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Problems in theory of interest

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  • Problems in theory of interest

    Hello. I need help in some of the problems in Stephen Kellison's Theory of Interest, 2nd Edition.

    Here's the first problem:

    "Deposits of $1000 are made into an investment fund at time 0 and at time 1. The fund balance is $1200 at time 1 and $2200 at time 2. Compute the annual effective yield rate which is equivalent to that produced by a time-weighted calculation."

    The concept of time-weighted is quite vague for me to understand... and I am thinking if this only applies for any time t, 0 <= t <= 1. So, when I use the formula stated in page 147of the book, I eventually get the yield rate to be 20%, and not 9.54%. What must be done here?

    The other problem that I am having hard time with is no. 25 of page 163. The problem asks to find the accumulated value of the annuity-due at time 5 assuming the first payment is made in calendar year z + 3 using the given table in the book. The table is included as an attached file. My solution is 1.092 + (1.092)(1.091) + (1.092)(1.091)(1.091) + (1.092)(1.091)(1.091)(1.09) + (1.092)(1.091)(1.091)(1.09)(1.09) but unfortunately, something seems to be incorrect. The answer given in the book is 6.5708.
    Attached Files
    Last edited by truth in lending; April 27 2005, 04:21 AM. Reason: To be more complete

  • #2
    I think the problem that you are having in the first question is that you forgot that the deposits occur over two years so you have to take the squareroot of your 1.2 to get your annual interest rate.

    What you need to do with the second problem is use the next row for each additional payment. Your first payment is in year z+3 accumulating for 5 years so your (1.092)(1.091)(1.091)(1.09)(1.09) is correct. The next payment is in year z+4 so you use that row and accumulate for 4 years, (1.09)(1.091)(1.092)(1.093). You do this for the 5 payments and I think your answer will match the book's answer.

    I hope this helps.
    Whether you are the lion or the gazelle, when the sun comes up, you better be running.

    Comment


    • #3
      Hello Ken.

      I want to thank you for guiding me in these two problems. But, after answering these two problems, I am still confused about them, so I will ask all my questions here.

      In my first problem, why must I take the square root? Actually, my frist approach (before I asked here) was this.... letting i to be my overall yield rate in the time-weighted method.... and j_k be the yield rates over the m subintervals for k = 1, 2, ... , m.

      [Blue]1 + j[/Blue] = (balance at the end of the subinterval)/(fund balance at the beginning of the subinterval with the contribution on that period).

      [Red]1 + i[/Red] = (1200 / (1000 + 0)) (2200 / (1000 + 1200)) = 1.2

      What is the effect if the deposits occur in 2 years, as you mentioned?

      In my 2nd problem, I editted my file there... this time it's complete... but anyways, I followed your hint and I got the answer. (thanks again) but I want to know why must I go "down one year" using the table...?


      I hope you have some time again...

      Comment


      • #4
        Hello Ken.

        I want to thank you for guiding me in these two problems. But, after answering these two problems, I am still confused about them, so I will ask all my questions here.

        In my first problem, why must I take the square root? Actually, my frist approach (before I asked here) was this.... letting i to be my overall yield rate in the time-weighted method.... and j_k be the yield rates over the m subintervals for k = 1, 2, ... , m.

        1 + j= (balance at the end of the subinterval)/(fund balance at the beginning of the subinterval with the contribution on that period).

        1 + i= (1200 / (1000 + 0)) (2200 / (1000 + 1200)) = 1.2

        What is the effect if the deposits occur in 2 years, as you mentioned?

        In my 2nd problem, I editted my file there... this time it's complete... but anyways, I followed your hint and I got the answer. (thanks again) but I want to know why must I go "down one year" using the table...?


        I hope you have some time again...

        Comment


        • #5
          Since the interest rate an annual effective rate and it is compounded over two years, the left side of your equation should be (1+i)^2. Your overall rate of return would be 20% but your yearly rate of return becomes the squareroot of that.

          You have to go down a row each time because the interest rates depend on both year the deposit is made (Z+n) and the number of years you are investing in the rates specified for that year (i_y).
          Whether you are the lion or the gazelle, when the sun comes up, you better be running.

          Comment


          • #6
            Hello again.

            First, I apologize for posting my reply twice accidentally... my mistake.


            Thank you very much, Ken.
            Last edited by truth in lending; April 28 2005, 05:36 AM.

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