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, 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.

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.

What monthly reducing balance means

Interest is not repeatedly calculated on the original loan amount. It is calculated on the principal still outstanding for that month. After the principal component of an EMI is deducted, the lower balance is used for the next month’s interest.

This is why the interest component normally falls and the principal component normally rises over the schedule when the EMI and rate do not change.

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.

Why early EMIs contain more interest

At the start, almost the full principal is outstanding. Applying the monthly rate to that larger balance produces a larger interest amount, leaving less of the EMI for principal.

Later in the loan, the outstanding principal is lower. Monthly interest is then lower too, so more of the same EMI can reduce principal.

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 applicable retail term loans, the lender’s Key Facts Statement should show key terms and the annual percentage rate, which reflects the all-in cost covered by the KFS rules. Check the KFS, sanction letter and loan agreement for the actual costs attached to an offer.