How do we calculate the EMI
P: Principle loan amount
n: Tenure of the loan in months.
E: Be the EMI
r: Rate of interest / Month.
(Suppose rate of interest is 12%, then r = 0.12/12 = 0.01)
In the monthly EMI mode of payment, at the end of First month the principle (P1) owed by bank is Original amount P plus the interest of that month i.e., r * P minus the EMI (E) paid for that month
P1 = P + rP – E
P1 = P(1+r) – E ---------------------- {1}
Similarly
P2 = P1(1+r) – E
On Substituting for P1 from 1
P2 = (P(1+r) – E)(1+r) – E
P2 = P(1+r)2 - E[ (1+r) + 1]
Similarly for duration of “n” months, we can generalize the above equation
Pn = P(1+r)n - E[ (1+r)n-1 + ……(1+r)2 + (1+r) + 1] ---------------------{2}
We know that at the end of loan term, the outstanding principle will become 0, hence Pn = 0
0 = P(1+r)n - E[ (1+r)n-1 + ……(1+r)2 + (1+r) + 1]
P(1+r)n = E [ (1+r)n-1 + ……(1+r)2 + (1+r) + 1]
From Geometric Series we know that
Sn = xn – 1 / x – 1
P(1+r)n= E [ (1+r)n – 1] / (1 + r -1 )
P (1+r)n= E [ (1+r)n – 1] / r
Therefore now E becomes
EMI = P * r * (1+r) n/[(1+r) n –1]
This is the formula for to calculate EMI for a given Loan.
Example Scenario:
P = Rs. 1,00,000/-
Rate of interest = 12 %
Then r = 0.12 / 12 = 0.01 (per month)
n = 60 months ( 5 years )
EMI is
1, 00,000 * 0.01 * (1 + 0.01) 60
------------------------------------------------- = Rs. 2243
(1 + 0.01) 60 – 1
