# home loan part payment with emi effect - revised emi amount?

``````Loan Amount             1,215,371.00
Annual Interest Rate    10.15%
Term of Loan in Years   12
First Payment Date      10/09/2014
Payment Frequency       Monthly
Compound Period         Monthly
Monthly EMI             14631
``````

On 6th Oct 2015 made part payment 80,000 and have opted for reduced emi option. Can someone tell me what will be the revised monthly emi amount? (approx.)

I am confused between which amount out of these two will be considered to calculate emi (original principal amount - part payment) or (current principal amount outstanding as on 7th Oct - part payment).

As per my calculation (not sure)

Screenshot of excel emi calculator which I am using and it shows principal outstanding.

• When is 10/09/2014? Oct 7, 2015 at 21:02
• @DJohnM. Its 10th sept 2014 Oct 7, 2015 at 23:34

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 itself.

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!

• Yes that is right. Oct 8, 2015 at 3:32
• In the United States, some mortgages also give the customer the option of "re-amortizing" the loan back to the original amortization time period after paying down the mortgage. The one bank that I know offers this feature charges a \$ 250 fee each time a customer uses this feature. Oct 8, 2015 at 5:48
• @Dheer Hi, I have edited question & have added my calculation, could you have a look and tell me whats wrong with it Oct 8, 2015 at 12:23
• @Santosh You are calculating a revised EMI for a 12 year period starting from October 10. If your mortgage allows for extending the term of the mortgage to 12 years after October 10, say so explicitly. If the reduced EMI keeps to the same period, then you have only 131 payments to make starting November 10, not 144 as your `PMT(...)` calculation uses. Note that Jasper's answer also uses 131 remaining payments. Oct 8, 2015 at 13:37

Here is another way to calculate the new monthly payment:

1. Start with your original monthly payment. For example, an EMI of 14,631 rupees per month (rounded up from 14,630.15 rupees per month).
2. Calculate the amount by which you are ahead of your original amortization schedule. If you have been making exactly your scheduled monthly payments exactly on your scheduled payment dates, and if your only extra payment was the 80,000 rupees on October 6, 2015, this is approximately 80,000 rupees. (I do not know whether the extra payment being 4 days before your scheduled monthly payment will save you about 89 rupees in interest, or not.)
3. Calculate the Present Value Interest Factor of an Annuity with your interest rate and time remaining on the loan, using the following formula: PVIFA = (1 - (1 + APR/12)^-n) / APR * 12, where APR is your annual percentage rate (0.1015 = 10.15%) and n is the number of months remaining on the loan (131). In this example, PVIFA ~ 79.00524874 months. (A similar formula was used to calculate your old monthly payment for the original 144 month loan term.)
4. Divide amount #2 by the PVIFA. This is the amount by which your monthly payment will be reduced. For example, 80,000 rupees / 79.00525 months = 1,012.59 rupees per month.
5. Subtract amount #4 from your original monthly payment. For example, 14,630.15 - 1,012.59 = 13,617.56 rupees per month, which rounds up to 13,618 rupees per month.
• Thanks a lot for answering. I have edited question & have added my calculation, could you have a look and tell me whats wrong with it. Oct 8, 2015 at 7:43
• As @Dilip Sarwate pointed out, you need to calculate your monthly payment during the time remaining on your mortgage using the time remaining on your mortgage. This is now 131 months, not 144 months. For example, 1,075,858.35 rupees / 79.00524874 months = 13,617.56 rupees per month, which rounds up to 13,618 rupees per month. A formula of =PMT(10.15%/12,131,C11,,0) would work. Oct 8, 2015 at 14:32