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Math Help - Problem on missed payments in annuity

  1. #1
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    Problem on missed payments in annuity

    okay so here's the problem:

    Mr. Go borrowed from Ms. Sy a certain amount payable at 9% compounded monthly after three years. Ms. Sy required Mr. Go to make regular payments of $9,000 at the end of each month to settle his obligation. Everything went as agreed upon for a year. After the first year, however, Mr. Go missed remitting his monthly payments for five months. In order to make up for his missed payments, Mr. Go paid $60,000 a month after the fifth month of missed payments and made regular installments of $9,000 at the end of each month only for six months. After which he decided to pay Ms. Sy the rest of his loan through three quarterly payments of $40,000 each.

    At the end of the three-year loan term, Ms. Sy claims that Mr. Go has not adequately paid the principal and all accumulated interests on the loan. Mr. Go, on the other hand, maintains that he has paid all his dues and has no obligation left unpaid. He adds that he, in fact, has paid more than he was supposed to.

    how much does Mr. Go either still owe or has overpaid Ms. Sy (if any)?


    for the reference purposes, the PV = 283021.2473 and FV = 370374.4451


    Here's the work I did in excel using the method of Outstanding Balance
    this work shows if Mr. Go had not missed any payments




    here's the work on Mr. Go's actual payments. At the end it shows that he has overpaid by $18235.483, pretty simple right?



    I thought about the perspective of Ms. Sy, however, and used the sinking fund method to double check, the table below is in exact sync with the first table given that Mr. Go had not compromised his payments.



    so far, it makes total sense, but then when I changed the table to fit the actual payments of Mr. Go, it all goes wrong...



    the table then shows that Mr. Go falls short of his payments.

    Can anyone help shed light into this?

    I may have overdone it so tell me where I went wrong with my line of thought. Much appreciation to all of you.
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  2. #2
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    Your last "table" is ok to month 12: $112,568

    Following that, you're not adding the interest to the balance
    each month where no payments received...

    Balances should be:
    month 18: 177,730
    month 24: 240,902
    month 27: 286,363
    month 30: 332,854
    month 33: 380,400 ; well over the 370,374 !

    Klear Nuff?
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  3. #3
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    hmmm

    hmmm... if the FV of table 4 leads to 380k, how come there is still a discrepancy from table 1? table 1 indicates that the overpayment is 18k, shouldn't that mean that the FV should be 370k+18k = 388k? somewhere along those figures?
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  4. #4
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    I stopped at 33 months TO ILLUSTRATE at that point.

    If you want to compare to your 36 months, just add
    another 3 months...kapish?
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  5. #5
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    ahh

    just did, much thanks wilmer, now I see where I went wrong hehe I stopped adding interest... silly me.. >_<
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  6. #6
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    Perhaps easier to "see" using PV's:

    PV of 12 $9,000 payments: 102,914
    PV of $60,000 (18 mo) :52,449
    PV of 6 $9,000 payments : 45,990
    PV of $40,000 (27 mo.) : 32,692
    PV of $40,000 (30 mo.) : 31,967
    PV of $40,000 (33 mo.) : 31,259

    Add 'em up: 297,271 ; compare to 283,021
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  7. #7
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    yea

    yea that's true hehe, thanks for all the help one last question though, in the 33rd month for table 4 its 380k, for the last month its 389023.3122, but when I add 370k and the overpayment its 391816.1, what do you think?
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  8. #8
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    Quote Originally Posted by Huami View Post
    ...in the 33rd month for table 4 its 380k, for the last month its 389023.3122, but when I add 370k and the overpayment its 391816.1, what do you think?
    Not sure what you're doing; I get:
    overpayment = 18,235 (33rd month) = 18,649 (36th month)
    370,374 + 18,649 = 389,023

    Now, will you please QUIT
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