Question

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)?

Answer 1

Answer:

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

$FV=PV\left(1+r)^t$

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

$FV=\ 24\left(1+0.055)^{386}=\ 22,680,919,665$

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