The EMI formula, derived from first principles
An equated monthly instalment is the fixed amount that, paid every month for a set number of months, exactly clears a loan at a given rate. The loan accrues interest on the outstanding balance each month, so each payment covers that month's interest first and whatever is left reduces the principal.
Let P be the loan, n the number of months, and i the monthly rate (the annual rate divided by 1200). A payment of E at the end of each month means the outstanding balance follows a simple rule: new balance equals old balance times one plus i, minus E. After n such steps the balance must be zero.
Working that out gives the standard closed form used on this page: E equals P times i times the quantity one plus i to the power n, divided by the quantity one plus i to the power n minus one. When i is zero (a rare zero-interest loan), the formula reduces to P divided by n: the payment simply splits the loan into equal parts across the months.
A ten-lakh worked example you can check
Take a loan of ₹10,00,000 at an assumed annual rate of 10 per cent, over 10 years. The monthly rate is 10 divided by 1200, which is 0.008333. The number of months is 120. Plug the three numbers into the formula and the EMI works out to ₹13,215 (rounded to the rupee). Multiplied by 120 months, the total you pay back is ₹15,85,809. Of that, ₹10,00,000 is the loan itself, so the interest paid is ₹5,85,809, and the interest share of the total paid is 36.94 per cent.
The numbers below are the year-end balances from the same run. Each row's principal plus interest adds up to twelve times the EMI, give or take a rupee of rounding.
| Year | Principal paid in year | Interest paid in year | Balance at year end |
|---|---|---|---|
| 1 | ₹61,342 | ₹97,239 | ₹9,38,658 |
| 3 | ₹74,861 | ₹83,720 | ₹7,96,032 |
| 5 | ₹91,360 | ₹67,221 | ₹6,21,972 |
| 7 | ₹1,11,495 | ₹47,086 | ₹4,09,551 |
| 10 | ₹1,50,315 | ₹8,266 | ₹0 |
Why the early EMIs are mostly interest
The EMI is constant, but the split between interest and principal is not. In the very first month, the interest due is the full outstanding (₹10,00,000) times the monthly rate (0.008333), which is ₹8,333. The EMI is ₹13,215, so only ₹4,882 of that first payment goes to reducing the loan. The second month works on a slightly smaller balance, so the interest is a shade less and the principal share a shade more. The crossover, where principal in the EMI first overtakes interest, falls at month 38 in this run.
By year ten, almost every rupee of each EMI is principal and the interest share has shrunk toward zero. This is a mechanical result of the schedule, not a lender choice, and the pattern on the stacked area chart holds for any reducing-balance loan.
How each input moves the answer
Three numbers move the EMI, each in a different way.
The loan amount moves it in a straight line. Double the loan and the EMI doubles, holding the rate and tenure. Nothing about the formula depends on the absolute amount.
The rate moves it faster than it looks. On the ₹10,00,000, 10-year loan above, a one-point rise to 11 per cent lifts the EMI to about ₹13,775 (up ₹560). A one-point drop to 9 per cent pulls it down to ₹12,668 (down ₹547). Across 120 months those small monthly differences add up to about ₹67,000 of extra or saved interest.
The tenure is the opposite of what many borrowers expect: a longer tenure cuts the EMI but adds a lot of interest, because the outstanding sits on the books for longer. Shorter tenure means a bigger EMI but far less interest in total.
Reducing balance against flat rate
This page uses the reducing-balance method, which is how home loans, education loans and most personal loans in India are structured. Interest in each month is calculated on what you still owe, not the amount you started with.
Some car dealers, consumer-durable sellers and smaller finance companies still quote a flat rate. Under flat, interest is charged on the starting principal every month, even after months of repayment. A flat rate of, say, 10 per cent for five years looks the same as 10 per cent reducing to a reader, but the reducing-balance rate that would produce the same EMI is close to 17 per cent. If a lender quotes a flat rate, the number does not compare like-for-like with the rate on this page; the dedicated car loan calculator on this hub shows the exact conversion.
Floating rates and the repo rate context
A home loan from most lenders today runs on a floating rate linked to the RBI repo rate (currently 5.50 per cent after the 25 basis-points hike on 7 October 2026) plus a spread. After a rate decision, the lender will reset the schedule: a hike can lift the EMI, or stretch the tenure, or divide the effect between the two. This EMI calculator does not read a live rate; whatever number you enter is held constant for the full term.
To see what a rate reset would do, run the calculator twice: once at the current rate and once at the rate you want to test. The two EMIs (and the two interest totals) bracket the range of outcomes. Personal loans and most car loans are fixed-rate, so a single run is enough.
What this calculator leaves out
- Processing fees, documentation charges and the 18 per cent GST on them. For a personal loan, the personal loan version includes a fee input and computes the effective annual cost.
- Prepayment. If you plan to pay extra each month or clear a lump sum in a given year, run the home loan version, which models both.
- A changing interest rate during the loan. A home loan rate that resets twice is not a single-rate calculation.
- Taxes on interest or principal. Home loans in particular carry deductions under the old regime; the home loan page sets out which cap each component sits under.
- Late fees, cheque-bounce charges and insurance bundled into the loan.
Frequently asked questions
What is an EMI?
An equated monthly instalment is the fixed amount that, paid every month for a set tenure, exactly clears a loan at a given interest rate. Each payment covers the interest accrued that month on the outstanding first, with the remainder reducing the principal.
How is EMI calculated on a reducing-balance loan?
EMI equals P x i x (1 + i)^n divided by ((1 + i)^n - 1), where P is the principal, i is the monthly rate (annual rate divided by 1200), and n is the number of monthly instalments. The formula falls out of the requirement that the outstanding reaches zero after n payments.
What is an amortisation schedule?
The month-by-month table of each EMI split into its interest portion and its principal portion, together with the running balance. This page rolls the schedule up by year, but the arithmetic inside is monthly.
Why do early EMIs have more interest than principal?
Because the interest in a month is the monthly rate times the outstanding balance at the start of that month. Early on, the outstanding is close to the full loan, so most of the EMI is eaten by interest. As the balance falls, the interest in each EMI falls with it and the principal share grows.
Does the page include processing fees and GST on them?
No. This general page uses only the loan amount, the rate and the tenure. Processing fees and the 18 per cent GST on them are modelled on the personal loan page, which also computes the effective annual cost after fees.
What is the difference between reducing balance and flat rate?
A reducing-balance rate is charged on the outstanding each month, so the interest in each payment falls as the balance falls. Under a flat rate, interest keeps being billed on the original loan every month even after most of it has been repaid, which pushes the real annual cost well above the quoted number. The car loan calculator on this hub converts any flat rate into its reducing-balance equivalent.
Will my EMI change if the interest rate moves?
On a fixed-rate loan, no: the EMI is set at sanction and does not move. On a floating-rate loan, the lender resets either the EMI, the tenure, or both when the benchmark moves. Run the calculator at two rates to see the range.
Courses that teach the subject behind the eMI calculator
Wealth Management Certificate Course
A wealth management course combining financial planning with NSE certification guidance.
₹1,950 + 18% GST
Financial Market Beginners Module
Structured online preparation for the NSE NCFM Financial Market Beginners Module.
₹1,400 + 18% GST
Retirement Adviser SEBI NISM Series XVII Certification Course
NISM Series XVII Retirement Adviser preparation, covering pension planning and the exam.
₹2,500 + 18% GST
