Business Math

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How long will it take a $400 investment to be worth $700 if it is continuously compounded at 12% per year?

I got the answer 6.71 years, but it was wrong, using the A=Pe^rt

Thank you

  • Business Math -

    Pt = Po*e^rt.

    r = 12%/100% = 0.12 = APR expressed as a decimal.
    t = Time in yrs.

    Pt = 400*e^0.12t = 700.
    e^0.12t = 700 / 400 = 1.75.
    0.12t = 0.55962.(Hit Ln key).
    t = 4.66 yrs.

    OR
    e^0.12t = 700 / 400 = 1.75.
    Take Ln of both sides:
    0.12t*Ln(e) = Ln1.75.
    0.12t*1.0 = 0.55962.
    t = 0.55962 / 0.12 = 4.66 yrs.

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