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What is the APY for money invested at each rate? (A) 6% compounded monthly (B) 4% compoumded continuously

  • math -

    APY = (1 + r)^n - 1.
    A. r = APR / 365 = rate per compounding
    period expressed as a decimal.
    n = 365 days=the number of compounding
    periods.

    APY = (1 + 0.00016438)^365 - 1,
    = 1.061830 - 1 = 0.061830 = 6.183%

  • math -

    Correction:

    P = Po(1+r)^n

    A. Let Po = $1.00 @ 6% for 1 year.

    r = (6%/12)/100% = 0.005 = Monthly% rate
    expressed as a decimal.

    n = 1comp/mo. * 12mo. = 12 Compounding
    periods.

    P = 1(1.005)^12 = 1.06168.

    I = P - Po = 1.06168 - 1.000 = $0.06168

    APY = (I/Po)*100% = (0.06168/1.0)*100% =
    6.168%.


    B. P = Po*e^(rt)

    r = (4%/100% = 0.04 = APR expressed as a decimal.

    t = 1 yr.

    rt = 0.04/yr. * 1yr = 0.04

    P = 1.0*e^0.04 = $1.04081

    I = 1.04081 - 1.00 = $0.04081

    APY = (I/Po)*100% = 0.04081/1.00)*100% =
    4.081%

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