What is EMI and how to calculate EMI?

EMI is acronym to an equated monthly installment (EMI). It is a fixed amount payable by a borrower to a lender at each calendar month at a stated date. Under this system the principal and interest thereon is repaid through equal monthly interest over the fixed tenure of the loan. EMI is fixed based on the loan amount, interest rate and period of loan. The EMI is dependent on multiple factors, such as:

1) Principal borrowed,

2) Rate of interest,

3) Tenure of the loan,

4) Monthly/annual resting period

The formula to calculate an EMI is as under:

EMI = [P x R x (1+R)^N]/ [(1+R)^N-1],
where P is the principal loan amount, R is the Interest rate per month. [To calculate rate per month: if the interest rate per annum is 10%, the per month rate would be 10/(12 x 100)], and N is the number of installments.

To simplify above formula, call compounding factor (1+R)^N as  X

So EMI=PRX/(X-1)

Illustration:

Suppose a loan of Rs. 20 lakh is to be repaid over 30 years in EMI, with 10 % annual interest. Here, the monthly EMI for this loan will be calculated as follows –

1. First calculate R (convert to monthly interest rate) = 10/(12×100) = 0.00833
2. Then calculate no. of monthly installments, N = 30 years x 12 = 360 months

Calculate compounding factor X = (1+R)^N=(1+0.00833)³⁶⁰ = 19.8138

EMI = PRX / (X-1) = (2000000 x 0.00833 x 19.8138) / 18.8138 = 17545.52 = rounded off to nearest Rupee. EMI is Rs. 17546