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

**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->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 …