Results 1 to 9 of 9

Math Help - Find out the original principal and payoff date

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    7

    Find out the original principal and payoff date

    Hi,
    this is my current situation. I need to find out what my original principal was, and the payoff date. I know the APR (8% pa) but don't know if the balance is calculated monthly or daily (I suspect daily). I know the monthly payment ($763.90 due first business day after 20eth of the month) and I know the breakdown into principal payment vs interest payment for the last few months:
    08/20/09 PRINCIPAL PAYMENT +$344.55
    08/20/09 INTEREST PAYMENT +$419.35
    07/20/09 PRINCIPAL PAYMENT +$355.59
    07/20/09 INTEREST PAYMENT +$408.31
    06/22/09 PRINCIPAL PAYMENT +$339.52
    06/22/09 INTEREST PAYMENT +$424.38

    Is this sufficient information or do I need something more? Trying to reconcile this info with Time Value of Money formulae is beyond my math abilities.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2009
    Posts
    7
    Quote Originally Posted by knighttof3 View Post
    Hi,
    this is my current situation. I need to find out what my original principal was, and the payoff date. I know the APR (8% pa) but don't know if the balance is calculated monthly or daily (I suspect daily). I know the monthly payment ($763.90 due first business day after 20eth of the month) and I know the breakdown into principal payment vs interest payment for the last few months:
    08/20/09 PRINCIPAL PAYMENT +$344.55
    08/20/09 INTEREST PAYMENT +$419.35
    07/20/09 PRINCIPAL PAYMENT +$355.59
    07/20/09 INTEREST PAYMENT +$408.31
    06/22/09 PRINCIPAL PAYMENT +$339.52
    06/22/09 INTEREST PAYMENT +$424.38

    Is this sufficient information or do I need something more? Trying to reconcile this info with Time Value of Money formulae is beyond my math abilities.
    If this is too vague, you can assume that the balance is calculated monthly and that I pay exactly on 20eth. Also, here are some more payment values.
    But I think someone with good math abilities can ignore the specifics and answeer this question:
    If I know the APR, and 2 months worth of principal+interest payment breakup; is that enough to calculate the original principal and the payoff date assuming all balances have monthly calculations?

    05/20/09 PRINCIPAL PAYMENT +$350.77
    05/20/09 INTEREST PAYMENT +$413.13
    04/20/09 PRINCIPAL PAYMENT +$334.58
    04/20/09 INTEREST PAYMENT +$429.32
    03/20/09 PRINCIPAL PAYMENT +$373.69
    03/20/09 INTEREST PAYMENT +$390.21
    02/20/09 PRINCIPAL PAYMENT +$329.50
    02/20/09 INTEREST PAYMENT +$434.40
    01/20/09 PRINCIPAL PAYMENT +$327.60
    01/20/09 INTEREST PAYMENT +$436.30
    12/22/08 PRINCIPAL PAYMENT +$340.02
    12/22/08 INTEREST PAYMENT +$423.88
    11/20/08 PRINCIPAL PAYMENT +$323.55
    11/20/08 INTEREST PAYMENT +$440.35
    10/20/08 PRINCIPAL PAYMENT +$335.21
    10/20/08 INTEREST PAYMENT +$428.69
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by knighttof3 View Post
    Hi,
    this is my current situation. I need to find out what my original principal was, and the payoff date. I know the APR (8% pa) but don't know if the balance is calculated monthly or daily (I suspect daily). I know the monthly payment ($763.90 due first business day after 20eth of the month) and I know the breakdown into principal payment vs interest payment for the last few months:
    08/20/09 PRINCIPAL PAYMENT +$344.55
    08/20/09 INTEREST PAYMENT +$419.35
    07/20/09 PRINCIPAL PAYMENT +$355.59
    07/20/09 INTEREST PAYMENT +$408.31
    06/22/09 PRINCIPAL PAYMENT +$339.52
    06/22/09 INTEREST PAYMENT +$424.38

    Is this sufficient information or do I need something more? Trying to reconcile this info with Time Value of Money formulae is beyond my math abilities.
    This is the information you supplied above.
    It's just in tabular form.

    08/20/09 PR PAYT $344.55 INT $419.35
    07/20/09 Pr.PAYT $355.59 INT $408.31
    06/22/09 Pr.PAYT $339.52 INT $424.38
    05/20/09 Pr.PAYT $350.77 INT $413.13
    04/20/09 Pr.PAYT $334.58 INT $429.32
    03/20/09 Pr.PAYT $373.69 INT $390.21
    02/20/09 Pr.PAYT $329.50 INT $434.40
    01/20/09 Pr.PAYT $327.60 INT $436.30
    12/22/08 Pr.PAYT $340.02 INT $423.88
    11/20/08 Pr.PAYT $323.55 INT $440.35
    10/20/08 Pr.PAYT $335.21 INT $428.69


    The Principal Payment, from the early date to current, should be getting larger -- it varies irratically.
    The Interest Payment (in the same time line) should be steadily decreasing -- it isn't.
    Something else is happening.

    You may have an adjustable rate loan that can vary on a daily basis.

    Read the fine print in your contract for your loan.


    .
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2009
    Posts
    7
    Quote Originally Posted by aidan View Post
    [SIZE=4]This is the information you supplied above.

    The Principal Payment, from the early date to current, should be getting larger -- it varies irratically.
    The Interest Payment (in the same time line) should be steadily decreasing -- it isn't.
    Something else is happening.

    You may have an adjustable rate loan that can vary on a daily basis.

    Read the fine print in your contract for your loan.


    .
    The loan is fixed rate. I think some variation in interest is due to days of the month, e.g. look at 2/20/09 vs 3/20/09 vs 4/20/09. Some variation may be due to some archaic rules like "first business day after 20eth". And then the principal payments fluctuate because the total payment is fixed.
    But as I said I don't necessarily need 100% accuracy. At this point I'd be happy if I can find if the loan is paid of in 2020 or 2030 or 2040! The basic Q is, if I know the APR and a few monthly payments with interest vs principal breakdown, is that enough info to calculate the original principal and the payoff date? Feel free to ignore all numerical data I quoted.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by knighttof3 View Post
    ...
    The basic Q is,
    if I know the APR
    and a few monthly payments with interest vs principal breakdown,

    plus some variation in interest is due to days of the month,
    may be due to some archaic rules like "first business day after 20eth".
    & if the interest is computed daily or continuously.

    the total MONTHLY payment is fixed.

    is that enough info to calculate the CURRENT principal and the payoff date?
    Yes, IF that is all of the factors affecting the payback.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Sep 2009
    Posts
    7

    Eliminating some clutter

    I think I put too much extraneous info in my original problem statement (but hey, real life is messy!)
    I would like to restate the problem as follows.

    I want to find out (if possible) P and X in terms of R, P1, I1, P2 and I2 where

    P = original loan principal
    X = payoff date

    given these facts:
    All balances calculated monthly
    R = interest rate per MONTH
    P1 = principal payment for month M
    I1 = interest payment for month M
    P2 = principal payment for month M+1
    I2 = interest payment for month M+1
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,105
    Thanks
    68
    What you have here is a loan that was originally contracted assuming
    12 "monthly" payments per year (monthly means 1/12 of a year), thus
    payments "due" on last day of each month; however making payments
    on 22nd or thereabouts is an "arrangement" with the lender.
    In the long run, a bit of interest is saved (payments received sooner).
    With computers that's no problem, as the interest is calculated using
    the exact number of days in between payments, thus the result of
    irregular interest amounts.

    With the info you provided, it is not possible to calculate the original
    amount, but a fairly accurate estimate of the payoff date is easy enough.

    > 08/20/09 PRINCIPAL PAYMENT +$344.55
    > 08/20/09 INTEREST PAYMENT +$419.35
    > 07/20/09 PRINCIPAL PAYMENT +$355.59
    > 07/20/09 INTEREST PAYMENT +$408.31
    > 06/22/09 PRINCIPAL PAYMENT +$339.52
    > 06/22/09 INTEREST PAYMENT +$424.38

    We can use a "rough" estimate of the current monthly interest;
    pick your poison...I'll use $420:
    .08/12 times balance = 420
    balance = 420 / (.08/12) = 63,000 (currently owing, approximately)

    The current payment of 763.90 will pay that off in 120 months.
    (easily calculated by formula, or a $9.99 financial calculator!)
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Sep 2009
    Posts
    7
    Quote Originally Posted by Wilmer View Post
    What you have here is a loan that was originally contracted assuming
    12 "monthly" payments per year (monthly means 1/12 of a year), thus
    payments "due" on last day of each month; however making payments
    on 22nd or thereabouts is an "arrangement" with the lender.
    In the long run, a bit of interest is saved (payments received sooner).
    With computers that's no problem, as the interest is calculated using
    the exact number of days in between payments, thus the result of
    irregular interest amounts.

    With the info you provided, it is not possible to calculate the original
    amount, but a fairly accurate estimate of the payoff date is easy enough.

    > 08/20/09 PRINCIPAL PAYMENT +$344.55
    > 08/20/09 INTEREST PAYMENT +$419.35
    > 07/20/09 PRINCIPAL PAYMENT +$355.59
    > 07/20/09 INTEREST PAYMENT +$408.31
    > 06/22/09 PRINCIPAL PAYMENT +$339.52
    > 06/22/09 INTEREST PAYMENT +$424.38

    We can use a "rough" estimate of the current monthly interest;
    pick your poison...I'll use $420:
    .08/12 times balance = 420
    balance = 420 / (.08/12) = 63,000 (currently owing, approximately)

    The current payment of 763.90 will pay that off in 120 months.
    (easily calculated by formula, or a $9.99 financial calculator!)
    Thank you! That helps quite a bit!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,105
    Thanks
    68
    Quote Originally Posted by knighttof3 View Post
    I think I put too much extraneous info in my original problem statement (but hey, real life is messy!)
    I would like to restate the problem as follows.
    I want to find out (if possible) P and X in terms of R, P1, I1, P2 and I2 where
    P = original loan principal
    X = payoff date
    given these facts:
    All balances calculated monthly
    R = interest rate per MONTH
    P1 = principal payment for month M
    I1 = interest payment for month M
    P2 = principal payment for month M+1
    I2 = interest payment for month M+1
    These are the standards:
    A = Amount of original loan
    n = number of months (is really the payoff month)
    i = interest monthly
    p = payment (principal + interest)

    Given any 3, the other can be calculated easily (except i which requires iteration).
    Basic formula used: A = p[1 - 1/(1 + i)^n] / i
    That formula is "re-arranged" if another variable is to be calculated.

    With your initial example of rate = 8% and payment = 763.90, and
    assuming the term was 25 years (300 months), then loan amount
    = 763.90[1 - 1/(1 + .08/12)^300] / (.08/12) = ~98,975

    To find out the principal/interest portions of a certain month's payment,
    you require the balance owing at previous monthend; easy enough:
    say you want that for 200th month; formula can be manipulated to
    give the balance at end of month 199; in example above: 56,015.26:
    interest for 200th month = 56015.26 * .08/12 = 373.44.
    Just subtract that from the payment to get the principal portion.

    Hope that helps. Come back if you need more.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. to find the original price
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 26th 2010, 10:19 PM
  2. extracting date ranges from date vectors
    Posted in the Math Software Forum
    Replies: 1
    Last Post: May 20th 2010, 03:26 PM
  3. Find expectated payoff
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: July 6th 2009, 06:17 AM
  4. Julian date from current date
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 22nd 2009, 02:03 PM
  5. Find the original number
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 24th 2008, 12:24 PM

Search Tags


/mathhelpforum @mathhelpforum