3.2.07

$MART $AVING AND $PENDING. Charlie Sykes takes an interest in the power of compounding, part of his continuing lament that the schools are failing to teach basic personal finance. When I do teacher training workshops, I'll sometimes bring a chessboard and some candy corn to introduce the concept.
There is a well-known story of the man who invented chess. The local ruler was so pleased with the invention that he offered the inventor a great reward in gold. The inventor suggested an alternative reward: he would get one grain of wheat on the first square of the chess board, two grains on the second square, four on the third, eight on the fourth, etc., doubling the number of grains each time. The ruler saw that this must be a much better deal for him, and accepted. The board has 64 squares. How many total grains of wheat did the ruler have to pay the inventor?
There's a longer version of the story here.

The National Council on Economic Education offers a number of teacher resources that will strengthen students' investing skills, including the Learning, Earning and Investing series. In the State Line and North West Frontier, see me. The Illinois Council on Economic Education maintains other centers that provide such resources elsewhere in the states. Economics Wisconsin offer similar services elsewhere in the Cheddar Curtain Free Trade Zone.

Now for a somewhat more subtle problem that I generally don't use at teacher workshops. Suppose I have identified an asset that will double in a year. I invest $1 today and I receive $2 in a year. Now let's extend the problem: the asset pays 100% annual interest, compounded semi-annually. I invest $1 today, it grows to $1.50 in six months and I receive $2.25 at years end. Extend the problem again: now my 100% annual interest compounds quarterly. In three months I have $1.25, which grows to $1.56 in six months, $1.95 in nine months, and $2.44 at year's end. Does it follow that if my asset compounds continuously, I will have even more money? If so, how much more? Can I exceed the payoff to the inventor of chess by compounding more rapidly?

(The answer is here, but remember, if I give this as a class exercise, no peeking.)

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