In 1626, Peter Minuit of the Dutch West Indies purchased Manhattan Island from the Native Americans for $24. Assuming an exponential rate of inflation of 6% per year, how much will Manhattan Island be worth in 2010?
The year 2019 is 384 years later.
The value after that many years at a 6% appreciation rate is
24*(1.06)^384 = 125 billion dollars
To calculate the worth of Manhattan Island in 2010, we need to account for the exponential rate of inflation since 1626. The formula for calculating future value with exponential growth is:
FV = PV * (1 + r)^n
Where:
FV = Future Value
PV = Present Value
r = Annual interest rate (expressed as a decimal)
n = Number of compounding periods (years in this case)
In this scenario:
PV = $24 (the purchase price in 1626)
r = 6% per year (0.06 as a decimal)
n = 2010 - 1626 = 384 years
Now, let's plug in the values and calculate the future value:
FV = $24 * (1 + 0.06)^384
To calculate this, you can use a scientific calculator or spreadsheet software. The result of this calculation will give us the worth of Manhattan Island in 2010 adjusting for the 6% exponential rate of inflation.