Algebra

Fiona invested $1000 at 8% compounded continuously. At the same time Maria invested $1100 at 8% compounded daily. How long will it take for their investments to be equal in value? Assume there are 365 days in every year. Please help I have tried everything and cannot solve this problem. If you can, please provide step by step explanations. Thank you!

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  1. continuously: A(t) = 1000*e^.08t
    daily: A(t) = 1100(1+.08/365)^(365t)

    so, when are they equal? When

    1000 e^.08t = 1100(1+.08/365)^(365t)
    t = 10,873 years.

    continuous compounding is so close to daily compounding (1.08328% vs 1.08327%) that it takes a long time to overcome the larger starting amount.

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    posted by Steve

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