In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 5.5% annual interest rate, what is its value as of 2012 (386 years later)?

Approximately $22 billion

Explanation:

Future Value (FV)

Given a present value (PV) of an investment, the annual interest rate r, the future value at time t years is given by

Care must be taken to properly express the time in years and the rate in yearly pertentage.

The estimated value of the Manhattan Island in 1626 was PV=$24. 386 years later, at a r=5.5% its value would be

The present value can be estimated in more than $22 billion

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reducing the scale of the market for a new product.