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Math Help - [SOLVED] Compound Interest Calculation

  1. #1
    Ife
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    [SOLVED] Compound Interest Calculation

    Not for heck can i figure this answer out! I have been working on it for quite a few hours!!!! I approached it from all angles and keep getting something different from what the answer should be... Can I PLEASE get some help???

    The question is as follows:

    A loan of $1000 with interest J4 = 10% will be repaid by a payment of $200 at the end of 3 months and three equal payments at the ends of 6, 9, and 12 months. What will the value of these payments be??

    The answer as quoted here is $288.86. How is this??

    I tried bringing each payment X to present value, i tried bringing the Principal to the future value at the end of the year with the compounded interest, and consequently bringing forward each payment including the $200 forward and equating, i tried using the 3 months as the focal point, but I still am not getting that $288.86. Please help???
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  2. #2
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    You must learn, and be very familiar with, Basic Principles.

    j4 = 0.10
    j = j4 / 4 = 0.025
    v = 1/(1+j) = 1/1.025

    x = The Mystery Payment

    Then: 1000 = 200v + xv^{2} + xv^{3} + xv^{4} = 200v + xv^{2}(1 + v + v^{2})

    Or

    \frac{1000-200v}{v^{2}} = x\frac{1-v^{3}}{1-v}

    Then rather obviously:

    x = \frac{1000-200v}{v^{2}} \cdot \frac{1-v}{1-v^{3}}

    Alternatively, of course, about three minutes with a spreadsheet and a "Goal Seek" leads to the same unique solution.
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  3. #3
    Ife
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    thanks,

    but wouldn't you have to take into consideration the months or the frequency of compounding? So that you would get each rate raised to a power of (total number of interest periods x frequency of compounding)? so it would really be 1.025^-4, -8, etc...??

    (of course this is what i was trying and not getting, so there must be something wrong, so tell me why not use those?? )
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  4. #4
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    Look very carefully at the definitions. That is why I wrote them clearly and distinctly.

    1) You defined "j4". This suggested to me that you intended quarterly compounding. I defined quarterly interest discount. Look at it closely. You seem to have missed this point. Why is "j4" defined. Did you do that or was it in the problem statement? Tell me why you decided compounding should be monthly. "j4" is VERY suspicious.

    2) Personally, I prefer positive exponents. This requires me to define v = 1/(1+i) when discounting and r = 1+i when accumulating. I don't have a problem with negative exponents; they are just easier to write poorly and get things wrong. Not everyone agrees with me.

    3) I did not take into account the different lengths of the different quarters. However, as the problem statement did not supply the month of the payments, it is reasonable to assume that each quarter is of a year.

    4) If your algebra skills are not top-notch, you DO need to upgrade a bit.

    5) I did reproduce the provided answer in both ways I suggested. This should be encouraging.

    6) You can do it monthly if you like. You just have to make the right definitions.

    j4 = 0.10

    j = j4 / 4 = 0.10 / 4 = 0.025

    i = (1+j)^{1/3}-1

    Now what?
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  5. #5
    Ife
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    what i simply meant was that we are shown that the calculation for the compounding is P (1+r)t where r = Jm/m , and t = m x n, but i see you used simply v^2, v^3, etc so that's what i was asking. (no need to be so condescending, i am just a bit confused with the formulae, that's all)

    Thanks a lot for your assistance though.

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  6. #6
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    Quote Originally Posted by Ife View Post
    what i simply meant was that we are shown that the calculation for the compounding is P (1+r)t where r = Jm/m , and t = m x n, but i see you used simply v^2, v^3, etc so that's what i was asking. (no need to be so condescending, i am just a bit confused with the formulae, that's all)

    Thanks a lot for your assistance though.

    1) Condescending? I dare you to point out where I was condescending. I simply answered your questions and asked some leading qeustions of my own. If you can find such a place, please reexamine the text and see if you can find some other way to construe the intent. Please try harder to come to more positive conclusions.

    2) Aha! "r = Jm/m" Here it is. You have just admitted that compounding is quarterly, having supplied j4. You have just run out of excuses for trying to do things monthly. Stop it. Go with quarterly

    3) Again, look very carefully at my definitions. I have defined 'v' in terms of QUARTERLY compouding. Discounting for one quarter, then, is simply 'v' - two quarters is v^2, etc. It's all in the definitions.
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  7. #7
    Ife
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    Thanks a lot. I guess i felt you a bit harsh, since i really don't completely have a full knowledge of this topic, so things are a bit confusing (hence my request for assistance). But no hard feelings, I am glad for your assistance, and i am still in the process of reading further into these topics so that i can have a better handle on this topic by the time i have finals.

    Thanks again for your assistance! and hopefully pretty soon I won't be in need of any assistance, and maybe I'll be assisting others like me soon enuf!

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  8. #8
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    "a bit harsh" - That I can live with.

    No worries. We're all in this together.

    Have you more of these annuities?
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