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March 27, 2017

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My son informed me that a comic book I purchased for 10 cents in 1948 is worth $55 today. What has been the average annual compound rate of return on that valuable asset?

  • investing - ,

    Pt = Po * (r + 1)^n.

    Pt = principal after time t (62 yrs.),
    Po = initial investment,
    r = rate per compounding period expressed as a decimal.
    n = the number of compounding periods.

    55 = 0.10 * (r + 1)^62,
    Divide both sides by 0.10 and Solve for r:

    550 = (r + 1)^62
    Take the log of both sides:
    log550 = 62*log(r + 1),
    divide both sides by 62:
    log550 / 62 = log(r + 1),
    0.04420 = log(r + 1),
    10^0.04420 = r + 1,
    1.107132 = r + 1,
    0.107132 = r, or

    r = 0.107132 = 10.7132 % = annual
    percentage rate ( APR ) compounded
    annually.

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