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.
In Housing Finance , Equated Monthly Installment(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
EMI = ( L x i ) X (( 1+ i ) ^ N) / ([(1+i)^N] – 1)
Where,
L = Loan amount
i = Interest Rate (rate per annum divided by 12)
^ = to the power of
N = loan period in months
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 : i = 11 percent / 12 = .11/12 = .00916
EMI caculator : http://contentlinks.asiancerc.com/mt/tools.asp?pageSubType=emi_calculator
Read : what is Net Present Value ?
Well i would like to raise a point here , or a 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 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->Infand 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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You are brilliant! Thank you for sharing your wonderful ideas and tools.
@Stock trading
Thanks a lot .. what do you think about the maths done here
.. just curious
Manish
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.
Brilliant conclusion man. Thanks for this
I saw this blog today for the first time, but I will visit again
Hi Ajeet
Thanks for stopping by and reading . I am sure you will get amazing things in future too
Manish
Manish ,
U Rockz . Tihs blog makes me to re check my math skills
. U r simply awsome
Amarnath
Thanks man … I am sure you are talking about the calculas part
Manish