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Math Help - Need help figuring loan pay off

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    Need help figuring loan pay off

    I am trying to pay off a loan I have sooner. I want to put a lump sum down and add extra payments a month. I need to know the new pay off date if I do this. Here are the details of the original loan: Loan amount is $40,000. at 7.75% for 130 bi-weekly payments.The first payment was 1/2/06, they are bi-weekly payments of $371.61. which would be payed off 12/27/2010. A balance of $23,464.60 as of now(4/08). I need to pay of this loan sooner and my plan is to send in a lump sum of $10,000 in May of 08 and then add $500.00 a month starting June 08. If I do this, I need to know how much sooner it will pay off my loan. What would be the new payoff date. If there is anybody who can give me a correct answer I would sure appreciate it. Thanks, Alois
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    I need to know the exact date (month/day/year) of the following:
    1. when your outstanding balance/principal was reduced to $23,464.60;
    2. when you plan to send in a lump sum of $10,000 in May of 08;
    3. the exact date when you plan to add $500.00 a month
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  3. #3
    Member jonah's Avatar
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    Quote Originally Posted by alois View Post
    I am trying to pay off a loan I have sooner. I want to put a lump sum down and add extra payments a month. I need to know the new pay off date if I do this. Here are the details of the original loan: Loan amount is $40,000. at 7.75% for 130 bi-weekly payments.The first payment was 1/2/06, they are bi-weekly payments of $371.61. which would be payed off 12/27/2010. A balance of $23,464.60 as of now(4/08). I need to pay of this loan sooner and my plan is to send in a lump sum of $10,000 in May of 08 and then add $500.00 a month starting June 08. If I do this, I need to know how much sooner it will pay off my loan. What would be the new payoff date. If there is anybody who can give me a correct answer I would sure appreciate it. Thanks, Alois
    I was recently cleaning up some clutter when I came across your old problem. After a closer look, I realized that there are several aspects of it that seems a bit off.

    Under the assumption that there are 26 “biweeks” or fortnights in a year (thus 26*14 days = 364 days) and with
    A = $40,000
    j = .0775
    m = 26
    t = 130/26 = 5 years
    we have
    A = R \cdot \frac{{1 - \left( {1 + \frac{j}<br />
{m}} \right)^{ - \left( {tm} \right)} }}<br />
{{\frac{j}<br />
{m}}} \Leftrightarrow R \approx {\text{371}}{\text{.60091969254}}<br /> <br />
or $371.60.
    The actual biweekly payment agreed upon is $371.61. If the first payment was made on 1/2/06 (Monday), then the loan was granted on 12/19/05 (also a Monday) since (1/2/06) minus (12/19/05) = 14 days. Under the agreement of 130 biweekly payments of $371.61, the loan would be paid off on 12/13/10 with a final payment of only $370.18 (not on 12/27/2010 as stated) since (12/13/10) minus (12/19/05) = 130 fortnights. See “Alois scenario 1.xls”.

    Accordingly, “a lump sum of $10,000 in May of 08” is a bit vague for me. Is the $10,000 lump sum an addition to the regular biweekly payment of $371.61 (making for a total of $10, 371.61), or is the $10,000 lump sum a replacement for the regular biweekly payment of $371.61 for that equally vague part of May of 08? Is it the early part of May of 08 (5/5/08) or the late part of May 08 (5/19/08)?

    Similarly, “and then add $500.00 a month starting June 08” is also a bit vague for me. Is the $500.00 a month starting June 08 an addition the regular biweekly payment of $371.61 (making for a total of $871.61), or is the $500 a month starting June 08 a replacement for the regular biweekly payment of $371.61 for that equally vague part of June of 08? Is it the early part of June of 08 (6/2/08) or the late part of June 08 (6/30/08)?

    From what I could tell, there are least 16 scenarios by which you can pay off your loan sooner under the vague conditions that you laid down. They are as follows:

    Scenario 2-1
    $10G on early part of May of 08 (5/5/08) and then regular biweekly payment increased to $500 on early part of June of 08 (6/2/08)
    Scenario 2-2
    $10G on early part of May of 08 (5/5/08) and then regular biweekly payment increased to $500 on late part of June 08 (6/30/08)
    Scenario 2-3
    $10G on late part of May 08 (5/19/08) and then regular biweekly payment increased to $500 on early part of June of 08 (6/2/08)
    Scenario 2-4
    $10G on late part of May 08 (5/19/08) and then regular biweekly payment increased to $500 on late part of June 08 (6/30/08)
    Scenario 2-5
    $10G on early part of May of 08 (5/5/08) and then regular biweekly payment of $371.61 + $500 on early part of June of 08 (6/2/08)
    Scenario 2-6
    $10G on early part of May of 08 (5/5/08) and then regular biweekly payment of $371.61 + $500 on late part of June 08 (6/30/08)
    Scenario 2-7
    $10G on late part of May 08 (5/19/08) and then regular biweekly payment of $371.61 + $500 on early part of June of 08 (6/2/08)
    Scenario 2-8
    $10G on late part of May 08 (5/19/08) and then regular biweekly payment of $371.61 + $500 on late part of June 08 (6/30/08)

    Scenario 3-1
    $10G + $371.61 on early part of May of 08 (5/5/08) and then regular biweekly payment increased to $500 on early part of June of 08 (6/2/08)
    Scenario 3-2
    $10G + $371.61 on early part of May of 08 (5/5/08) and then regular biweekly payment increased to $500 on late part of June 08 (6/30/08)
    Scenario 3-3
    $10G + $371.61 on late part of May 08 (5/19/08) and then regular biweekly payment increased to $500 on early part of June of 08 (6/2/08)
    Scenario 3-4
    $10G + $371.61 on late part of May 08 (5/19/08) and then regular biweekly payment increased to $500 on late part of June 08 (6/30/08)
    Scenario 3-5
    $10G + $371.61 on early part of May of 08 (5/5/08) and then regular biweekly payment of $371.61 + $500 on early part of June of 08 (6/2/08)
    Scenario 3-6
    $10G + $371.61 on early part of May of 08 (5/5/08) and then regular biweekly payment of $371.61 + $500 on late part of June 08 (6/30/08)
    Scenario 3-7
    $10G + $371.61 on late part of May 08 (5/19/08) and then regular biweekly payment of $371.61 + $500 on early part of June of 08 (6/2/08)
    Scenario 3-8
    $10G + $371.61 on late part of May 08 (5/19/08) and then regular biweekly payment of $371.61 + $500 on late part of June 08 (6/30/08)

    From these 16 scenarios, I believe the one that will allow you to pay off your loan soonest (as soon as 12/15/08) has to be Scenario 3-5. See “Alois scenario 3-5.xls”.

    Note: Another statement that’s a bit off is “A balance of $23,464.60 as of now(4/08).” It’s not exactly clear to me how you or your lender arrived at this amount. Is there perhaps an exact date and hour that you envisioned this balance amount? See “Alois scenario 2 daily (rounded).xls”.
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