How Home Loan EMI is calculated.

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->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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