This question is most likely from India where the concept of equal
monthly payments on a mortgage seems to be new and exciting and
deserving of an acronym (EMI = equal monthly installment?) all to
In many countries and many mortgage contracts, paying
something over and above the EMI reduces the principal amount owed
but does not relieve the borrower from paying the next month's
installment when it is due, or the one after that, and so on.
What happens instead is that the loan term effectively gets
shortened because the loan gets paid off sooner. In India, in
some mortgage contracts, the borrower apparently has the
option of asking that the monthly payment be reduced instead.
In this case, the borrower continues to make equal monthly payments
that are smaller than before, and the
loan gets paid off at the end of the agreed-upon term. Should a
second extra payment be made later with the same parameters, the
monthly payments would reduce again, but again continue
(in equal installments of even smaller amounts) until
the loan is paid off in full at the end of the term.
If the above is the correct description of how it works (perhaps
@Dheer, who is far more knowledgeable about money matters in
India than most everyone else here is,
might chime in), then the calculation is relatively straightforward.
Suppose that the EMI has value E currently, and that on the date
that the EMI is due, the borrower pays E plus an additional
amount T which is applied to reducing the principal still owed.
If the EMI payment by itself would leave an amount P of principal still
owing, then with the extra payment of T, the amount of principal
still owing will be P-T. Consequently, the new reduced EMI will be
F = ((P-T)/P)E
that is, the EMI is reduced by the factor (P-T)/P. The new reduced
EMI F will be due on the same dates as the original payments,
and the payments will continue till the loan is paid off
at the end of the agreed-upon term.
For the specific dates that you have, just pretend that the payment
of 6th October was made at the same time as the EMI payment that
you will make on 10th October. From 10 November onwards, your reduced
EMI will be smaller than INR 14631 by a factor of (P-80000)/P where
P is whatever your amortization schedule shows as the principal
still owed after the payment of 10 October (P = INR 1,151,004.84
and F = INR 13614.08 maybe?)
If you want to argue with the bank
over the four days of interest, and insist that the reduced
EMI start as of 10 October itself, go for it!