calc2

At what constant, continuous annual rate should you deposit money into an account if you want to have $1,000,000 in 25 years? The account earns 5% interest, compounded continuously. Round to the nearest dollar.

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asked by CJ
  1. FV = Pe^Yr
    where FV = future value = 1,000,000
    r here = .05
    Y = 25
    1,000,000 = P e^(1.25)
    P = 1,000,000 / 3.49
    P = 286,533

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    posted by Damon
  2. online calculator:
    http://www.moneychimp.com/articles/finworks/continuous_compounding.htm

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    posted by Damon
  3. dP/dt = r P

    dP/P = r dt

    ln P = r t

    e^ln P = e^(rt) + C

    P = C e^(rt)

    when t = 0, e^(rt) = 1
    so C = value of P when t = 0
    so
    P = Po e^(rt)

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    posted by Damon
  4. How do I find the continuous rate though?

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    posted by CJ
  5. Oh, sorry
    Try this, sinking fund "Continuous compounding at nominal rate r, uniform series"

    http://ece.uprm.edu/~s016965/ININ%204015%20-%20Analisis%20Economico%20Para%20Ingenieros/Engineering%20Economic%20Analysis%208th%20ED.pdf

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    posted by Damon

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