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I have a 30 year fixed-rate mortgage. Yearly interest rate is r. If my initial principal is P and monthly payment is p, but this month i decide to pay p+Delta, how do i calculate how much of the (p+Delta) goes to the principal, and how much goes to the interest?

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Don't do that. Specify that all of your extra payment is applied to the principal. –  MrChrister Jan 25 '13 at 5:01
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Delta goes to the principle. To the best of my knowledge, there's no option to even make such a distinction, certainly no reason to make it. –  littleadv Jan 25 '13 at 5:03
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@littleadv - I am just remembering, but when I had a coupon book to pay my mortgage, it had a line for "extra to principal" (or something) and a line for total payment. I was under the impression from high school econ that they bank didn't have to apply the extra amount. Things change though... –  MrChrister Jan 25 '13 at 5:11
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I think they're not allowed to do it now. I have several iterations of mortgages and HELOC, and they all say explicitly that any extra is applied to principle, as long as the payments are made on time. If I'm late - then they don't have to do that. –  littleadv Jan 25 '13 at 5:29
    
I guess we are talking about US. In quite a few Asian countries, there is a option and one has to specify ... there is minimum amount [typically equal to one or three EMI] that needs to be paid towards principal. Also one can pay EMI in advance if one knows he is not able to pay in future due to some reason. The excess is held by the bank and applied on due dates –  Dheer Jan 26 '13 at 2:47
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4 Answers

The bank. upon request, should give you an amortization table. The remaining principal dropping a bit each month which means the next month, the payment will have a slightly lower amount going to interest. The table will show you each month's principal, and each month's interest.

The addition payments you're trying to make will go 100% to principal.

I recall an example, $200K 6% 30year mortgage, the Payment was $1200. Very early on in the mortgage, this was $1000 interest, $200 principal. If you paid $200 extra that month, you'd skip ahead a full month on the amortization table. By looking ahead at the next month's principal, you might keep this up for a number of years, effectively paying 2 months off at a time with this slightly higher payment.

Years ago, I wrote an amortization spreadsheet, which would help illustrate my response, and let you tinker with the idea of prepayments. It was part of a series to counter a mortgage acceleration scam. In a few hours, I wrote a spreadsheet that reproduced what a $3500 product claimed to do.

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You claim Delta all goes to the principle, but does not bank need to get interest on this Delta which i have loaned from them for up til now since the initial loan agreement? –  user1664196 Jan 26 '13 at 22:40
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Yes. And they did. The moment you make a full payment, you and the bank are even. You owe them the remaining principal, of course, but you are 'even' on accruing interest. At that moment, you can pay what ever principal you wish. And interest then accrues on the lower amount. –  JoeTaxpayer Jan 27 '13 at 0:03
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Delta is always applied to the principal. The only thing that increases monthly is how much of p is applied to the principal.

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Suppose on the day the payment is received the accrued interest on you loan is $200, then $200 of your payment goes to interest and the rest to the principal.

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Keep in mind, most mortgages do not save you interest by making even every payment, say, 20 days early. Nor will I end the mortgage with leftover payments to make if I make every payment the day before it turns late (usually 15 days past the due date). Yet, if mortgages were calculated on a daily accrual basis as HELOCs are, that's exactly what would happen. –  JoeTaxpayer Jan 26 '13 at 16:47
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There have been cases where banks choose to keep the extra payment "on account" and not apply it directly towards the principal, so it pays to be specific.

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This sounds more like a comment than an answer. Additionally, I have never heard of nor experienced that happening on a mortgage. On other loans, such as a car loan, that can be the case. –  Aaron D. Marasco Jan 25 '13 at 11:59
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