How Home Loan EMI Is Calculated: Principal, Interest and Reducing Balance

What a home-loan EMI contains

A home-loan EMI has two parts: interest for the period and repayment of principal. The EMI may stay constant when the rate and tenure stay constant, but the split between those two parts changes each month.

Under a monthly reducing-balance loan, the month’s interest is calculated on the outstanding principal. The rest of the EMI reduces that principal, so the next month starts with a slightly lower balance.

The EMI formula

For a standard monthly amortizing loan at a positive constant rate, EMI = [P × r × (1 + r)^n] ÷ [(1 + r)^n − 1].

Here, P is the loan principal, r is the monthly interest rate, and n is the total number of monthly instalments. The formula sets one regular payment that repays the principal and calculated interest over the selected tenure, subject to the stated assumptions. At zero interest, EMI is simply P ÷ n.

Monthly rate and number of instalments

If the annual interest rate is R per cent, the monthly rate used by this model is r = R ÷ 12 ÷ 100. A 20-year tenure has 240 monthly instalments, so n is 240.

The monthly rate is a decimal in the formula. For example, 8.5% a year becomes 0.085 ÷ 12, or about 0.0070833 per month.

How monthly interest and principal are calculated

For each modeled payment period: monthly interest = opening outstanding principal × annual interest rate ÷ 12 ÷ 100. Use the annual rate as a percentage, such as 8.5.

Principal component = EMI − interest component. Closing balance = opening outstanding principal − principal component. That closing balance becomes the next month's opening balance.

This monthly model does not calculate interest using actual days between lender debit dates. Check the lender's schedule for its accrual convention.

Worked example: the first three EMIs

Consider a ₹10,00,000 loan at 8.5% a year for 20 years. Using the same monthly reducing-balance convention as the ArthaSiddhi Home Loan EMI Calculator, the EMI is ₹8,678 when rounded to the nearest rupee. Each value in the table is rounded separately, so the displayed principal and interest may differ from the displayed EMI by ₹1.

Read the first payment from opening to closing balance

Using the same example, follow month 1 before moving to the later rows. These amounts show paise; the table above rounds to whole rupees.

• Opening outstanding principal: ₹10,00,000.00.
• Interest component: ₹10,00,000.00 × 8.5 ÷ 12 ÷ 100 = ₹7,083.33.
• Principal component: EMI of ₹8,678.23 − interest of ₹7,083.33 = ₹1,594.90.
• Closing balance: ₹10,00,000.00 − principal repaid of ₹1,594.90 = ₹9,98,405.10.

Why the interest share falls over the schedule

At the start, almost the full principal is outstanding. In this example, that makes interest the larger part of the early EMIs. The split depends on the rate and tenure; interest need not exceed principal in every loan's first payment.

In a standard constant-rate reducing-balance schedule, each principal payment lowers the balance used for the next month's interest. As the interest component declines, more of the same scheduled EMI goes towards principal.

How tenure and the assumed rate change the result

At the same principal and positive annual rate, a longer repayment period lowers monthly EMI but increases scheduled interest. See the Home Loan tenure comparison for the 15, 20, 25 and 30-year trade-off.

Changing the assumed constant rate also changes EMI and scheduled interest. Each calculator scenario holds its rate constant throughout; comparing two rates does not predict future RBI rates or simulate a lender's floating-rate resets.

What the amortization schedule shows

An amortization schedule lists each EMI, its principal and interest components, and the outstanding balance after payment. It lets you see the shift in the EMI split rather than treating the EMI as one unexplained number.

A floating-rate reset, a missed payment, a prepayment, lender rounding or a different interest-accrual convention can change the actual schedule.

What the EMI formula does not include

The formula above covers principal and interest under its assumptions. It does not automatically include processing fees, legal or valuation charges, insurance, switching charges, penalties or every other borrowing cost.

For retail term loans covered by RBI's KFS requirements, use the Key Facts Statement to compare the annual percentage rate and disclosed charges, as well as the repayment schedule. The calculator's principal plus scheduled interest is not an APR or a complete borrowing-cost figure. RBI's current commercial-bank directions retain KFS requirements for covered loans.

The formula also does not determine the contractual first due date. Read when a Home Loan EMI starts for the distinction between sanction, disbursement, possible pre-EMI and regular repayment.