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.
Pn = 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
