CFA CFA Level 2 Math Help Needed

Math Help Needed

  • This topic has 3 replies, 3 voices, and was last updated Mar-20 by avannoord.
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  • Lawrence21236
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    Alright, I cannot figure out all of the steps to get the answer to a problem shown in Reading 36, page 128 of Level 2 in the physical book copy.

    The bottom of the page is showing steps to solve for a Spot Rate from a Par Rate. Specifically, it’s a 2 year spot rate that we are trying to solve. Any help is greatly appreciated to show all steps to isolate the 2 yr Spot Rate and get the answer they show of 3.008.

    Par = 100
    Par Rate = 3%
    N = 2 yearly payments
    1 Yr Par Rate =2.500%
    2 Yr Spot Rate = ??

    equation the reading shows:
    3/1.025 + 103 / (1 +r) ^2 = 100

    I get that 3/1.025 = 2.9268

    Then subtracting 2.9268 from both sides gives:

    103 / (1+r)^2 = 97.0732

    From this point on I get stuck on the exact steps to isolate and solve for r.

    policedog
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    103 / (1+r)^2 = 97.0732
    103 / 97.0732 = (1+r)^2
    1.0611 = (1+r)^2
    (1.0611)^(1/2) = 1+r
    1+r = 1.0301
    r = 0.0301
    r = 3.01%

    Lawrence21236
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    Thanks for responding… For the 2nd line you’re showing: 103/97.07 = (1+r)^2. I’m still a little confused. How did you get this line? I “thought” that you would have to multiply both sides by ((1+r)^2) / 1 to arrive at 103 (1+r)^2 = 97.07 (1+r)^2. But I know that’s not right.

    avannoord
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    Multiply both sides by (1+r)^2. That will get you to => 103*(1+r)^2 / (1+r)^2 = 97.0732*(1+r)^2. The (1+r)^2 term on the left cancels out. And then you divide both sides by 97.0732.

    Once you get there you take the square root of both sides to get rid f the square term and subtract 1 from both sides. Leaves you with “r = ……”

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