How EMI Is Calculated: Formula, Worked Example & Prepayment

EMI (Equated Monthly Instalment) is calculated with this formula:

EMI = P x r x (1 + r)^n / ((1 + r)^n - 1)

where P is the loan amount, r is the monthly interest rate (annual rate divided by 12, then by 100) and n is the number of months. For a ₹10 lakh loan at 9 percent a year for 5 years, the EMI is about ₹20,758.

You can try any amount, rate and tenure in our EMI calculator, which also shows the total interest and total amount you will pay.

Worked example in rupees

Loan: ₹10,00,000, interest 9 percent per year, tenure 5 years.

1. Monthly rate: r = 9 / 12 / 100 = 0.0075
2. Number of months: n = 5 x 12 = 60
3. (1 + r)^n: 1.0075^60 is about 1.5657
4. Top of the formula: 10,00,000 x 0.0075 x 1.5657 is about 11,743
5. Bottom of the formula: 1.5657 - 1 = 0.5657
6. EMI: 11,743 / 0.5657 is about ₹20,758

Over 60 months you pay about ₹12,45,500 in total, which means about ₹2,45,500 is interest.

Why early EMIs are mostly interest

Each month the bank first charges interest on the balance you still owe, and the rest of the EMI reduces that balance.

Take a ₹30 lakh home loan at 8.5 percent for 20 years. The EMI is about ₹26,035. In the first month:

• Interest = 30,00,000 x 8.5 / 12 / 100 = ₹21,250
• Principal repaid = 26,035 - 21,250 = about ₹4,785

So in month one, over 80 percent of the EMI is interest. After the first year you have paid about ₹3.12 lakh in EMIs, but the balance has only fallen to about ₹29.4 lakh. This is normal and is called amortisation. The split slowly reverses over the years.

The tenure trade-off

A longer tenure lowers the EMI but increases total interest, often by a lot.

₹10 lakh at 9 percent

₹30 lakh home loan at 8.5 percent

Going from 20 to 25 years cuts the EMI by under ₹1,900 a month but adds about ₹10 lakh of interest. Pick the shortest tenure whose EMI you can comfortably pay every month, with room for emergencies.

How prepayment changes the picture

A prepayment (part payment) goes straight to reducing the principal, so all future interest is calculated on a smaller balance. After a prepayment, lenders usually let you choose:

• Keep the EMI the same and reduce the tenure, or
• Keep the tenure the same and reduce the EMI.

Example

Same ₹30 lakh loan at 8.5 percent for 20 years. After 12 EMIs, you prepay ₹2 lakh.

• Reduce tenure (EMI stays ₹26,035): the remaining tenure falls from 228 months to about 194 months, roughly 34 EMIs fewer, and total interest falls by about ₹6.9 lakh.
• Reduce EMI (tenure stays 228 months): the EMI drops to about ₹24,264 and total interest falls by about ₹2 lakh.

Both help, but reducing the tenure saves far more because you keep paying a higher amount against a smaller balance. Reducing the EMI is useful if you need breathing room in your monthly budget.

These figures assume the interest rate stays the same. On floating-rate loans the rate can change, and banks usually adjust the tenure or EMI when it does.

Are there prepayment charges?

Under RBI's rules, banks, NBFCs and housing finance companies cannot charge prepayment or foreclosure fees on floating-rate loans taken by individuals for non-business purposes, such as most home loans. Fixed-rate loans, and some business and personal loans, can carry charges. These must be disclosed in your loan agreement, so read the sanction letter before you prepay.

Flat rate vs reducing balance

Some lenders, especially for consumer durables or vehicles, quote a flat rate. Interest on a flat rate is calculated on the full original amount for the whole tenure, even as you repay. A 10 percent flat rate is far more expensive than a 10 percent reducing-balance rate. The EMI formula above is for reducing balance, which is what home loans and most bank loans use. If a lender quotes a flat rate, ask for the equivalent reducing rate or the APR.

Common mistakes

• Using the annual rate directly. The formula needs the monthly rate: divide by 12 and by 100.
• Using years instead of months. n is the number of monthly instalments.
• Looking only at the EMI. A low EMI with a long tenure can cost lakhs more.
• Ignoring processing fees and insurance. These add to the real cost of the loan, and GST is usually charged on top of the processing fee. The GST calculator shows the final amount.
• Choosing "reduce EMI" by default after prepaying. Check how much more interest you would save by reducing tenure.
• Forgetting the rate can change. On a floating loan, recheck your schedule after every rate revision.

To compare loan offers side by side, run each one through the EMI calculator and look at total interest, not just the monthly figure. For quick checks like "what share of my salary is this EMI?", the percentage calculator helps.

Questions