Continuously compunded interest

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SUMMARY

The discussion centers on calculating the future value of an investment using continuously compounded interest based on an initial amount of $24 invested in 1626. The calculations for the year 2005 at interest rates of 5% and 7% yield results of approximately $4,074,662,794 and $7.98 trillion, respectively. Participants confirm that these large figures are accurate due to the effects of exponential growth over 379 years, validating the calculations performed using the formula P = P0e^(rt).

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  • Understanding of continuously compounded interest
  • Familiarity with the mathematical constant e
  • Basic knowledge of exponential functions
  • Ability to use scientific notation in calculations
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  • Study the formula for continuously compounded interest: P = P0e^(rt)
  • Learn about the mathematical constant e and its applications
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Students in mathematics or finance, educators teaching compound interest, and anyone interested in the implications of long-term investments and exponential growth.

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Homework Statement


The island of Manhattan was sold for $24 in 1626. Suppose the money had been invested in an account which compounded interest continually.

a) How much money would be in the account in the year 2005 if the yearly interest rate was:
i: 5%? ii: 7%

The Attempt at a Solution



I put the numbers into the function P0ert and got

i:24e.05(379) and ii:24e.07(379)

but when I put that in my calculator I get VERY large numbers:

i: 4074662794 and ii: 7.980752573E12

For some reason, I don't think the homework answers would be such ridiculously large numbers. Did I do this right?
 
Last edited:
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The numbers are ridiculously large but that doesn't mean they are wrong. Exponential growth is fast and 379 years is a ridiculously long time. I think you are correct.
 

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