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Manhattan Island

Almost everyone`s favorite example of the power of compound interest is the sale of Manhattan Island for $24 in 1626 to Peter Minuit. Based on New York real estate prices today, it seems that Minuit got a great deal. But consider the future value of that $24 if it had been invested for 374 years (2000 minus 1626) at an interest rate of 8 percent per year:

$24 (1.08)374 = $75,979,000,000,000 = $75.979 trillion

Perhaps the deal wasn`t as good as it appeared. The total value of land on Manhattan today is only a fraction of $75 trillion.

Though entertaining, this analysis is actually somewhat misleading. First, the 8 percent interest rate we`ve used to compute future values is quite high by historical standards. At a 3.5 percent interest rate, more consistent with historical experience, the future value of the $24 would be dramatically lower, only $24 (1.035)374 = $9,287,569! Second, we have understated the returns to Mr. Minuit and his successors: we have ignored all the rental income that the island`s land has generated over the last three or four centuries.

All things considered, if we had been around in 1626, we would have gladly paid $24 for the island.

The power of compounding is not restricted to money. Foresters try to forecast the compound growth rate of trees, demographers the compound growth rate of population. A social commentator once observed that the number of lawyers in the United States is increasing at a higher compound rate than the population as a whole (3.6 vs. .9 percent in the 1980s) and calculated that in about two centuries there will be more lawyers than people. In all these cases, the principle is the same:

Compound growth means that value increases each period by the factor (1 + growth rate). The value after t periods will equal the initial value times (1 + growth rate)t. When money is invested at compound interest, the growth rate is the interest rate.