How EMI Is Calculated: Formula, Example and Amortization Explained

The standard EMI formula used by every bank and NBFC in India is derived from the present value of an annuity:

EMI = P × r × (1 + r)^n / [(1 + r)^n − 1]

• P — Principal loan amount
• r — Monthly interest rate = Annual rate ÷ 12 ÷ 100
• n — Loan tenure in months

The (1 + r)^n term is what makes this a reducing-balance calculation, not a flat-rate one. Each month, interest is charged only on the outstanding principal, not the original amount — which is why EMI loans are cheaper than flat-rate products even when the stated rate looks the same.

Take a loan of ₹10,00,000 at an annual interest rate of 9% for a tenure of 10 years (120 months).

1. Monthly rate: r = 9 ÷ 12 ÷ 100 = 0.0075
2. Compute (1.0075)^120: this works out to approximately 2.4514
3. EMI = 10,00,000 × 0.0075 × 2.4514 ÷ (2.4514 − 1)
   = 10,00,000 × 0.018386 ÷ 1.4514
   = ₹12,668 per month (rounded)

Over 120 months you pay: 12,668 × 120 = ₹15,20,160. The total interest cost is therefore ₹5,20,160 — more than half the original principal. That figure is what most borrowers never calculate upfront.

Every EMI payment splits into two parts: interest for that month and principal repaid. In early months, most of your EMI goes to interest. In later months, most goes to principal. This is called an amortizing loan.

The split for month m works as follows:

• Interest component = Outstanding principal at start of month × monthly rate
• Principal component = EMI − Interest component
• Closing balance = Opening balance − Principal component

Here are the first four months of the ₹10 lakh / 9% / 10-year example:

Notice that in Month 1, ₹7,500 out of ₹12,668 (59%) is pure interest. The principal repaid grows slowly each month as the outstanding balance falls.

Both tenure and rate have a direct, nonlinear effect on your EMI and total interest outgo. The table below shows how the same ₹10 lakh loan changes across scenarios:

Key takeaways:

• Extending tenure from 10 to 15 years reduces your EMI by ₹2,525, but adds ₹3 lakh in interest.
• A 2% higher rate (9% vs 11%) over 10 years costs you an extra ₹1.33 lakh in interest despite only a ₹1,107 increase in monthly EMI.
• Short tenure is almost always cheaper in total cost. Choose longer tenure only when cash flow forces it.

Making a lump-sum prepayment directly reduces your outstanding principal, which cuts future interest calculated on that balance. The effect is most powerful early in the tenure when the outstanding balance — and therefore monthly interest — is highest.

Example: In Month 12 of the ₹10 lakh / 9% / 10-year loan, the outstanding balance is roughly ₹9,37,000. If you make a prepayment of ₹1,00,000 at this point, the new balance is ₹8,37,000. Keeping the same EMI, your remaining tenure shrinks by approximately 11 months, and you save roughly ₹55,000–₹60,000 in total interest.

A few practical rules on prepayment:

• Home loans (floating rate): RBI guidelines prohibit prepayment penalties for individual borrowers on floating-rate loans. You can prepay any amount, any time, at no cost.
• Home loans (fixed rate) and personal loans: Lenders may charge a foreclosure fee of 2–4% on the prepaid amount. Factor this into your calculation.
• Tax angle: For home loans, the principal component of EMI is eligible for deduction under Section 80C (up to ₹1.5 lakh/year) and interest under Section 24(b) (up to ₹2 lakh/year for self-occupied property). A large prepayment may reduce your future 24(b) deduction — worth checking with a tax advisor.

Some consumer lenders (particularly for vehicle or personal loans) quote a flat rate. This is not the same as the reducing-balance rate used in the EMI formula above.

Under a flat rate, interest is calculated on the original principal for every month, regardless of how much you have repaid. A flat rate of 7% is roughly equivalent to a reducing-balance rate of 12.5–13% — nearly double. Always ask whether the quoted rate is flat or reducing before signing.

The EMI formula above, and tools such as the UtilityApp EMI calculator, always use the reducing-balance method, which is the standard for all RBI-regulated scheduled bank loans in India.