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Homework Help: Rate of return with logs [engineering economics]

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data

    In 1903, a Picasso painting was purchased for $600. The family of the original owner sold the painting in 1995 for $29,152,000. What rate of return (interest) did the family receive on the investment?

    2. Relevant equations

    Single Payment Compound Interest Formula:

    F = P(1+i)n


    F= a future some of money (future value)
    P= a present sum of money
    n= number of interest periods
    i = interest rate per interest period.

    3. The attempt at a solution

    solve for i:

    F = P(1+i)n
    F/P = (1+i)n
    log(F/P) = n log (1+i)

    This is as far as I get. I know that n log (1+i) does not equal n log 1 + n log i, but I don't know what to do to isolate the i. I can't just divide both sides by n log because there is no such thing as n log. I thought about moving n log (1+i) to the left side and setting the equation to zero, but I didn't get anywhere with that either.
  2. jcsd
  3. Sep 11, 2010 #2


    User Avatar
    Gold Member

    Think about how you would invert a logarithmic function:

    [tex]y = \log x \Leftrightarrow x = {10^y}[/tex]
  4. Sep 11, 2010 #3
    get rid of the power of n by raising both sides by 1/n. i don't think that log trick you're pulling is even accurate
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