An interesting example of the power of compound interest is the sale of Manhattan Island for $24 in 1626 to Peter Minuit. Based on New York real estate prices today, it seems that Minuit got a great deal. But consider the future value of that $24 if it had been invested for 395 years (2021 minus 1626) at an interest rate of 8 percent per year: $24\times FVIF(.08, 395)=$24\times (1.08)395=$382,467,607,417,429 or about 382.5. Perhaps the deal wasn’t as good as it looked. The total value of land in Manhattan today is only a fraction of $382.5 trillion. Though entertaining, this analysis is actually somewhat misleading. First, the 8 percent interest rate we’ve used to compute future values is quite high by historical standards. At a 3.5 percent interest rate, which is more consistent with historical experience, the future value of the $24 would be dramatically lower, only $24\times 1.035395 = $19,127,112! Second, we have understated the returns to Mr. Minuit and his successors: we have ignored the rental income that the island’s land has generated over the last three or four centuries. All things considered, if we had been around in 1626, we would have gladly paid $24 for the island. Questions 1, What was the future value of the $24 paid for Manhattan Island by 1726, that is, after 100 years of compounding? What about by 1826? What was the growth in value during the second 100 years? What was the growth in value in the last 95 years of the “investment? 2, Why is the growth of value so much greater in the later years than in the earlier years? 3,Suppose that Peter Minuit did not become the first real estate tycoon in New York, but instead had invested his $24 at a 5 percent interest rate in New Amsterdam Savings Bank. What would have been the balance in his account after 5 years? 50 years? 4,Start-up Enterprises had sales last year of only $0.5 million. However, a stock market analyst is bullish on the company and predicts that sales will double each year for four years. What are projected sales at the end of this period?
An interesting example of the power of
$24\times FVIF(.08, 395)=$24\times (1.08)395=$382,467,607,417,429
or about 382.5. Perhaps the deal wasn’t as good as it looked. The total value of land in Manhattan today is only a fraction of $382.5 trillion.
Though entertaining, this analysis is actually somewhat misleading. First, the 8 percent interest rate we’ve used to compute future values is quite high by historical standards. At a 3.5 percent interest rate, which is more consistent with historical experience, the future value of the $24 would be dramatically lower, only
$24\times 1.035395 = $19,127,112!
Second, we have understated the returns to Mr. Minuit and his successors: we have ignored the rental income that the island’s land has generated over the last three or four centuries.
All things considered, if we had been around in 1626, we would have gladly paid $24 for the island.
Questions
1, What was the future value of the $24 paid for Manhattan Island by 1726, that is, after 100 years of compounding? What about by 1826? What was the growth in value during the second 100 years? What was the growth in value in the last 95 years of the “investment?
2, Why is the growth of value so much greater in the later years than in the earlier years?
3,Suppose that Peter Minuit did not become the first real estate tycoon in New York, but instead had invested his $24 at a 5 percent interest rate in New Amsterdam Savings Bank. What would have been the balance in his account after 5 years? 50 years?
4,Start-up Enterprises had sales last year of only $0.5 million. However, a stock market analyst is bullish on the company and predicts that sales will double each year for four years. What are projected sales at the end of this period?
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