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Math Help - Effective Interest Rate

  1. #1
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    Effective Interest Rate

    I can't seem to get the right effective interest rate for the following question:

    - Savings account with a nominal annual interest rate of 4.5%, compounded semi-annually, with interest payable monthly. Find the effective interest rate.

    My process: (I'm not quite sure if I'm going the right way approaching this problem)
    1. Finding the semi annually rate: EAR = [1+0.045/2]^2 - 1 = 1.04551-1 = 0.45516

    2. Solving for monthly: [1 + 0.4551]^ (1/12) -1 = 0.0037 or 0.37%

    I got 0.37% <---definitely wrong.

    Any help/input will be greatly appreciated.
    Last edited by Mmike; January 12th 2011 at 07:40 AM. Reason: Missed an important word
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  2. #2
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    "nominal annual interest rate of 4.5%, compounded semi-annually"
    means effective of (1 + .045/2)^2 - 1 = 1.04550625 - 1 = .04550625 or ~4.55%

    The frequency that the interest is paid does not affect this.
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  3. #3
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    Quote Originally Posted by Wilmer View Post
    "nominal annual interest rate of 4.5%, compounded semi-annually"
    means effective of (1 + .045/2)^2 - 1 = 1.04550625 - 1 = .04550625 or ~4.55%

    The frequency that the interest is paid does not affect this.
    If the question was nominal annual interest rate of 4.5%, compounded monthly, would the effective interest rate be 0.37% as calculated above?

    Thanks.
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  4. #4
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    Quote Originally Posted by Mmike View Post
    If the question was nominal annual interest rate of 4.5%, compounded monthly, would the effective interest rate be 0.37% as calculated above?
    Effective annual rate = (1 + .045/12)^12 - 1 = (1.00375)^12 - 1 = 1.045939825 - 1 = .045939825 or ~4.59%
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