$15 million in 1803, now in 2024 worth $2.65 trillion!
5.61% ARR over 22@ years!
logarithmic growth!
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To estimate the Annualized Rate of Return (ARR) from the original $15 million investment in 1803 to the current land value of the Louisiana Purchase territory, we’ll follow these steps:
1. Estimate the Current Land Value of the Louisiana Purchase Territory
2. Calculate the ARR using the Compound Annual Growth Rate (CAGR) formula
3. Present the Final Estimate
1. Estimating the Current Land Value
Area of the Louisiana Purchase:
• The Louisiana Purchase covered approximately 827,000 square miles.
• Conversion to acres: .
Estimating Average Land Value per Acre:
• The land encompasses a diverse range of terrains, including agricultural land, urban areas, forests, and mineral-rich regions.
• As of recent data, the average value of U.S. farm real estate is about $4,000 per acre.
• Urban and mineral-rich lands are significantly more valuable. To account for this, we’ll use a conservative average value of $5,000 per acre.
Total Current Land Value:
• Estimated Current Value: $2.65 trillion
2. Calculating the Annualized Rate of Return (ARR)
Formula:
• Present Value (PV): $15,000,000 (initial investment in 1803)
• Future Value (FV): $2,646,400,000,000 (estimated current value)
• n: Number of years from 1803 to 2024:
Calculations:
1. Compute the Growth Factor:
2. Calculate CAGR:
3. Using Logarithms for Precision:
• Calculate the natural logarithm:
• Divide by the number of periods:
• Exponentiate to find the growth rate:
• Subtract 1 to find the CAGR:
Result:
• Annualized Rate of Return (ARR): Approximately 5.61%
3. Summary
• Initial Investment (1803): $15 million
• Estimated Current Value (2024): $2.65 trillion
• Annualized Rate of Return: 5.61% over 221 years
Important Considerations:
• Simplifications:
• The estimate uses an average land value that doesn’t account for specific high-value urban areas or natural resources.
• It assumes consistent value across the entire territory, which is not the case in reality.
• Inflation and Currency Value:
• The calculation doesn’t adjust for inflation or changes in the purchasing power of money over time.
• $15 million in 1803 had significantly more purchasing power than $15 million today.
• Economic Impact Beyond Land Value:
• The Louisiana Purchase contributed to economic growth beyond land appreciation, including resource extraction, agriculture, and commerce.
• The strategic and geopolitical advantages are not quantified in this financial estimate.
Conclusion:
Estimating the ARR from the Louisiana Purchase to the present day yields an approximate annual return of 5.61%. This calculation provides a broad perspective on the financial growth of the investment over more than two centuries, highlighting the significant appreciation in land value and the long-term benefits of the acquisition.