Math

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Find the effective rate corresponding to the given nominal rate. (Round your answer to the nearest hundredth of a percentage point.)
(a) 4%/year, compounded quarterly

? %

(b) 3%/year, compounded monthly

? %

  • Math -

    P = Po(1+r)^n.

    Po can be any amount, but it should be invested for one year.

    a. Po = $1.00. = Initial investment.

    r = (4%/4) / 100% = 0.01 = Quarterly %
    rate expressed as a decimal.

    n = 4Comp/yr * 1yr = 4 Compounding
    periods.

    P = 1.00(1.01)^4 = $1.0406.
    Int. = $1.0406 - $1.00 = $0.0406.
    R=I/Po = (0.0406/$1.00)*100% = 4.06%.

    b. Po = $1.00.
    r = (3%/12) / 100% = 0.0025 = Monthly %
    rate expressed as a decimal.

    n = 12Comp/yr * 1yr = 12 Compounding
    periods.

    P = 1(1.0025)^12 = $1.03042
    I = $1.03042 - $1.00 = $0.03042.
    Rate = (0.0304/1.00) = 0.0304 = 3.04%.

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