EQUATED MONTHLY INSTALLMENTS(EMI)

This is the most common method of repayment of loan is adopted in banking. Under this system, the principal and interest thereon is repaid through equal monthly installment over the fixed tenure of loan.
The formula for calculation of EMI
 EMI = [(P*r)*(1+r)^n]/[1+r)^n-1]
Where P = principal (amount of loan)
           r = rate of interest per installment period
           n = no. of installments in the tenure
For Example, for a loan of Rs. 1,00,000 at an interest rate of 12% p.a. is to be repaid in 12 months, the EMI is
P = 1,00,000
r = 12%/12 = 1% i.e. 1/100 = 0.01



EMI = [(1,00,000*0.01)*(1+0.01)^12]/[(1+0.01)^12-1]
        = (1,000*0.01^12)/(1.01^12-1)
        = 1,000*1.126825/0.126825
        = 8,884.8789 rounded to 8,885
Thus the EMI = 8,885.
Illustration:
Find out the EMI for a housing loan of Rs. 10,00,000/- at an interest rate of 10.50 per annum repayable in 15 years.
Solution:
 P = 10,00,000
 r = 10.50%/12 = 0.00875
 n = 15*12 = 180

EMI = [P*r*(1+r)^n]/[(1+r)^n-1]
        = 10,00,000*0.00875*(1+0.00875)^180/(1.00875^180-1)
        =  8,750*4.797761/3.797761
EMI = 11,054