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Math question regarding a car loan

Posted on 2012-04-07
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I just got approved for 15k for a car loan with a 3.5% interest.  This will be for 5 years, as far as the loan.  I was told that this loan is based on simple interest.

Here are my questions:

1.  How much will I pay on a daily interest?
2.  How much will my payment be, monthly?
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Question by:vulture71
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Your monthly payment will be 272.88.

Your daily interest will vary month to month as you pay off the principle.

Kevin
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The total amount of interest you will pay over the life of the loan is the total amount paid less the financed amount or (272.88 x 12 x 5) - 15,000 = 1,372.80.

Kevin
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daily interest 0.2876712328767123
days 1825
monthly payment 293.75

http://www.csgnetwork.com/simpleloansdailyintcalc.html
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however my own calc is:

Total daily interest 1371.31
Total repayments 16371.00
Monthly Payment 272.85

which makes zorvek right in the first place.
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>>Your daily interest will vary month to month as you pay off the principle<<
This is not quite true with simple interest. See the link here -
http://online.morainevalley.edu/websupported/jsukta/handouts/simple_interest_car_loan.htm
Which points out the pitfall of simple interest versus an amortized loan.
The calculation of 293.75 as a monthly payment is the more accurate one, although the amount of interest paid will actually depend on what day of the month it's paid and how many days from the time the last payment was made. The monthly payment of 272.88 would be correct if the loan were amotized.
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Ah,  separated by a commin language,  we call that the "flat rate" which resulted in a law change (years ago now)  to require the apr to be disclosed like on your linjed lian agreement.

All it is is a way to make it simple to work with,  while being unrelated to the time cost of money.

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Which is, although legal, a crime as far as I'm concerned.

vulture71, before you sign anything, I strongly suggest you call the lending institution and ask them what the monthly payment will be. Given that answer - and they most definitely will comply - you will be able to determine if you are getting taken to the cleaners. My guess is that if the lending institution is a bank or credit union, it will be the better deal. But if it's through the car dealer - especially a used car dealer - you may be getting a bad deal. And the dealer is probably getting a bit of a kickback.

Kevin
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I was in the banking business for a number of years and we always had a saying, "Figures don't lie, but liars figure."
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Really we need just a bit more information than was given. Or even the apr which I imagine is legally required there as it is here.

@kevin no argument with that here.
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All lenders are required to provide a "truth in lending" statement, which includes the apr.
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Now the question is: where is vulture71?

Kevin
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simple interest means to me that you pay 3.5% of the 15,000 per year as interest, all added together with the capital then divided by 60 months

15000 x (1 + .035 x 5) / 60 = 293.75
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Same here for "flat rate".
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apr = 6.736%
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deighton,
I calculated an apr of 6.537%. Am I missing something?
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awking,

I made it monthly apr -     i  = 1.06736^(1/12) - 1 = .005447

present value = 293.75 *(1 - (1+i)^-60) / i = 293.75 * 51.06396  = 15000

assuming payments are monthly in arrears

to solve for i, I used IRR function of excel

the present value formula is one I've used in the past that I recalled
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The present value for a series of equal payments is the summation of the payments divided by one plus the interest rate per period to the power of the period, where the period ranges from 1 to n and is generally written as:
n
PV = S   PMT/(1 + i)^n
1
Applying that to this case where the number of periods is 60 would be:
60
15,000 = S   293.75/(1 + i)^n
1
And the present value of 15,000 would determined by:

15,000 = 293.75/(1 + i) 1 + 293.75/(1 + i) 2 + 293.75/(1 + i) 3 + â€¦ + 293.75/(1 + i) 60

Unfortunately, there is no direct method for solving i in this equation, so we need to solve for the present value using an iterative process of estimating i until the value of 15,000 is reached. The attached spreadsheet shows the complete calculations.
apr.xls
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Note - the S in the equations above was intended to be a sigma (signifying a summation) but didn't convert with the fonts on this site.
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XX% begin
YYY% end

Depending whether payments are at the begin or end of each payment period.

This is calculated the old fashioned way with an HP12C,  Originally the HP38c from the 70s... the financial calculator of choice for finance.There's even an app these days. Anthony
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Dudes,

The guy is buying a used car and wants to know what the payment and interest is. I really don't think he is all that interested in various percentage calculations to six decimal places. He's not a hedge fund manager working with a few billion dollars.

Speaking of whom, I wonder where the hell he is...

Kevin
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reckon he's on Easter break.

15000 x 3.5% = 525
2625.00 = 525.00 x 5 = total interest
-------------
17,625.00 / 60 = 293.75 per month. .. 17625 is total paid.

(6.772097% begin)
6.536679% end - this is the one to expect.

Depending whether payments are at the begin or end of each payment period.

This is calculated the old fashioned way with an HP12C,  Originally the HP38c from the 70s... the financial calculator of choice for finance.There's even an app these days.

assuming simple interest method = flat rate method.

pays total 17625 at 293.75 per month.

Anthony
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Question: How many Experts does it take to answer a simple used car loan payment/interest question?

Answer: Ask it, go skiing for a week, and then tabulate the fun!

Kevin
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Accepted Solution

awking00 earned 500 total points
zorvek,
My latest posts were directed at deighton and not vulture71 regarding computation of the apr. Hopefully, vulture71 will receive a truth in lending statement that will include the apr, which will verify or refute the payment of 293.75 that I posted. As far as the interest payment is concerned, the total intest paid over the life of the loan is 2,625.00 (293.50 * 60 - 15,000). How it may be applied is somewhat at the lenders discretion. It might be 43.75 for each monthly payment or it could be calculated at 7.18 per day and applied based on the number of days between payments, or some other method. Whatever it is will be made known upon the receipt of the truth in lending statement.
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I realize that. I'm more concerned with the OP getting his question answered. This is his question, not ours. I'm not saying don't - just observing and making sure we don't get too carried away and take the OP's question into areas it really shouldn't go.

Kevin
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awking, in your spread sheet you have calculated monthly interest as i/12
but in uk rules it has to be calculated as (1 + i)^(1/12) - 1

I seem to recall
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