Setting a car loan

[Andy Pastuszak]

Thank you everyone!  You help has been amazing!

On Sat, Feb 21, 2015 at 2:50 PM, Edward Doolittle <
edward.doolittle at gmail.com> wrote:

> I had a similar issue last year. I requested a Statement of Account for my
> car loan from my bank and it was all over the place. Very disturbing to my
> mathematical mind. So I sat down to try to understand it. What I found was:
>
> - My bank continually shifts the actual payment date ahead from the
> nominal date by a few days so that the payment date does not fall on
> weekends or holidays.
> - My bank counts the number of days between payments, divides by 365,
> multiplies by the APR, and multiplies by the outstanding balance to
> calculate the interest.
> - My bank rounds that number, adds to the outstanding balance, and
> subtracts my payment to determine the new balance each period.
> - Even when I mirrored those calculations, my calculations differed from
> those of the bank by plus or minus one cent ($0.01) about four times per
> year. I can't explain the discrepancy yet, so I add a correction (of -0.01,
> 0.00, or 0.01) to each loan calculation which I used to compensate for the
> discrepancy.
>
> Mathematical formulas based on geometric series are nice, but you should
> keep in mind that they are only an approximation to what the bank does. If
> you're going to try to mirror what the bank does, for accurate bookkeeping,
> you'll really have to use a spreadsheet instead.
>
> It isn't hard to set up a spreadsheet with the basic features. I did one
> for Andy in a few minutes here:
> https://docs.google.com/spreadsheets/d/1LWOGrwNpHNa6Qf68J6FDAc5KchXHjV-G4Dnp64tKRaw/edit?usp=sharing
>  . The first row of the spreadsheet is irregular, so I had to enter the
> second row also by hand, then just copied that row and pasted up to row 61.
> Note that I did not include a Date Correction column to shift the date
> ahead to avoid weekends or holidays. It's not that hard to figure out a
> formula to place in the Date Correction column to move the date ahead to
> avoid weekends; I could share my formula for that if anyone is interested.
> It is harder to avoid holidays; if you really need to do that I suggest a
> manual correction to the Date Correction column to offset the date; maybe
> it could be automated using a table lookup. I didn't put any date
> correction columns into Andy's spreadsheet because I don't know whether
> they're relevant.
>
> When I got the spreadsheet for my car loan more or less correct with date
> corrections and 1 cent rounding(?) corrections, I entered the data into
> GnuCash as transactions crediting Liabilities:Loans:Car and debiting
> Expenses:Interest:Car. The next time I get a statement of account, I will
> reconcile it against Liabilities:Loans:Car and will likely have to make a
> few more 1 or 2 cent corrections. (I can make them on my spreadsheet too,
> then update my future predictions in GnuCash, but that's not really
> necessary and means I would have to modify a whole bunch of predictions I
> had entered into GnuCash each time I received an updated statement.)
>
> Anyway, back to Andy's question. Something does indeed seem to be wrong.
> 61 payments is too much. 60 payments is probably exactly right. However,
> there may be some explanation. I think that the bank may round down when it
> calculates the monthly payment; in that case there will be a small payment
> #61 that is less than the normal payment. (My spreadsheet shows $0.20
> balance after payment 60 is made.) The bank may tell you 61 payments
> because A) the last is technically a payment no matter how small, and B)
> they want you to make sure you have funds to cover the last partial
> payment.
>
> Saying 61 payments could conceivably be just a way for them to avoid the
> error-prone calculation that I attempted to do in my spreadsheet. It's
> really hard to predict holidays by formula, particularly Easter, so the
> bank just covers its donkey by warning you of an extra payment that may or
> may not be significant.
>
> The ultimate arbiter of the loan is the bank's Statement of Account. You
> should get in touch with your bank/loan officer and get periodic statements
> sent to you. Every month is probably not necessary, but an initial
> statement and then at least once at the beginning of the year would be
> helpful.
>
>
> On 21 February 2015 at 12:28, Andy Pastuszak <apastuszak at gmail.com> wrote:
>
>> Thank you.  That does help.
>>
>>
>>
>> On 02/21/2015 01:00 PM, jcard21 xxxxxxx wrote:
>>
>>> On Sat, Feb 21, 2015 at 12:08 PM, Andy Pastuszak <apastuszak at gmail.com>
>>> wrote:
>>>
>>>> • Loan Principle Value $16,261.32
>>>> • Loan Duration (number of years) 5 years (61 payments)
>>>> • Loan Interest Rate 3.89%
>>>> • Your Payment Frequency (monthly?) monthly
>>>> • Bank's Required Monthly Payment Amount $299.11
>>>>
>>>> Car was purchased on 12/22/2014.  First payment was due on 2/5/2015.
>>>>
>>> Using your figures ($16,261.32 principle, 61 months, 3.89%) , I get a
>>> monthly payment of $294.23 (using my Texas Instruments BA-II financial
>>> calculator.)
>>>
>>> Using 60 months, I get a monthly payment of $298.67, a lot closer to
>>> the dealer's amount.
>>>
>>> Could you and the dealer have included any other fees (motor vehicle
>>> registration, under-body weatherproofing, etc) totaling $269.46 on top
>>> of your loan principle of $16,261.32, so your actual/real loan
>>> principle would be the $16,530.78 ?
>>>
>>> A Loan Principle of $16,530.78 would give you a monthly payment of
>>> $299.11?
>>>
>>> I'd go back to the dealer and politely ask them to explain why your
>>> calculated monthly payment  doesn't equal their monthly payment of
>>> $299.11.
>>>
>>> I'd start by verifying with the dealer the number of months/payments
>>> (60 or 61), and I'd verify the Loan Principle ($16,261.32 or
>>> 16,530.78).
>>>
>>> I hope this helps.
>>>
>>>
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>
>
>
> --
> Edward Doolittle
> Associate Professor of Mathematics
> First Nations University of Canada
> 1 First Nations Way, Regina SK S4S 7K2
>
> « Toutes les fois que je donne une place vacante, je fais cent mécontents
> et un ingrat. »
> -- Louis XIV, dans Voltaire, Le Siècle de Louis XIV, Chap. XXVI
>