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Math Help - Equivalent Payment Streams

  1. #1
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    Equivalent Payment Streams

    Marvin was supposed to make three payments of $2,500 each the first one year ago, the second one year from now, and the third three years from now. He missed the first payment and proposes to pay $3,500 today and a second amount in two years. If money can earn 5.5% compounded semiannually, what must the second payment be to make the proposed payments equivalent to the scheduled payments?

    My Answer:

    I'm trying to solve for x, which is the second payment that is to be made in 2 years from now. I drew a timeline to explain the scenario.
    Basically, all the payments in the first stream (Option 1) must be moved to 2 years to make sure they will equal the same amount of money paid in Stream B (option 2)
    View the timeline I drew:

    Equivalent Payment Streams-evpa.png

    Since it is semi-annually, interest is compounded 2x a year. And 5.5%=2.75% per compounding period.
    FV1 + FV2 + PV = X + $3500

    FV1 = 2500(1.0275)2 = 2639.39
    FV2 = 2500(1.0275)6= 2941.92
    PV = 2500(1.0275)-2= 2367.97

    x= $4449.28

    However, the answer checker says this answer is WRONG. I don't understand why because I followed all the examples in the textbook properly.
    Where did I go wrong?? I even used the Financial App on my calculator where you just input the values, and they match my values but answer x is still calculating wrong.
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  2. #2
    MHF Contributor
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    Ottawa, Canada
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    Re: Equivalent Payment Streams

    Code:
    YR  PAYMENT    INTEREST     BALANCE
    1   2500.00         .00     2500.00           
    3   2500.00      286.55     5286.55
    5   2500.00      605.95     8392.50
    
    2   3500.00         .00     3500.00
    4   4048.11      401.17     7949.28 ******
    5       .00      443.22     8392.50
    ******Notice 4048.11 + 401.17 = 4449.28, the amount that you calculated.
    So you did everything ok, except 4048.11 is the required payment, the rest being interest.

    One GOOD thing from this: you'll NEVER do this again!!

    [2500(1.0275^12 - 1) / (1.0275^4 - 1)] / 1.0275^2 - 3500(1.0275^4) = 4048.107946....
    Play with that
    Last edited by Wilmer; October 30th 2013 at 08:44 PM.
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