Calculating a Payment (PMT) with varying days to first payment date


I need to calculate an auto loan using the PMT function, or by "long hand" if it's easier for this scenario, that will take into account varying days to first payment.  For example, I have a $10000 auto loan for 60 months at 10% interest with monthly payments.  However, let's say the first payment is not due in 30 days, but in 45 days.  Or the first payment may be due in 15 days.  How do I incorporate the 15 day swing into the payment accurately?

Right now, I'm calculating the 15 days and adding/subtracting it from the principal balance before running the PMT calculation.  I just can't reconcile in my head how I wouldn't be overcharging interest in the former scenario.  I'd like to see how you recommend doing it.

Thanks in advance!

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tommyboy115Author Commented:
And by calculating the 15 days, I mean calculating the interest:

InterestAdjustment = ((AmountFinanced * (InterestRate / 100)) / 365) * DaystoFirstPayment
Looks good to me. The key is when you said "accurately"
The 15 day swing is not much in a 5 year (1500 day) loan. for a quick interest calculation ignore it. for a better approximation use your procedure. If you want more accuracy you have to consider how you want to incorporate compounding. You method will be good for most purposes.

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Richard DanekeTrainerCommented:
The PMT function assumes each period is of the same length, so you are correct to estimate additional interest due when the first payment extends beyond the standard period length (30 days).  I don't think the interest should be added to the principal unless it is detailed in the closing statement.  
Your formula is correct, but I think the confirmation of the loan officer from the lending institution would be a better source than here.
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