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Math Help - equivalent compounded monthly interest of a loan.

  1. #1
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    equivalent compounded monthly interest of a loan.

    The equivalent annual rate of a 8% a compounded semi-annual loan is 8.16%((1.04)^2).What is the equivalent compounded monthly interest of this loan?(Hint:Some where you'll need to use the nth root (x) in your calculations.)

    a)Draw a time line of the above situation.

    b)What is the equivalent monthly interest rate expressed as a precent,rounded to 4 decimal places?
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  2. #2
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    Semi-Annual ==> 2

    0.08 / 2 = 0.04

    1.04^2 = 1.0816

    Monthly ==> 12

    0.08 / 12 = 0.0066666666666666...

    (1 + .0066666...)^12 = 1.0829995068075107437314206786755...

    Clearly, you will have to decide on some rounding rules.
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  3. #3
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    Being Canadian, where "standard" mortgage rates are (unfortunately!)
    compounding semi-annually (unless otherwise specified), then I believe
    you're after the monthly rate that will achieve the 8.16% :

    (1 + i)^12 = 1.0816
    i = 1.0816^(1/12) - 1 = .00655819692...

    And .00655819692... * 12 = .07869836304... : ~7.87%

    In other words, by using .00655819692... to calculate the interest
    each month, you end up charging an effective 8.16% annual rate.

    Sorry Mr T.K.
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  4. #4
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    No worries. I did, indeed, miss the flag.
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