EMI Formula Explained With a Worked Example
EMI = P x r x (1+r)^n divided by ((1+r)^n - 1), where P is the loan amount, r is the monthly interest rate, and n is the number of months. For Rs 5,00,000 at an assumed 9% annual rate over 5 years, the EMI works out to about Rs 10,379 a month.
The EMI formula is 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 and by 100), and n is the number of monthly instalments. For a Rs 5,00,000 loan at 9% annual interest over 5 years (60 months), the EMI works out to about Rs 10,379.
Breaking the formula into plain steps
Before touching the formula, convert your inputs into the units it expects: the loan amount in rupees, the interest rate as a monthly decimal, and the tenure in months rather than years.
- P: the principal, or the amount you actually borrow.
- r: the monthly rate. If the annual rate is 9%, r = 9 / 12 / 100 = 0.0075.
- n: the number of months. Five years is 5 x 12 = 60 months.
Skip the manual math and get the exact EMI, total interest and a month-by-month breakdown with the EMI calculator.
Worked example: Rs 5,00,000 at 9% for 5 years
Using the assumed values P = Rs 5,00,000, annual rate 9% and tenure 60 months:
| Input | Value |
|---|---|
| Principal (P) | Rs 5,00,000 |
| Annual interest rate | 9% (assumed for this example) |
| Monthly rate (r) | 0.0075 (0.75%) |
| Tenure (n) | 60 months |
| EMI | Rs 10,379 (rounded) |
| Total payment over 5 years | Rs 6,22,751 (rounded) |
| Total interest paid | Rs 1,22,751 (rounded) |
These figures use an assumed 9% annual rate purely to demonstrate the formula. Always use your own loan's actual sanctioned rate; even a 0.5% difference changes the EMI meaningfully over a multi-year tenure.
Month-by-month: interest vs principal
Every EMI is split between interest on the outstanding balance and repayment of principal, and this split shifts over the life of the loan even though the EMI itself stays fixed under a standard reducing-balance loan.
- Month 1: interest = outstanding balance x monthly rate = 5,00,000 x 0.0075 = Rs 3,750. Principal repaid = EMI - interest = 10,379 - 3,750 = Rs 6,629 (rounded).
- Month 2: the balance drops to about Rs 4,93,371. Interest for this month = 4,93,371 x 0.0075 = about Rs 3,700. Principal repaid = about Rs 6,679.
- Later months: as the balance keeps shrinking, the interest portion of each EMI keeps falling and the principal portion keeps rising, even though the EMI amount itself never changes.
This is why paying even one or two extra EMIs early in a loan, when interest is a larger share of each instalment, saves more total interest than making the same extra payment near the end of the tenure.
Why the formula has that exact shape
The (1+r)^n terms come from compounding the interest forward across every month of the loan and then spreading the total repayment evenly, so that the same fixed EMI covers a shrinking interest amount and a growing principal amount each month. This is standard reducing-balance EMI math used by Indian banks and NBFCs for home, car and personal loans.
Checking your own EMI by hand
- Confirm your P, r and n are in the right units before plugging into the formula: months, not years, for n, and a monthly decimal, not the annual percentage, for r.
- Round only at the final step; rounding r or intermediate values too early introduces small errors that compound over many months.
- Cross-check any hand calculation against the EMI calculator before relying on it for a real financial decision.
Reducing-balance EMI vs flat-rate interest
Almost all bank and NBFC loans in India use the reducing-balance method shown in this formula, where interest is charged only on the outstanding principal each month. Some older personal loans and a few informal lenders instead quote a flat rate, calculated once on the full original principal for the entire tenure, which sounds similar but works out far more expensive for the same quoted percentage, because you keep paying interest on money you have already repaid. If a lender quotes a rate that seems unusually low compared to others, always ask directly whether it is a flat rate or a reducing-balance rate before comparing it to another loan offer.
Using the same formula for tenure comparisons
Once you are comfortable with the formula, the most useful thing to do with it is compare tenures at the same rate, not just compute one EMI in isolation. A shorter tenure means a higher EMI but noticeably less total interest, since you are borrowing the lender's money for less time. A longer tenure lowers the monthly outgo but can roughly double or triple the total interest paid over the life of a large loan such as a home loan. Try the EMI calculator with two or three different tenures at the same rate to see this trade-off for yourself before deciding what monthly outgo is comfortable for your budget. A useful habit is to also calculate what happens if you make one or two extra payments a year toward the principal, since even small prepayments early in a long tenure can shorten it meaningfully because of how the interest-vs-principal split works.
This is a worked example for understanding the formula, not financial advice. Your actual EMI depends on the rate, processing fees and terms your lender offers; always confirm the final figures with your bank or NBFC before signing a loan agreement.
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Frequently asked questions
What do P, r and n stand for in the EMI formula?
P is the principal loan amount, r is the monthly interest rate (annual rate divided by 12 and by 100), and n is the total number of monthly instalments.
Why is the interest portion higher in early EMIs?
Interest is charged on the outstanding balance each month, which is highest at the start of the loan. As you repay principal, the balance falls, so the interest portion of each EMI falls too, even though the EMI amount stays fixed.
Does a higher interest rate change the EMI a lot?
Yes, even a small change in the annual rate changes the EMI and the total interest paid meaningfully over a multi-year loan, since the rate compounds every month.
Can I use this formula for any loan type?
Yes, the same reducing-balance EMI formula applies to home loans, car loans and personal loans in India, though some lenders may structure fees or add-on charges differently.
Is the worked example in this post my actual EMI?
No, it uses an assumed 9% rate purely to demonstrate the calculation. Use your own loan's sanctioned rate and tenure with the EMI calculator for your real numbers.
Sources
- Reserve Bank of India (checked 2026-09)
Rules and limits change. Always check the latest official notification or portal before you submit a form.