How EMI Is Calculated: The Reducing-Balance Formula Explained
Understand exactly how your loan EMI is calculated using the reducing-balance formula, with a step-by-step worked example in rupees and an amortisation table.
What EMI Actually Means
EMI stands for Equated Monthly Instalment, the fixed amount you pay your lender every month until the loan is cleared. Each EMI has two parts: a portion that repays the principal (the amount you borrowed) and a portion that pays interest on the outstanding balance.
Almost all retail loans in India, personal loans, home loans and car loans, use the reducing-balance method, where interest is charged only on the outstanding principal. As you repay, the outstanding shrinks, so the interest portion falls and the principal portion rises, even though your EMI stays constant.
The Formula
The standard EMI formula is:
EMI = P · r · (1 + r)^n / ((1 + r)^n − 1)
Where:
- P = principal (the loan amount)
- r = monthly interest rate = annual rate ÷ 12 ÷ 100
- n = number of monthly instalments (tenure in months)
Two things trip people up. First, the interest rate must be the monthly rate, not the annual one. Second, the exponent n is the total number of months, not years.
Step-by-Step Worked Example
Let us calculate the EMI on a ₹5,00,000 personal loan at 12% annual interest for 3 years.
Step 1: Find the monthly rate (r).
r = 12 ÷ 12 ÷ 100 = 0.01 (that is 1% per month)
Step 2: Find the number of instalments (n).
n = 3 years × 12 = 36 months
Step 3: Compute (1 + r)^n.
(1 + 0.01)^36 = (1.01)^36 ≈ 1.43077
Step 4: Plug into the formula.
EMI = 500000 × 0.01 × 1.43077 / (1.43077 − 1)
EMI = 500000 × 0.01 × 1.43077 / 0.43077
EMI = 7153.85 / 0.43077
EMI ≈ ₹16,607 per month
Step 5: Find the total cost.
Total paid = 16,607 × 36 = ₹5,97,852
Total interest = 5,97,852 − 5,00,000 = ₹97,852
You can verify any of these figures instantly with our EMI calculator.
Why the Interest Portion Shrinks Over Time
Even though your EMI is fixed, its split changes every month. Here is the first few months of the amortisation schedule for the loan above:
| Month | Opening balance | Interest (1%) | Principal | Closing balance | | --- | --- | --- | --- | --- | | 1 | ₹5,00,000 | ₹5,000 | ₹11,607 | ₹4,88,393 | | 2 | ₹4,88,393 | ₹4,884 | ₹11,723 | ₹4,76,670 | | 3 | ₹4,76,670 | ₹4,767 | ₹11,840 | ₹4,64,830 | | ... | ... | ... | ... | ... | | 36 | ₹16,442 | ₹164 | ₹16,443 | ₹0 |
Notice how in month 1, ₹5,000 of your EMI is interest and ₹11,607 is principal. By the final month, almost the entire EMI is principal. This front-loading of interest is why prepaying early saves so much.
Reducing Balance vs Flat Rate
Beware of loans quoted on a flat rate, common with some informal lenders and older schemes. Under flat rate, interest is charged on the full original principal for the entire tenure, ignoring the fact that you are repaying it down.
A "10% flat" loan is far more expensive than a "10% reducing" loan. As a rough guide, a flat rate is nearly double the equivalent reducing rate. Always ask lenders to quote the reducing-balance (annual effective) rate so you can compare like with like.
How Tenure Affects Your EMI and Interest
Stretching the tenure lowers your EMI but raises total interest, because you owe money for longer. Using the same ₹5,00,000 at 12%:
| Tenure | Approx. EMI | Total interest | | --- | --- | --- | | 2 years | ₹23,536 | ₹64,864 | | 3 years | ₹16,607 | ₹97,852 | | 5 years | ₹11,122 | ₹1,67,320 |
The longer tenure nearly triples the interest. Choose the shortest tenure whose EMI you can comfortably afford.
What Changes Your EMI Mid-Loan
Your EMI can change if:
- You have a floating rate and the benchmark moves. Lenders usually keep the EMI fixed and adjust the tenure, or vice versa.
- You make a part-prepayment, which reduces the outstanding and can lower either your EMI or your tenure.
For floating-rate products, understand how resets work; our guide on fixed vs floating interest rates explains this in detail.
Quick Tips to Reduce Your Interest Burden
- Prepay early. Because interest is front-loaded, a lump sum in year 1 saves far more than the same amount in year 4.
- Choose a shorter tenure if your cash flow allows.
- Negotiate the rate. Even 0.5% lower meaningfully cuts total interest on a large loan.
- Improve your CIBIL score before applying to qualify for lower rates; check yours with our free CIBIL score tool.
Key Takeaways
- EMI = P · r · (1 + r)^n / ((1 + r)^n − 1), where r is the monthly rate and n is the number of months.
- Retail loans use reducing balance, so interest is charged only on the outstanding principal, which shrinks over time.
- A ₹5,00,000 loan at 12% for 3 years costs about ₹16,607 a month and ₹97,852 in total interest.
- Flat-rate loans are much costlier than they sound, always compare on a reducing-balance basis.
- A shorter tenure and early prepayment cut your total interest sharply.
LoanServ Editorial
Written by LoanServ's lending team — DSA advisors who help borrowers across AP, Telangana, Bangalore and Chennai compare loans daily. Information is educational and indicative; confirm terms with the lender.