EMI formula explained

Definition

The EMI formula is E = P × r × (1+r)ⁿ / ((1+r)ⁿ − 1). It converts loan principal (P), monthly interest rate (r), and tenure in months (n) into one fixed monthly payment on a reducing-balance loan. This is the same math behind a free EMI calculator online. Banks and lenders commonly use it for home loan EMI, car EMI, personal loan EMI, and education EMI. EMI stays broadly constant when the rate is unchanged; early instalments are interest-heavy, and later ones repay more principal.

The formula and inputs

What is the EMI formula?

E = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ - 1)

• E: equated monthly instalment
• P: principal, or the amount borrowed
• r: monthly interest rate as a decimal
• n: total number of monthly instalments

Convert annual rate and tenure first

The formula does not use 10.5 directly for a loan quoted at 10.5% a year. Convert it to a monthly decimal: r = 10.5 ÷ 12 ÷ 100 = 0.00875. Convert 10 years to n = 10 × 12 = 120 months.

Worked example: ₹10 lakh at 10.5% for 10 years

For principal P = ₹10 lakh, monthly rate r = 0.00875, and n = 120, substitute the values into the formula. The calculated EMI is approximately ₹13,494. Small differences of a few rupees can arise from lender rounding.

How amortization works

How each EMI is split

EMI stays broadly constant when the rate is unchanged, but its composition changes. Monthly interest equals the opening balance multiplied by r. Principal repaid equals EMI minus that interest. The closing balance becomes next month's opening balance.

These values are rounded illustrations. Your lender may use daily accrual, different posting dates, or currency-level rounding, so its statement can vary slightly.

Why early EMIs are interest-heavy

Interest is highest when outstanding principal is highest. In month one of the example, ₹8,750 of the approximate ₹13,494 EMI is interest. As the balance falls, monthly interest falls and more of the same EMI repays principal. This pattern is amortization, not a separate bank fee.

How inputs and loan changes affect EMI

How rate, amount, and tenure change EMI

• Higher principal: EMI and total interest rise in direct proportion when rate and tenure stay unchanged.
• Higher rate: EMI rises, and more of the early payment goes toward interest.
• Longer tenure: EMI falls, but interest is charged across more months, so total interest usually rises.
• Prepayment: outstanding principal falls immediately, reducing future interest.

Compare a longer tenure with a lower principal rather than looking only for the smallest EMI. The compare loan offers calculator keeps assumptions consistent.

What changes on a floating-rate loan?

The original formula remains valid, but the lender recalculates the schedule when the applicable rate resets. It may raise EMI, extend tenure, or use both. Recalculate using the current outstanding principal, revised monthly rate, and remaining months. Do not restart with the original principal.

Stress-test a home loan EMI at 1 and 2 percentage points above the current rate. A stable EMI can still conceal a longer repayment period.

How prepayment changes the calculation

A prepayment reduces principal outside the normal EMI schedule. The next interest amount is calculated on the lower balance. If EMI remains unchanged, tenure usually shortens. If tenure remains unchanged, EMI can fall. Keeping EMI unchanged generally saves more interest when cash flow permits. Test both outcomes in the prepayment calculator.

EMI calculator in Excel (free download)

In Excel or Google Sheets the EMI formula is one function: =PMT(annual rate ÷ 12, months, −loan amount). For the example above, =PMT(10.5%/12, 120, -1000000) gives about ₹13,494. Leave out the minus sign and Excel shows the same number as a negative cash flow.

A single cell tells you the EMI but not where the money goes. The sheet below builds the full month-by-month schedule with the same reducing-balance math as this site, so you can see the interest and principal split, and test part payments without a bank statement.

• Edit five yellow cells: loan amount, annual rate, tenure in years, an optional monthly extra payment, and an optional lump sum with the month it goes in.
• EMI, total interest, interest saved and the month the loan closes all update on their own.
• The schedule runs up to 40 years and stops when the balance reaches zero.
• No macros, so it opens in Excel, Google Sheets, LibreOffice and Numbers.

Download the EMI calculator Excel sheet (.xlsx)

As a check: ₹10 lakh at 10.5% for 10 years with ₹5,000 extra every month and a ₹2 lakh lump sum in month 24 closes in 58 months instead of 120, and total interest falls from about ₹6.19 lakh to about ₹2.72 lakh. The online EMI calculator with prepayment gives the same answer if you prefer not to download anything.

Limits of the basic formula

Cases where this formula needs adjustment

• Interest-only or pre-EMI periods before full repayment begins.
• Step-up, step-down, balloon, or irregular instalment structures.
• Daily reducing-balance products with non-monthly cash flows.
• Flat-rate quotations that are not stated as reducing-balance rates.
• Fees, insurance, taxes, and penalties, which are outside the basic EMI formula.

Try it live

Open the free EMI calculator, enter principal, annual rate, and tenure, then compare the result with the lender's written repayment schedule for a home, car, or personal loan.

Sources and further reading

• RBI notifications: Key Facts Statement and related retail-lending disclosures that sit beside the EMI maths in a real sanction letter.
• Your lender’s amortization schedule: product rounding, broken periods, and reset rules can differ slightly from the textbook reducing-balance formula on this page.
• About this site: how the calculation engine is tested and how guide copy is prepared.