EMI Formula: How Loan EMI Is Calculated, with Worked Examples
An EMI, or equated monthly instalment, is the fixed amount you pay every month on a loan until it is fully repaid. The term is used for home loans, car loans and personal loans across South Asia and the Middle East; elsewhere the same thing is simply called the monthly payment. Every EMI contains some interest and some repayment of the amount you borrowed. This guide shows the formula, works through real numbers and explains how changing the rate or the term changes what you pay. To skip the maths, use the loan calculator.
The EMI formula
EMI = P × r × (1 + r)n ÷ ((1 + r)n − 1)
- P = principal, the amount borrowed
- r = monthly interest rate = annual rate ÷ 12 ÷ 100 (so 9% a year is 0.0075 a month)
- n = number of monthly instalments (5 years = 60)
The formula comes from treating the loan as an annuity: the present value of n equal payments, discounted at the monthly rate, must equal the amount borrowed. If the interest rate is 0%, the formula cannot be used (it divides by zero) and the EMI is simply P ÷ n.
Worked example: a 500,000 personal loan
Borrow 500,000 at 9% a year for 5 years.
- Monthly rate r = 9 ÷ 12 ÷ 100 = 0.0075.
- Number of instalments n = 5 × 12 = 60.
- (1 + r)n = 1.007560 ≈ 1.565681.
- EMI = 500,000 × 0.0075 × 1.565681 ÷ (1.565681 − 1) = 5,871.30 ÷ 0.565681 ≈ 10,379.18.
Over 60 months you pay 10,379.18 × 60 = 622,750.66, so the total interest is 122,750.66.
How each EMI splits into interest and principal
The EMI stays the same, but its make-up changes every month. Interest is charged on the balance still owed, so early instalments are mostly interest and later ones are mostly principal. For the loan above:
| Month | Interest (balance × 0.0075) | Principal repaid | Balance left |
|---|---|---|---|
| 1 | 3,750.00 | 6,629.18 | 493,370.82 |
| 2 | 3,700.28 | 6,678.90 | 486,691.93 |
| 3 | 3,650.19 | 6,728.99 | 479,962.94 |
This list of payments is called an amortisation schedule. It explains why prepaying early in a loan saves far more interest than prepaying near the end: an extra payment early reduces the balance on which every later month's interest is charged.
More examples
| Loan | Rate | Term | EMI | Total interest |
|---|---|---|---|---|
| 100,000 personal loan | 12% | 1 year | 8,884.88 | 6,618.55 |
| 20,000 car loan | 7% | 4 years | 478.92 | 2,988.39 |
| 1,000,000 loan | 10% | 10 years | 13,215.07 | 585,808.84 |
| 2,500,000 home loan | 8.5% | 20 years | 21,695.58 | 2,706,939.40 |
On the 20-year home loan the interest is larger than the amount borrowed. That is normal for long loans, and it is why the mortgage calculator also shows the effect of extra payments.
What changes your EMI
A longer term: lower EMI, more interest
The same 500,000 at 9%:
| Term | EMI | Total interest |
|---|---|---|
| 3 years (36) | 15,899.87 | 72,395.19 |
| 5 years (60) | 10,379.18 | 122,750.66 |
| 7 years (84) | 8,044.54 | 175,741.29 |
Stretching from 5 to 7 years cuts the EMI by about 2,335 a month but adds about 52,991 of interest. Choose the shortest term whose EMI you can comfortably afford.
A higher rate
At 11% instead of 9%, the 5-year EMI on 500,000 rises from 10,379.18 to 10,871.21, and total interest grows from 122,750.66 to 152,272.69. Two percentage points cost about 29,500 over the loan, which is why comparing offers matters.
Reducing-balance vs flat-rate loans
The EMI formula above is for a reducing-balance loan, where interest is charged only on what you still owe. Some lenders quote a flat rate instead: interest is calculated on the original amount for the whole term. A 9% flat rate on 500,000 over 5 years means 500,000 × 9% × 5 = 225,000 of interest and an EMI of 725,000 ÷ 60 = 12,083.33.
That payment matches a reducing-balance loan at about 15.7%, not 9%. Always ask whether a quoted rate is flat or reducing, and compare loans by their reducing-balance rate or APR. The APR vs APY guide explains how quoted rates differ.
How much EMI can you afford?
Lenders usually look at the share of your monthly income that goes on all loan payments together. Many banks are cautious once total EMIs pass roughly 40–50% of take-home pay, and a lower share leaves room for savings and emergencies. These limits vary by lender and country, so treat them as a starting point. If you already have several debts, the debt snowball calculator shows how quickly one fixed budget can clear them.
Common mistakes
- Using the annual rate as r. Divide by 12 and by 100 first: 9% becomes 0.0075, not 9 or 0.09.
- Using years as n. n is the number of monthly instalments: 5 years is 60.
- Comparing a flat rate with a reducing rate as if they were the same thing.
- Ignoring fees. Processing fees and insurance add to the real cost even when the EMI looks the same.
- Looking only at the EMI. A lower EMI from a longer term often means much more interest in total.
Calculate it in seconds
The loan calculator uses exactly this formula. Enter the amount, the annual rate and the term to see the EMI, the total interest, a year-by-year schedule and how much an extra monthly payment would save. It runs on your device and nothing you type is sent anywhere.