$24 for Manhattan a Good Deal? Peter Minuit of the Dutch West India Company purchased the island of Manhattan from Native Americans on May 26, 1626 for goods valued at 60 Dutch guilders, which was estimated to be the equivalent of $24 (or $680 today). Instead of purchasing the island,

Question

$24 for Manhattan a Good Deal?

Peter Minuit of the Dutch West India Company purchased the island of Manhattan from Native Americans on May 26, 1626 for goods valued at 60 Dutch guilders, which was estimated to be the equivalent of $24 (or $680 today). Instead of purchasing the island, if Minuit had invested the $24 in a savings account that earned 8% interest, how much would it be worth in 2015?

Accepted Answer

Given: P = $24, i = 8% per year, and N = 389 years.

Find: F, based on (a) 8% simple interest, and (b) 8% compound interest.

(a) With 8% simple interest,

[latex]F=\$24 \left[1+\left(0.08\right) \left(389\right) \right] =\$771[/latex]

(b) With 8% compound interest,

[latex]F = \$24 \left(1+0.08\right) ^{389} = \$241,019,469,461,115[/latex]

Comments: The significance of compound interest is obvious in this example. Many of us can hardly comprehend the magnitude of $241 trillion. In 2015, the total population in the United States was estimated to be around 320 million. If the money were distributed equally among the population, each individual would receive $753,186. Certainly, there is no way of knowing exactly how much Manhattan Island is worth today, but most real-estate experts would agree that the value of the island is nowhere near $241 trillion. (Note that the U.S. Domestic Gross Product for 2013 was merely $15.68 trillion. The total value of all New York City property was assessed at $914.8 billion for the 2015 fiscal year.)

Question 3.2: $24 for Manhattan a Good Deal? Peter Minuit of the Dutch Wes...

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