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

Note  at  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 …

110 CommentsAdd Comment

  1. Anonymous

    I have taken a fixed home loan of 20,00,000 for 15 years with 9.5% rate. My EMI was 22K, however i started paying 30K instead to save some interest.
    Current outstanding is 17.40 Lacs,
    With my calculation i will be closing the loan in next 6 years.
    I have some money now around 1 Lac, Should i pay this one and save interest or invest in a mutual fund and continue as per plan to close in 6 years.

  2. Ajeet Khurana

    Brilliant conclusion man. Thanks for this :) I saw this blog today for the first time, but I will visit again :)

  3. Geo thomas

    hi manish i read this mail, i adviced my sister to take a longer duration home loan, the reason is every year she does top up of 1lac rs in principal and the difference from 20 years to 15yrs is small, she invest the small part in sip, which we book book profit and prepay the loan, we have planned to stop the loan in ten years . this way she is paying more of principal in the initial 6 years.
    is it a good statergy.

    • Geo

      I dont think so . If it was increasing the tenure from 5 to 10 yrs or 10 to 15 yrs, the reduction in EMI would be good enough , but just try to see what is the EMI reduction happenening when you increase the tenure from 20 to 25 yrs ?

      For a 40 lacs loan @10% interest and tenure 20 yrs , EMI per month = 38601

      However when you increase the Tenure to 25 yrs , the EMI comes to 36348 . Thats very insignificant decrease .

      Manish

  4. Srikar

    your work is commendable..
    but you forgot to take into account time value of money.

    Value of money after 30 years is going to be much less than what it is going to be after 10 years. So, repaying the loan in 30 years is much beneficial than repaying back in 10 years. ( in accordance to your stats mentioned above)

    You are right when it comes to comparison for 100 years..but I dont think it applies in real world as no bank would offer you that…

    cheers,
    Srikar

  5. Thangavel

    Dear Manish,

    First of all my sincere thanks to you for writing this blog. It really educates me a lot and helps me to lead a wealthy life.

    I’ve a query to you regarding housing loan per-repayment of principal while the loan is in partial disburse sate (the loan amount is not fully disbursed).

    In details:

    – I booked a FLAT which is under construction
    – For that, I opt for home loan from SBI (EASY HOME LOAN product)
    – The load got sanctioned for 35L on Dec 2009 but the payout(disburse) of the loan amount is linked with the progress of the my flat.
    – So for, I the bank disbursed 20L as my flat progressed
    – The repayment(EMI) will start in one of the following cases which ever comes first.
    1. on July 2011
    2. after completion of my flat (i.e. once the full loan amount is disbursed)

    – And I don’t need start any repayment(pre-EMI) before the EMI commences.
    – But the interest will be calculated for the partial disburse amount and it’s accumulated(again, interest is applicable for the interest) in my loan account.
    – From my loan account statement, I can see around 1.5L is accumulated a interest for the partial disburse.
    – Meanwhile, I’ve saved around 5L from my salary and put it in a FD (in a different bank) where the interest rate is lower than the home loan interest.

    My question here is:
    Can I pay 5L towards my loan account now? (1.5L towards interest + 3.5L towards principle)
    I asked the same question to my SBI bank manager, he confirmed about the interest part (1.5L) but he is not sure(he don’t know the T&C) about the principle part. He recommend me to not payback the principle now but after the EMI starts.
    My problem is, loosing money because of,
    – the interest difference between my FD and my home loan
    – and the TDS for interest earned form my FD.

    And I fear, if any penalty applicable for if I prepay principle(3.5L) at this stage.

    Thanks!

  6. Satish12

    Fantastic job done by you Manish. Thanks to people like you who are working for the benefit of all without looking for any personal benefits. Kudos.

  7. Prithvi

    Hi Manish,

    I have taken 30,71,000 home loan from SBI for a tenure of 20 years. Interest rate is 8 % 1st year, 9% for 2nd and 3rd year and then floating. SBI has included 18 months of Moratorium period since property will be ready by then, and they will charge only interest part and not principal during this period. Now builder is demanding me to avail ADF facility with SBI. I feel that ADF is not good for me because even on face I am paying extra with Moratorium option, if I invest balance part of EMI for a period of 20 years with average 10 % yearly return that would fill the extra amount I am paying. And second advantage is that I can keep check on builder for work completion to my satisfaction. Can you please help me decide on which option to choose ADF or Moratorium period?

  8. Rajashekar

    I”ve applied a home loan by structured EMI, Where I am paying 1st 4 EMI of Rs. 1000/- and 6th EMI as 11320.00 & nest 5 EMI as 1000.00 and 6th EMI as 11320 for this process entire 60 month paying.

    Kindly provide the EMI repayment schedule with EMI, Interest Portion, Principal Protion and Outstanding Principal after EMI.

    Loan Amount 100000.00
    Tenure – 60 Months
    Sturctured EMI – Monthly 1000.00 & Half Yearly 11320.00
    Rate of Interest: 20.00%

    Pls replay as per the details, if you can provid ethe schdule in Excel than better for me.

  9. Mukesh Shaw

    Hi,

    I want know how bank calculate home loan limit of a person based on his earning power.

    Thanks & regards,
    mukesh

    • Mukesh

      I am not sure on that, but it should be easy , it should be X times the yearly income , where X can range from bank to bank and is calculated based on job sector , security , past repaying capacity

      Manish

  10. Amish

    I have a plan to take home loan up to 15 lacs.Right now my property is in underconstruction. Now, i want to know if i get the loan from bank during that peroid. How should i have to pay EMI if bank give a money to contractor on progress based.

  11. NVLN

    What is the procedure to find out the break-up of Principal and Interest within a Constant EMI. For Example,

    Loan Amount = INR 100,000/-
    EMI = Constant Amount of INR 3,145.00Per Month, for 36 Months.
    Rate of Interest = 8.25%PM
    Thus, from Month 1 to Month 36, the Principal Component would increase while the Interest Component would decrease.

    Please let me know how the appropriation of the EMI happens, between Principal and Interest Amounts, across these 36 Months.

    Thanks in advance.

  12. Manish

    Hi Manish,

    I have taken a home loan of 17 lakh for 20 years of which only 9.5 lakh is disbursed as yet.Pre EMI interest is being deducted of approx Rs8k .
    Can you pls recommend the best options out of below:
    1. Get Pre-emi converted to full EMI (of 17k) so that prinicpal also gets reduced
    2. Continue paying interest only till full loan disbursement & pay partial repayments from after some intervals to reduced liability

    Thanks in advance…!
    Manish

  13. nirmal

    loan amount 1000000, 60 months , interest 12.25 % how to calculat education loan emi method ? i want step method to find out principle and interest

  14. nirmal

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

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

    EMI = Rs 1,136

    reply me step method : how to calculate ( 1+.00916) ^180
    what is mean ^

  15. Aditya

    Hi Manish – great to see the black magic maths behind the EMI, i do have a question on this though, the above formulae seem to calculate for ‘repayment type loans’ which is fine most of the time. Quite curious what would be the formalae when only the ‘interest component is being paid’ as is common in western countries, clearly the above does not suit those cases?

    Thanks
    Aditya

  16. selvi sathyanarayanan

    Mr. Manish
    I wanted to know whether the duration of the loan repayment will reduce or not if i increase the EMI.IF yes, kindly give me the benefits of doing so from the borrower’s point of view.

  17. Vasundhara

    My home loan (sbi) Rs 20,00,000. tenure 15 yrs emi Rs 19226 I pre paid Rs 3,00,000 towards principle .now i like to pay another 4,00,000 towards principle also want to reduce tenure to 10 yrs . Please give me suitable suggestion

    • Vasundhara

      You can keep prepaying the amount , when your prepay , your EMI will be same, but the tenure will automatically come down ! . Dont worry on that. I am sure when you prepay 7 lac in total out of 20 lacs, your tenure will be below 10 lacs only . Ask your bank to give you the updated tenure now

  18. SACHIN

    DEAR MANISH
    Thanks for writing the mindblowing blog
    My quiry is
    I have purchased a under construction flat, it will be ready in next 1 yr., my construction company asking for the documents for making loan case. the EMI for which will be started after i get the possession of the flat.
    1. do i have to pay the intertest on the money the construction company using for the period untile EMI start date. if yes can i pay some principle also with this interest.
    2. if i have some money with me now, is it better to pay to the construction company & reduce the loan amount or to prepay this lumpsump amount to the bank after the loan case strat.

  19. Binu Mathew

    I have taken 12 lakh loan. The interest rate is 8.25 for the first six months and then 9.25 for the next twelve months. How will I calculate the EMI for this loan? I’d be grateful to hear your solutions please. Thanks Binu

  20. naresh Agarwal

    Please advice
    1. shall i withdraw my pf fund to reduce my home loan as home loan intrest @ 9.8 % and PF intrest rate is 8.6 % only
    2. How the home loan intrest is calculated compounded quarterly or monthly as pf intrest rate is compounded monthly basis…..

  21. Rajesh

    Dear Manish Ji,
    Pls tell me how to calculate this figure
    Thanks
    ((1+.00916)^180 ) / ([(1+.00916)^180] – 1)

    (5.161846 / 4.161846)

    EMI = Rs 1,136

  22. Dinesh

    Manish

    My loan amount is 1500000 lakh, for 20 years & rate if int is 11.10
    EMI – 16310

    Please tell me what is the calculation. Interest & Principle amount in EMI.

  23. SANTOSH

    Ihave taken the loan of Rs. 8500000 for 15 years@ 9.5% in 2004. Now after 8 years, how much should I pay totally if I want clear the loan now. And is it wise to do so?

  24. Reshu

    Thanks for putting the calculations Manish. I am planning to transfer my home loan from one bank to another. I want to calculate how much money i am going to save before i make this decision. Can you please point me to calculations which i can do, considering i will keep prepaying some amount in loan time to time?

  25. Murugan

    Hello Manish,

    Thank you for your valuable information. I have already obtained a Home Loan in my Native place (for which EMI is yet to start) and would like to avail a new loan where I am currently put up.

    Could you kindly let me know or point to any information that would be helpful for me (in terms of using the money wisely – reduce loss of cash as interest etc.) and others who are in a similar situation?

    Thanks in advance for your guidance.
    Murugan.

  26. harsh

    hello sir i ‘ve taken a loan of 1500000 @10.75 i just want to know which tenure period would be beneficial for me if emi can be paid up to 25000.

  27. Sundar

    I have a question Manish,
    We have taken a loan of Rs3590000 and pay an EMI of Rs 40900 from Jan12.
    During September and October we paid Rs one lakh each as partial repayment. We would like to know how many instalments we need to pay further at the same rate of EMI
    Kindly answer me by mail.
    Regards,
    Sundar

  28. Deepesh Khatri

    Thank you Manish for writing such informative articles.

    I have following query about Home Loan.
    I have selected a builder who is running a scheme called “Live Lite” where at booking we have to pay 20% & Bank will pay rest 80% to the builder(upfront – I think). Till flat possession Pre-EMI is paid by Builder.

    Its looks beneficial to me, what is your view?

  29. sudhakar

    Dear Manish,
    Found your blog interesting.Please tell me how to calculate the total amount to be repaid ? how to calculate the break up of Principle and interest for the first month?
    How to calculate the break up from the month 2 ?

    Please guide me. I have applied for a loan of 13lakhs for 10 % interst with HDFC for a tenure of 20 years.

  30. Budhi Singh Negi

    hello sir I ‘ve taken a loan of Rs. 23,00,000 @10.75 for 20 years period. please calculate EMI rate as per above loan amt, interest and period.

  31. santosh kumar khanna

    Dear shri Chouhan,

    I shall be highly obilized if you please send me per year interest and principal for a housing loan of rs 2000000 for a240 months tenure @ 9.95% intt
    Thanking you

    s.k.khanna

  32. manjunath

    hello sir,
    im plannin to construct a home, hence forth im applyin loan for 15lakh, where in interest rate is 10%.. hw 2 calculate emi?? usin ur formula, im endin up in an unknown number.. can u plz explain me.. thank u in advance

  33. 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

  34. 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?

  35. 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

  36. 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 !

  37. 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!!

  38. 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.

  39. 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 !

  40. 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

  41. 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

Leave a Comment