How Home Loan EMI is calculated ?

January 18, 2008 · 38 comments

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 …

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{ 37 comments… read them below or add one }

1 stock market September 11, 2009 at 12:36 am

You are brilliant! Thank you for sharing your wonderful ideas and tools.

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2 Manish Chauhan September 11, 2009 at 3:29 pm

@Stock trading

Thanks a lot .. what do you think about the maths done here :) .. just curious :)

Manish

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3 Anonymous September 30, 2009 at 3:20 am

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.

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4 Ajeet Khurana January 8, 2010 at 6:08 pm

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

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5 Manish Chauhan January 8, 2010 at 6:14 pm

Hi Ajeet

Thanks for stopping by and reading . I am sure you will get amazing things in future too :)

Manish

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6 Amarnath January 21, 2010 at 10:08 pm

Manish ,

U Rockz . Tihs blog makes me to re check my math skills ;) . U r simply awsome

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7 manish January 21, 2010 at 10:59 pm

Amarnath

Thanks man … I am sure you are talking about the calculas part :)

Manish

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8 Anand August 13, 2010 at 3:39 am

Was just browsing through old posts of yours. Would be good if readers also browse this loan amortization schedule @ http://office.microsoft.com/en-us/excel-help/using-the-loan-amortization-and-loan-analysis-templates-HA001034640.aspx

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9 Geo thomas August 23, 2010 at 6:04 pm

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.

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10 Manish Chauhan August 23, 2010 at 7:15 pm

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

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11 Srikar August 31, 2010 at 11:57 am

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

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12 Manish Chauhan August 31, 2010 at 12:06 pm

yup

Agree with you

Manish

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13 sagar November 25, 2010 at 4:02 pm

good this is helpfull.

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14 Thangavel December 31, 2010 at 2:48 pm

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!

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15 Manish Chauhan January 13, 2011 at 11:23 pm

Thangavel

Please ask your questions at http://www.jagoinvestor.com/forum/ and please make it short

Manish

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16 Satish12 January 25, 2011 at 10:27 am

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.

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17 Manish Chauhan January 25, 2011 at 11:48 am

Satish

Thanks :) . Keep reading

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18 Manish Chauhan January 25, 2011 at 12:46 pm

Satish

Thanks :)

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19 Prithvi March 31, 2011 at 4:19 pm

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?

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20 Manish Chauhan March 31, 2011 at 4:51 pm

Prithvi

Dont go for ADF , choose pre-EMI , here is why : http://www.rediff.com/getahead/2006/jul/03loan.htm

Manish

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21 Prithvi April 1, 2011 at 11:07 am

Thanks Manish..

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22 Rajashekar June 1, 2011 at 5:50 pm

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.

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23 Mukesh Shaw June 9, 2011 at 12:12 pm

Hi,

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

Thanks & regards,
mukesh

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24 Manish Chauhan June 9, 2011 at 2:44 pm

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

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25 Amish June 18, 2011 at 1:47 pm

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.

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26 Manish Chauhan June 18, 2011 at 6:23 pm

Amish

the whole procedure whold be almost same as you take a new flat , where exactly are you finding the problem ?

manish

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27 NVLN July 2, 2011 at 3:25 am

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.

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28 Manish Chauhan July 2, 2011 at 2:29 pm
29 NVLN July 2, 2011 at 3:26 am

In my Query, please read the Interest Rate as 8.25 % PA (type error – mentioned this as 8.25% PM).

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30 Manish September 15, 2011 at 4:27 pm

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

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31 nirmal January 13, 2012 at 5:49 pm

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

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32 Manish Chauhan January 13, 2012 at 6:51 pm
33 nirmal January 13, 2012 at 5:51 pm

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 ^

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34 Manish Chauhan January 13, 2012 at 6:50 pm

Nirmal

That means to the power of , you can use our calculator on EMI : http://www.jagoinvestor.com/calculators/html/loan-amortization.html

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35 tejkant January 30, 2012 at 4:26 pm

That was really an eye opener

thanks

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36 Manish Chauhan January 30, 2012 at 11:43 pm

Tejkant

Good to hear that you liked it :)

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37 Aditya February 2, 2012 at 6:36 pm

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

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