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March 27, 2017

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Wnat to have $60,000 in an account after 40 years. How much needs to be deposited inthe APR is 16.3% compounded daily?

  • compounded continously - ,

    Compounded Continuously

    Pt = Po*e^rt = $60000,

    r = (16.3%/365) / 100% = 0.0004466 = Daily % rate expressed as a decimal.

    t = 40yrs * 365days/yr = 14600 days.

    rt = 0.0004466 * 14600 = 6.52.

    Po * e^6.52 = 60000,
    Po = 60000 / e^6.52 = $88.42 = initial deposit.


    ComPounded Daily

    Pt = Po*(1+r)^n = $60000,
    r = (16.3%/365) / 100% = 0.0004466 =
    daily % rate express as a decimal.

    n = 365comp./yr * 40yrs = 14600 comp.
    periods.

    Po*(1.0004466)^14600 = 60000,
    Po = 60000 / (1.0004466)^14600 = $88.52 = initial deposit.

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