In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate...

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 the 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 4.75% annual interest rate, what is its value as of 2012 (386 years later)?

Expert Solution

Solution :

The formula for calculating the future value of an Investment is

= P * ( 1 + r ) ^t

Where

P = Present value ; r = rate of interest ; t = Time in years

As per the information given in the question we have

P = $ 24 ; r = 4.75 % = 0.0475 ; t = 386

Applying the above values in the formula we have

= $ 24 * ( 1 + 0.0475 ) ³⁸⁶

= $ 24 * ( 1.0475 ) ³⁸⁶

= $ 24 * 60,180,558.2983

= $ 1,444,333,399.1603

= $ 1,444,333,399.16 ( when rounded off to two decimal places )

Thus the Future Value of $ 24 at 4.75 % interest rate after 386 years = $ 1,444,333,399.16

Note : ( 1.0475 ) ³⁸⁶ = 60,180,558.2983 is calculated using the excel formula =POWER(Number,Power) =POWER(1.0475,386)

jeff jeffy answered 2 months ago

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