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This question already has an answer here:

I just took a car loan. The amount financed is $12,865.57, the APR is 3.06%, and the length is 48 months.

The finance company charges $285.47 monthly. I would like to know how they calculated such monthly payment?

marked as duplicate by Pete B., D Stanley, Brythan, Michael, Nathan L May 31 '17 at 20:07

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    See amortization – CactusCake May 31 '17 at 18:25
  • Are you certain it's compounded daily? – D Stanley May 31 '17 at 19:24
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    This may have a duplicate, but the chosen duplicate doesn't address the nuance of daily compounding with monthly payments that this question asks about. – Hart CO May 31 '17 at 21:28
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I would like to know how they calculated such monthly payment

The formula is:
enter image description here

Your values would come out to be:

r = (1+3.06/(100*365))^31-1=0.002602 (converting your annual percentage to a monthly rate equivalent of daily compounded interest)
PV = 12865.57
n = 48

Inserting your values into the formula:

P = [r*(PV)]/[1-(1+r)^(-n)]
P = [0.002602*(12865.57)]/[1-(1.002602)^(-48)]
P = 285.47

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    You often get minor discrepancies on this -- like the 36 cents here -- because the first payment usually does not represent the same amount of time, and therefore the same amount of interest, as other payments. Often the first payment isn't due for some time longer than one month after you take out the loan, so they can make the payment date fall on the last day of the month or whatever their schedule is. So you have to pay a little more to make up the interest for that partial month. – Jay May 31 '17 at 19:52
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    This is technically incorrect, as the interest is compounded daily, while payments are made monthly, your calculation assumes the same interval for payments and compounding. You need to calculate effective interest per period, not just divide APR by 12. That would be (1+0.0306/360)^30 - 1, or instead of 360 and 30 another convention is 365 and 30.416. If you rounded the effective rate down it'd be the same answer, so if you just update your formula for effective rate this will be good. – Hart CO May 31 '17 at 21:18
  • In reality, the payments won't be due 30 days apart. Some months it will be 30 days, others 31, and early each year there will be a payment due only 28 or 29 days later. I'm not aware of a simple formula that would account for that. – chepner May 31 '17 at 21:38
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    Further to Hart's comment r = (1 + 0.0306/365)^31 - 1 gets $285.47 – Chris Degnen May 31 '17 at 22:00
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    Oh, I was trying to keep calculations as simple as possible for ease of understandability....is the answer now sufficient? – Nosrac Jun 1 '17 at 11:37

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