How to calculate EMI amount for Loan

Calculating EMIs:

P = Loan Amount

n = Tenure (in months)

i = Rate of interest/month

if interest is 24% p.a, then i = .24/12 = 0.02

E = EMI to be paid per month

Suppose first month, you are paying E,

then P1 is the balance amount to be paid after first month.

P₁ = P + P.i – E

      = P(1+i) – E

P₂ = P₁(1+i) – E

     = [P(1+i) – E](1+i) – E

     = P(1+i)² – E(1+i) –E

     = P(1+i)² – E[(1+i)+1]

Substitute r = (1+i) for easy calculation,

P₂ = P.r² – E(1+r)

P₃ = P.r³ – E(1+r+r²)

Atlast, after n months, the Principal to be paid will be zero.

P_n = P.rⁿ – E[1+r+r²..r^(n-1)] = 0

So, P.rⁿ = E[1+r+r²..r^(n-1)]

As per Geometric series, [1+r+r²..r^(n-1)] = (rⁿ-1)/(r-1)

So P.rⁿ = E. (rⁿ-1)/(r-1)

E = P.rⁿ.(r-1)/(rⁿ-1)

Since r = (1+i),

E = P . i . (1+i)ⁿ / [(1+i)ⁿ – 1]

where,

P = Loan Amount

n = Tenure (in months)

i = Rate of interest/month

if interest is 24% p.a, then i = .24/12 = 0.02

E = EMI to be paid per month