How EMI Is Calculated, With a Full Worked Loan Example
Most people meet the EMI (equated monthly instalment) as a single number on a loan offer: pay this much every month until the loan is gone. It looks arbitrary, but it is the output of a short formula, and once you see how it works you can judge a loan offer far better than by looking at the monthly figure alone. This guide walks through the formula, one loan calculated by hand, and what changes when you alter the tenure, the rate, or pay part of the loan early.
The formula
For a loan repaid in equal monthly instalments on a reducing balance:
EMI = P × r × (1 + r)n / ((1 + r)n − 1)
- P is the amount borrowed (the principal).
- r is the monthly interest rate: the annual rate divided by 12, then by 100 to turn it into a decimal. A 10% annual rate gives r = 0.10 / 12 = 0.008333.
- n is the number of monthly payments: years multiplied by 12.
The formula is built so that the last payment brings the balance to exactly zero. Every instalment pays that month’s interest first, and whatever is left reduces the principal.
A worked example
Suppose you borrow 500,000 at 10% a year for 5 years. Then P = 500,000, r = 0.10 / 12 = 0.0083333, and n = 60.
- Compute (1 + r)n = (1.0083333)60 ≈ 1.645309.
- Numerator: P × r × 1.645309 = 500,000 × 0.0083333 × 1.645309 ≈ 6,855.45.
- Denominator: 1.645309 − 1 = 0.645309.
- EMI = 6,855.45 / 0.645309 ≈ 10,623.52.
Over 60 months you pay 10,623.52 × 60 = 637,411.34. Subtract the 500,000 you borrowed and the total interest is 137,411.34. (If you do this on a handheld calculator, small rounding differences in the last decimal places are normal.)
Where the first payment goes
In month one, interest is the full balance times the monthly rate: 500,000 × 0.0083333 = 4,166.67. The rest of the instalment, 10,623.52 − 4,166.67 = 6,456.85, reduces the principal. Next month the balance is a little lower, so the interest slice is a little smaller and the principal slice a little bigger. That is why early payments feel like they barely dent the loan: on a long loan the interest slice at the start is a large share of every instalment. An amortization schedule lays this out month by month.
How tenure changes the cost
A longer tenure lowers the monthly instalment, which is the part lenders emphasise, but the interest is charged for more months on a balance that falls more slowly. The same 500,000 at 10%:
| Tenure | EMI | Total paid | Total interest |
|---|---|---|---|
| 3 years (36 months) | 16,133.59 | 580,809.37 | 80,809.37 |
| 5 years (60 months) | 10,623.52 | 637,411.34 | 137,411.34 |
| 7 years (84 months) | 8,300.59 | 697,249.73 | 197,249.73 |
| 10 years (120 months) | 6,607.54 | 792,904.42 | 292,904.42 |
Stretching from 3 to 10 years cuts the instalment by roughly 59%, but the interest bill more than triples. Neither extreme is automatically right. The sensible question is: what is the shortest tenure whose instalment fits comfortably in my monthly budget, including a cushion for months when money is tight?
How the interest rate changes it
Holding the loan at 500,000 for 5 years:
| Annual rate | EMI | Total interest |
|---|---|---|
| 9% | 10,379.18 | 122,750.66 |
| 10% | 10,623.52 | 137,411.34 |
| 11% | 10,871.21 | 152,272.69 |
Each extra percentage point adds about 245 to the monthly instalment here and roughly 14,700 to 14,900 to the total cost. On a short loan, shaving a point matters less than on a long one, because the interest has fewer months to accumulate.
Reducing balance versus flat rate
Some lenders, especially on consumer and vehicle loans in some markets, quote a flat rate. With a flat rate, interest is calculated on the original principal for the whole period, even though you are repaying the loan as you go.
Take the same loan at a 10% flat rate for 5 years. Interest is 500,000 × 10% × 5 = 250,000, so you repay 750,000 in 60 instalments of 12,500. Compare that with the reducing-balance version above, where total interest was 137,411.34 at the same “10%”. Solving for the reducing-balance rate that produces a 12,500 instalment gives about 17.3% a year. A flat rate always understates the real cost, because you are paying interest on money you have already returned.
So when comparing offers, ask for the annual percentage rate or the effective reducing-balance rate, or compute it yourself. Two loans advertised at “8%” are not comparable if one is flat and the other is reducing.
What prepayment does
Because interest is charged on the outstanding balance, any lump sum you pay early removes all the future interest that balance would have generated. Using the 5-year loan again, suppose that after 12 instalments you pay an extra 100,000.
- After 12 payments the balance is about 418,865.94. After the 100,000 prepayment it is 318,865.94.
- Option A, keep the EMI at 10,623.52: the loan finishes after about 35 more months, which is 47 months in total instead of 60. Total interest over the life of the loan comes to about 95,976, a saving of roughly 41,435.
- Option B, keep the 48-month end date and let the EMI fall: the new EMI is about 8,087.26. Total interest is about 115,671, a saving of roughly 21,740.
Both options help; shortening the term saves more interest, while lowering the EMI gives you breathing room. The earlier in the loan you prepay, the more it saves. Before you do it, check the loan agreement for prepayment or foreclosure charges, and whether the lender lets you choose between reducing the tenure and reducing the EMI. Also consider whether the money is needed for your emergency fund first.
Things the EMI formula does not include
- Fees: processing fees, insurance, and documentation charges are usually separate and raise the real cost of borrowing.
- Floating rates: if your rate is linked to a benchmark and resets, the EMI or the tenure will change. The formula gives you the figure for the rate in force today.
- Payment timing: the standard formula assumes the first payment is due one full month after disbursal. Odd first periods, or loans with moratoriums, differ slightly.
- Rounding: lenders round each instalment, so the final payment may differ by a small amount.
A quick way to sanity-check an offer
- Multiply the EMI by the number of months and subtract the principal to see the total interest.
- Check that the quoted rate is reducing-balance, not flat.
- List every fee and add it to the cost.
- Try two or three tenures and pick the shortest one that you can afford with room to spare.
- Ask what happens if you prepay, and whether there is a charge.
The numbers in this guide are illustrations of the arithmetic, not a quote for any lender’s product. Your actual terms will depend on your loan agreement.
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Sources and further reading
This guide is general information, not professional medical, veterinary, tax, legal or financial advice. Figures in examples are illustrative; confirm current rules and rates with the official source.