How Home Loan EMI is calculated ?

Do you know how home loan EMI is calculated ? Its not just about Home loan , it can be any loan EMI . In this post we will learn how do we calculate monthly EMI for home Loan and how increasing Tenure does not help much after a certain point. A lot of people do not know that increasing the tenure only leads to increase in Interest amount payable and nothing else . The decrease in EMI is not proportional to the increase in Loan tenure . In Housing Finance , Equated Monthly Installments (EMI) refers to the monthly payment towards interest and principal made by a borrower to a lender. EMI is calculated using a formula that considers .

  • Loan Amount
  • Interest Rate
  • Loan Period

home loan EMI formula

Where,

L = Loan amount
i = Interest Rate (rate per annum divided by 12)
^ = to the power of
N = loan period in months

Example

Assuming a loan of Rs 1 Lakh at 11 percent per annum , repayable in 15 years, the EMI calculation using the formula will be :

EMI = (100000 x .00916) x ((1+.00916)^180 ) / ([(1+.00916)^180] – 1)

====> 916 X (5.161846 / 4.161846)

EMI = Rs 1,136

NoteĀ  atĀ  i = 11 percent / 12 = .11/12 = .00916

Q. How much benefit we get by increasing the Tenure of the Loan. Considering a Loan of Rs 30 Lacs at 12% interest rate.

Ans : I did a bit of my so called “mathematical skills” … and found out that EMI is of form

EMI(n) = C1 X C2^n / C2^n-1 , where
C1 = L * i
C2 = 1+i

So the difference in the EMI value for n+1 and n is nothing but

by a bit of caculation i got :

EMI(n) – EMI(n+1) = C1 x (C2^2n – C2^n) / (C2^2n – 1)

and when n becomes very large … and appling limit, we get

Lim C1 x (C2^2n – C2^n) / (C2^2n – 1)
-> Inf

=>

Lim C1 / C2^n
n->Inf

and as C2 > 1 (C2 = 1+i)

=>

Lim C1/C2^n = 0
n->Inf

Or in other words if we differentiate the EMI formula … we get a constant …

It shows and proves that the difference in EMI value is not very significant copmpared to the change in tenure and at one stage its almost of no gain to increase the tenure.

To show this argument : i would like to present an example, considering my old question:

Q. How much benefit we get by increasing the Tenure of the Loan. Considering a Loan of Rs 30 Lacs at 12% interest rate.

I am listing down the EMI value for different Tenures from 10 years to 100 years

Tenure EMI Differnce in EMI when tenure increased by 5 years

10 43041 7036
15 36005 2972
20 33032 1435
25 31596 738
30 30858 391
35 30466. 211
40 30254 115
45 30139 63
50 30076 34
55 30042 18
60 30023 10
65 30012 5
70 30007 3
75 30003 1
80 30002 0.95
85 30001.17 0.52
90 30000.64 0.29
95 30000.35 0.159

What it tells us is that it’s almost useless to extend the tenure after some time …

115 CommentsAdd Comment

  1. Rahul

    Hi Manish,

    I have taken a loan from LICHFL amounting 15 lacs out of which they have disbursed around 6 lacs.
    This month they sent message of EMI due on 10th July for Rs. 13537. Ideally this amount of EMI is applicable only after 100 % disbursement.
    They say you have to options i.e. pay as per disbursement or start the full EMI right from the beginning.

    I don’t understand what to do. Please throw some light over this and guide.

    Thanks

    • Raj

      Bank provides 2 options :
      1.pay as per disbursement : It means you need to pay interest only for disbursed amount until full amount get disbursed .After full amount disbursed ,Full EMI will start .
      2.start the full EMI right from the beginning:
      From 1st disbursement onward start paying full EMI .Initially Principle component will be more and interest component will be less in EMI .

      If you have money to pay ,it is good to go with 2nd option because less outstanding amount will cause less interest to pay.

  2. Neil

    pls let me know the calculation for loan amounting to 150000 at 2.99 as intrest with 36months and 189000 at 2.99 as intrest for 48 months.

    • badrinath

      loan amount rs.1200000 rate of interest 10.5% tenure of repayment 114 months, after the fourth emi i will do a partial prepayment of Rs.500000 keeping the tenure same what will be the revised emi

    • Hi Neil

      Your cases is a bit complex and I think we are not the right people to comment on it.

      My suggestion would be hire someone who is professional in this area and consult them

      Manish

  3. Anju

    Dear Manish,
    I had taken home loan of Rs 21 L from LICHFL for 20 yrs in July 2009. For only about four months the rate was 8.75% and then they increased to 12%, its continued so till now. I paid EMI of 22007. Now I have savings and want to return the loan ASAP. Is it a good strategy if I pay RS 10 Lakhs now and then the rest (My o/s loan is 19,40,000) after another three months from our savings (my, husband and daughter). Some people say it was useful had you paid in small amounts from the beginning. Now its not very useful to pay, and that we should invest the amount elsewhere. Would like to know your opinion.
    Thanks,
    Anju

      • Raj

        You need to give application to wave off penalty for pre-payment in case of LICHFL else they may charge for this prepayment .
        There is another condition which LICHFL has ,you can’t do pre-payment for first 6 months .Pls cross verify with LICHFL before paying .Clear all penalty clauses related doubts .

  4. varun taneja

    Dear Manish,

    You need to be thanked for the work you are doing , I regularly read your comments and the way you answer all the queries is commendable . now coming to my query , i had taken a home loan for Rs 30 lacs ( under construction flat , payment goes based on amt disbursed) at 10.25% interest rate for 20 years from x bank , now i am transferring this loan to Y bank at 10.1% interest rate and was also thinking of reducing the tenure from 20 years to 10 /12 years , what do u suggest . thanks

    • Varun

      First thing you can do is approach the existing bank and ask for the interest rate change if they allow . For change of tenure, the only option is to increase the EMI amount, you can do that if you can afford that !

  5. Shyam Ramani

    Hi,

    I have taken loan of 19,30,000 at 10.5 % variable rate of interest for the period of 20 years. The first part disbursement of the loan was for amount 13,00,000 (13 Lacs) done in Dec 2012. After two month of disbursement (i.e. in Feb) the rate of interest was reduced to 10.25%, and again in Sep 2013 it was increased to 11.00%. I had signed an agreement for reduced rate of interest at 10.25% from Dec 2013. The remaining amount of the loan (i.e. 6,30,000) will be disburse in Feb 2014. Kindly let me know, how to calculate the tenure after full disbursement and also if the rate of interest changes later on.

  6. Chetan Ambi

    Manish,
    Thanks for the detailed explaination on home loan. I don’t have home loan but in future this information is going to help me a lot. Thanks a lot!!

  7. Deena

    Hi Manish,

    I have taken a home loan from ICICI bank “EMI Under Construction”, So far I have got two disbursements and two more disbursements are pending. When I got the sanction letter of home loan the interest rate was “10.5”, I had to pay EMI say “x” for 20 years. So far I have paid EMI for 9 months. Now, the interest rate has been increased to “10.75” and I was informed that still I have to pay EMI for 20 years and 4 months. I understood that “EMI under construction” doesn’t increase the EMI amount instead the tenure. But I am shocked that 0.25 increase in interest rate costs me so much i.e. increase in tenure means obviously I have to pay 12 months EMI extra?

    Could you please throw some lights on this?

    I am really confused about this loan and its traps

    Thanks,
    Deena

    • Deena

      They are NOT Wrong . A small increase in interest rate can push your tenure by a big margin. You can calculate this yourself, In the EMI calculator, change interest rate number and see what tenure satisfied the same EMI amount.

      But this should happen in start only , not at the end leg of the loan . Welcome to the world of Home loans !

      • Raj

        Deena,
        If you have some money to pay as re-payment ,pls pay ,it will reduce your tenure a lot .Suppose if you do prepayment of Rs.100000 ,it will reduce your tenure a lot .As said by Manish ,in starting year it makes lots of diff .Inquiry with your bank and if you have low interest generating saving use them for pre payment.

  8. Rohit Prajapati

    Hi Manish,

    I have two queries,

    1) In my Provisional certificate the intrest expected amount written as 59000/- per anum, However in final Intrest certificate the actual amount written as 83000/- per anum, How the calculation is been done? and To whom i concern about this(The Branch or Home loan department)

    2) My Rate of Intrest gets down from 10.75 to 10.50 and 10.50 to 10.25 but no change in EMI. how do bank is working on this calculations….. would they decrese my loan tenure or intermediate amount adjustable?

    Loan from Bank of India.

    Please guide me on same.

    Regards,
    Rohit Prajapati

  9. Pranav Wagde

    Hi Manish, your blog is very useful.

    I have my home loan in SBI with 10.25% for 20 years for loan amount of Rs. 17,60000/-
    I did the calculation as per the formula given in your blog.
    It says my loan amount should be 17296/-, but i am paying 17580/-

    Am I missing anything in the calculations?

  10. amit

    Say i have taken a home loan with following details:
    loan amount: 3000000 (thirty lakh)
    interest:11%
    tenure:25yrs(300 months)

    Now my question is if i don’t pay any emi and I say that I will pay full amount after 300 months. What would be the amount I have to pay after 300 months

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