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?
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, at that time sold as "Money Merge Account" and reincarnated more recently as "Wealth Unlimited". In a few hours, I wrote a spreadsheet that reproduced what either of these $3500 products claimed to do.
Delta is always applied to the principal. The only thing that increases monthly is how much of
p is applied to the principal.
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.
One thing that you may want to check is if you are penalized for pre-payment or not. From the bank's perspective, if you pay down principal early they lose out on interest, so some lenders penalize for this.
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.