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Thread: Redeeming Promissory notes

  1. #1
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    Redeeming Promissory notes

    To redeem a $100,000 promissory note due in 12 years. Flinstone Inc. has set up a sinking fund earning 7.25% compounded semi-annually. Equal deposits are made at the beginning of every six months.
    What is the size of the semi-annual deposits?
    How much of the maturity value of the fund is deposits?
    How much is interest?
    So far this is what I worked out for 1st question.
    FV=100,000 P/Y=2 C/Y=2 n=12(2) I/Y=7.25 i=7.25/2 =3.625 =.03625
    100,000=PMT (1.03625^24-1/.03625)
    100,000=PMT(37.25349873)
    PMT=2684.311633 Correct answer is 2590.41 could this be a rounding issue?
    (2590.42)(24) = 62169.84
    100,000-62,169.84 = 37,830.16
    So then maturity value is 62,169.84 and interest is 37,830.16 so the semi-annual deposits would be 2590.41. I can get 2590.42 using financial calculator but I need to show my work in long form. Could someone please check where I went wrong in first part of Question? Thanks

  2. #2
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    Let's not think about rounding issues until we check our assumptions.

    This expression: 1.03625^24-1 gives away the error. Your payments are at the END of each period, the last being on the maturity date. Whoops.

  3. #3
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    Don't understand!

    To redeem a $100,000 promissory note due in 12 years. Flinstone Inc. has set up a sinking fund earning 7.25% compounded semi-annually. Equal deposits are made at the beginning of every six months.
    I don't understand it says it's a the beginning of every 6 months.


    This expression: 1.03625^24-1 gives away the error. Your payments are at the END of each period, the last being on the maturity date. Whoops.

  4. #4
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    Use a 1-period example

    Take a loan of $100,000.

    You get 1 year to pay it off, paying 10% compounded annually.

    What will you pay if your single payment is at the END of that 1-year period?
    What will you pay if your single payent is at the BEGINING of the 1-year period?

  5. #5
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    Confrustion

    Quote Originally Posted by tkhunny View Post
    Use a 1-period example

    Take a loan of $100,000.

    You get 1 year to pay it off, paying 10% compounded annually.

    What will you pay if your single payment is at the END of that 1-year period?
    What will you pay if your single payent is at the BEGINING of the 1-year period?
    So it should be 100,000=PMT(1.03625^23-1/.03625

    This is so confusing my head is pounding! BECAUSE IT'S AT THE END OF PERIOD IT'S 23 PAYMENT.....

  6. #6
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    Learn "Basic Principles". It will ALL become clear.

    i = 0.0725 (annual interest)

    m = 2 (compounding periods per year)

    j = i/m = 0.03625 (modal interest)

    r = 1+j (modal accumulation factor)

    Accumulation in 24 periods, paying at the beginning of the period

    Pmt*(r^24 + r^23 + r^22 + ... + r^2 + r^1) = 100,000

    Accumulation in 24 periods, paying at the end of the period

    Pmt*(r^23 + r^22 + r^21 + ... + r^1 + r^0) = 100,000

    Most easily observed is the very last payment. For "beginning" there is one more period to collect interest. For "end" it lands on the date of maturity.

    You should also notice this:

    Accumulation in 24 periods, paying at the beginning of the period

    Pmt*(r^24 + r^23 + r^22 + ... + r^2 + r^1) = 100,000
    Pmt*r*(r^23 + r^22 + r^21 + ... + r^1 + r^0) = 100,000

    After factoring out the common 'r', we have left inside the parentheses exactly what we ahd in the "end" version shown above. In other words, they differ by only that one factor of 'r'!!

    Your only remaining task is to add up those nasty-looking expressions.

    r^23 + r^22 + r^21 + ... + r^1 + r^0 = [TEX]\frac{1 - r^{24}}{1-r}[/TEX]

    Are you familiar with this process? It would be worth your time to work on it.

  7. #7
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    Never seen this in our course and were at the end of course.

    Never had to find r or m or j so not sure what this is.
    I was taught to do using formula below.
    So I'll just use it and play around till I get answer.

  8. #8
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    Quote Originally Posted by Sue0113 View Post
    Never had to find r or m or j so not sure what this is.
    I was taught to do using formula below.
    So I'll just use it and play around till I get answer.
    No need to find. They are defined. This is how the world works.

    You can't have a formula for everything. You MUST know how to create them.

    You may need a little more backgound in algebra.

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