Home Loan EMI Formula: Rs 30 Lakh Worked Example

A home-loan EMI is calculated from the outstanding principal, monthly interest rate and number of monthly instalments. In an illustrative Rs 30 lakh loan at a constant 8.5% annual rate for 20 years, the monthly payment works out to Rs 26,034.70. That payment covers both interest and repayment of principal, with their proportions changing each month.

The 8.5% rate here is an assumption for explaining the maths, not a bank quotation. The calculation assumes the entire loan is disbursed at the start, payments are made at each month's end and there are no fees, missed payments or rate changes.

Illustrative loan calculation, rounded
Item	Amount or assumption
Original principal	Rs 30,00,000
Annual interest rate	8.5%, assumed constant
Repayment period	240 months
Monthly EMI	Rs 26,034.70
Total interest without prepayment	Rs 32,48,327.28

What is the home-loan EMI formula?

The formula shown on ICICI Bank's official EMI calculator is E = P × r × (1 + r)^n / [(1 + r)^n - 1]. E is the monthly EMI, P the principal, r the monthly rate expressed as a decimal and n the number of monthly payments.

For this example, r = 8.5/12/100 = 0.0070833333 and n = 20 × 12 = 240. Substituting those inputs produces an unrounded EMI of about Rs 26,034.697. Total interest is E × n - P. Calculations here retain the unrounded EMI internally; multiplying a displayed rounded payment can produce a small difference.

A frequent input error is putting the annual rate directly into the monthly formula. Another is entering 20 as the tenure when the formula requires 240 months. Both mistakes change the result substantially, even though the loan amount is correct.

How much of the first EMI repays the loan?

The first month's interest is Rs 30,00,000 × 0.085/12 = Rs 21,250. Deducting it from the EMI leaves Rs 4,784.70 to reduce principal. After that payment, the outstanding balance is approximately Rs 29,95,215.30.

The next month's interest is calculated on that lower balance. With a constant rate and EMI, the interest portion gradually falls and the principal portion rises. This is why subtracting five years of total EMI payments directly from the original loan does not give the outstanding principal: part of every payment has covered interest.

How does a Rs 3 lakh prepayment change the EMI?

The balance immediately after k payments can be calculated as B = P × (1 + r)^k - E × [(1 + r)^k - 1]/r. After 60 payments in this example, B is Rs 26,43,815.49. A Rs 3 lakh part-payment made immediately then reduces it to Rs 23,43,815.49.

If the remaining tenure stays at 180 months and the assumed rate stays unchanged, applying the EMI formula to that new balance gives Rs 23,080.48 a month. The monthly reduction is approximately Rs 2,954.22. This is one possible mathematical recalculation; it does not establish how a particular lender will process a request.

If instead the original EMI continues, the term can be solved using n = -ln(1 - r × B/E)/ln(1 + r), where B is the balance after prepayment. The answer is about 143.84 months. In a monthly schedule, that means 143 full payments followed by a smaller final payment in month 144, instead of the original 180 remaining payments.

Why can the lender's schedule change?

A floating rate can reset, changing the relationship between the payment and the term. RBI's interest-reset FAQs describe quarterly statements showing principal and interest recovered, the EMI, instalments left and the annualised interest rate. Those account figures provide the inputs for checking an actual schedule.

For a real part-payment calculation, the relevant balance is the amount outstanding on that date. The examples above do not include any applicable charges or a different interest-accrual convention. They explain the arithmetic, rather than recommend borrowing or prepayment.