### Compounding

In an update on an old story, an investment banker asks the client to pay by placing one penny on the first square of a chessboard, two pennies on the second square, four on the third, doubling the number on each square that follows. If the banker had asked for this on only the white squares, the initial penny would double thirty-one times to \$21,474,836 on the last square. Using both the black and the white squares, the sum on the last square is \$92,233,720,368,547,758.

People are reasonably good at estimating how things add up, but for compounding, which involved repeated multiplication, we fail to appreciate how quickly things grow. As a result, we often lose sight of how important even small changes in the average rate of growth can be. For an investment banker, the choice between a payment that doubles with every square on the chessboard and one that doubles with every other square is more important than any other part of the contract. Who cares whether the payment is in pennies, pounds, or pesos? For a nation, the choices that determine whether income doubles in one generation or two dwarf all other economic policy concerns.

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