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Math Help - Gic fv

  1. #1
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    Gic fv

    A bank offers a rate of 5.3% compounded semiannually on its four -year GICs. What monthly and annually compounded rates should it quote in order to have the same effective interest rate at all three nominal rates?

    {___|____|____|_____|_____}
    0 yr1 yr2 yr3 yr4

    P =
    i = 5.3%/2
    n = 4

    p(1 + 0.053/2)^2 * 4

    That's as far as i got and after that i am stuck on what to do next?
    Last edited by diehardmath4; August 4th 2009 at 03:05 PM. Reason: new info came to mind
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  2. #2
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    Quote Originally Posted by diehardmath4 View Post
    A bank offers a rate of 5.3% compounded semiannually on its four -year GICs.
    The fact that this rate is on 4year GIC's has nothing to do with solution.
    The question can be simplified to:
    what annually compounded rate and what monthly compounded rate
    is equivalent to 5.3% compounded semiannually?

    5.3 cpd s/a = (1 + .053/2)^2 - 1 = 1.05370225 - 1 = .0537 :
    that's 5.37% annually (approximately).

    For monthly, you need a rate that achieves 5.37 when compounded 12 times:
    (1 + r/12)^12 = 1.0537
    1 + r/12 = 1.0537^(1/12)
    r/12 = 1.0043685 - 1
    r/12 = .0043685
    r = .052422 : 5.24% (approximately)

    SO: both 5.37 cpd annually and 5.24 cpd monthly = 5.3 cpd semiannually.

    Ya'll ok with that?
    Last edited by Wilmer; August 4th 2009 at 07:38 PM. Reason: none
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