawer as there were the day before."

How much money would you have at the end of a month? If the month has 30 days, you will have _____________. If the month has 31 days, you'll have double the amount you answered above. That's $______________.

The money increased (grew) by 100% per day. After it increases by 100% a day for a month, at the end of the month you get to take all of the money (pennies) out of the drawer. This is an example of daily "compounded interest."

Compound Interest

The power of compound interest is that the interest of the previous period (day, week, month or year) is added to the original amount before the interest is figured for the next period. One penny is doubled on the second day. On the third day, the doubling happens to the penny (now 2¢) that was doubled the day before!

Q: Which is heavier: a pound of feathers or a pound of lead?

I loved that joke when I was in the second grade. A playmate that wasn't listening carefully would give the wrong answer, and everyone around could laugh.

A: Lead is much heavier by volume, but the question asks about weight, not size. A handful of feathers is much lighter than a handful of lead! Still, a pound is a pound!

Here's another of my favorites…

Q: Which would you rather have: $1,000,000.00 or 1¢ doubled every day for a month?

A penny doubled is only 2¢, right? That’s right for the first day. If you’ve learned your 2X multiplication table, you know that the next day, 2 X 2¢ = 4¢. The next day it will be 8¢, then 16¢.

Are you ready to take the million dollars and run?

Compounding

“The most powerful force in the universe is compound interest.” This statement is generally attributed to Albert Einstein, but I've found no proof he said it. That's a picture of him at 14. (According to Wikimedia Commons, the photo is in the public domain, so you can reproduce it for home school lessons.)

Compounding, in this case, means "to add to," "to augment," "to increase." Choosing intelligently between one million dollars or a penny double for a month depends upon a basic understanding of compounding." How powerful is doubling?

Should you choose $1,000,000 or 1¢?