How EMI Is Calculated: Formula, Interest and Repayment

What an EMI pays for

An equated monthly instalment, or EMI, is a regular payment that covers interest and reduces the outstanding principal. For a fixed-rate, fully amortizing loan with equal monthly periods, the payment can stay constant even though its interest and principal portions change.

The Loan EMI Calculator models that simple schedule. It does not quote a lender's offer. These examples use rupees for illustration, but the equation works in any single currency. It does not convert currencies or apply country-specific fees.

The reducing-balance formula

EMI = P × r × (1 + r)ⁿ / ((1 + r)ⁿ − 1)

• P is the amount borrowed.
• r is the monthly rate as a decimal: annual nominal percentage rate ÷ 100 ÷ 12.
• n is the number of monthly payments: whole years × 12, or the term entered in months.

At 12% nominal annual interest, r = 0.01, or 1% per month. Do not enter 12 or 0.12 as the monthly decimal rate. At zero interest, use EMI = P/n; the interest-bearing expression otherwise divides zero by zero.

The formula comes from the balance recurrence B_k = B_k−1(1+r) − EMI. After n payments, B_n = P(1+r)ⁿ − EMI × ((1+r)ⁿ−1)/r. Setting the final balance to zero gives the payment formula above.

₹100,000 at 12% for 12 months

Enter loan amount 100000, annual rate 12 and term 12 months. With P = 100000, r = 0.01 and n = 12, the payment is approximately ₹8,884.88. Using the unrounded payment gives total repayment ₹106,618.55 and total interest ₹6,618.55.

Month one's interest is 1% of ₹100,000. Month two charges interest on the smaller remaining balance, so more of the same payment reduces principal. The table is an educational calculation; the tool reports totals rather than a full repayment schedule.

Multiplying the displayed ₹8,884.88 by 12 gives ₹106,618.56, one paisa more than the unrounded calculation. A lender may round each payment or adjust the last instalment. Do not interpret that rounding difference as a different interest rate.

A lower EMI can still cost more overall

Keep ₹100,000 and 12% fixed but extend the term to 24 months. The monthly payment falls to ₹4,707.35; total repayment rises to ₹112,976.33, including ₹12,976.33 interest. The smaller payment helps monthly cash flow, but the balance stays outstanding longer. Compare both EMI and total cost.

A flat-rate calculation is different. Charging 12% of the original ₹100,000 for one year would produce ₹12,000 interest and ₹9,333.33 per month over 12 months. That is not the reducing-balance example above, despite the same “12%” label. Ask which rate convention a quote uses.

What this estimate leaves out

Use whole payment months for a conventional monthly schedule. The formula assumes payments at the end of equal monthly periods, one disbursement, a constant rate and no missed or extra payments. Daily interest, irregular first instalments, prepayments, rate resets, fees, taxes, insurance and penalties can change actual payments or cost.

A nominal borrowing rate is not automatically the same as an APR or another all-in cost measure. Use the lender's stated rate basis and repayment schedule. For a housing illustration, the Home Loan EMI Calculator and Mortgage Calculator have their own inputs and assumptions; neither replaces loan documents.

Sources and scope

The CFPB's explanation of amortization describes how principal and interest portions change as a fixed-rate balance is repaid. The algebra and numerical examples here are independently calculated for the simplified model, not a quoted lender product. This is an educational explanation, not a recommendation to borrow or a personalized affordability assessment.

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