Loans Term

EMI (Equated Monthly Instalment)

Definition

The fixed monthly payment a borrower makes to repay a loan, split between interest and principal, where the interest share falls and the principal share rises each month on a reducing-balance loan.

Mathematical Formula

EMI=P×r×(1+r)n(1+r)n−1EMI = P \times r \times \frac{(1 + r)^n}{(1 + r)^n - 1}

Context & Practical Application

What is EMI? (Simple Terms)

EMI is the fixed amount you pay your lender each month until a loan is fully repaid. Every EMI has two parts: the interest the lender charges, and repayment of the money you actually borrowed.

On a ₹50 Lakhs home loan at 8.5% for 20 years, the EMI is about ₹43,391, the same amount every month.

Understanding EMI

Interest is charged on the outstanding balance, so the split inside each EMI shifts month by month. On the loan above, month one is ₹35,417 interest and ₹7,974 principal; the final month is ₹305 interest and ₹43,086 principal.

A longer loan tenure lowers the EMI but increases total interest. Model your own numbers with the EMI Calculator, and read the full walkthrough in What is EMI?.

Mathematical Analysis of EMI

The EMI is the fixed annuity payment that amortises a loan to zero over nn months. With principal PP, monthly rate rr (annual rate ÷ 12), and nn instalments:

EMI=P×r×(1+r)n(1+r)n−1\text{EMI} = P \times r \times \frac{(1 + r)^n}{(1 + r)^n - 1}

The first instalment’s interest is P×rP \times r; each later month charges rr on a balance already reduced by the principal portion. As r→0r \to 0 the formula tends to P/nP/n; a zero-interest loan still needs repaying in full.

Referenced In Guides & Comparisons

Learn how EMI (Equated Monthly Instalment) is applied in real-world scenarios across our pathways:

Guide (curriculum-lesson)What is EMI?