EMI Formula
The formula banks actually use to calculate your monthly loan installment, broken down variable by variable — plus a quick calculator if you just want the number, not the derivation.
| Symbol | Meaning | How to find it |
|---|---|---|
| P | Principal | The loan amount you're actually borrowing |
| r | Monthly interest rate | Annual rate ÷ 12 ÷ 100 (e.g. 8.5% annual → r = 0.0070833) |
| n | Number of installments | Loan tenure in months (a 20-year loan is n = 240) |
This is the reducing balance formula, used by essentially every bank, NBFC and mainstream lender for home, car, personal and education loans. It answers one question: what fixed monthly payment, over n months, at rate r, exactly clears a loan of P — with interest recalculated each month on whatever balance is left.
Quick Calculator
Plug your own numbers into the formula above — same engine as the full EMI calculator, including an amortization schedule.
Principal —
Interest —
| Year | Principal Paid | Interest Paid | Balance |
|---|
Special Case: 0% Interest
The formula above divides by zero when r = 0, so it mathematically breaks at an exact 0% rate. For a genuinely interest-free loan, the calculation simplifies to just splitting the principal evenly:
The Flat Rate Variant
The formula above is specifically the reducing balance EMI formula. A different, simpler formula exists for flat rate loans, which charge interest on the full original principal for the entire tenure instead of a shrinking balance:
The two formulas produce different EMIs for the identical P, rate and n — flat rate is always higher. See the reducing balance vs flat rate calculator linked below to compare both on your own numbers, including the flat rate's true equivalent reducing-balance rate.
Frequently Asked Questions
What is the EMI formula?
EMI = P × r × (1+r)^n / ((1+r)^n − 1), where P is the principal loan amount, r is the monthly interest rate (annual rate ÷ 12 ÷ 100), and n is the number of monthly installments.
How do I convert annual interest rate to r in the formula?
Divide the annual percentage rate by 12 (for months in a year), then by 100 (to convert from a percentage to a decimal). An 8.5% annual rate becomes r = 8.5 ÷ 12 ÷ 100 = 0.0070833.
What if the interest rate is 0%?
The standard formula divides by zero when r = 0, so it breaks down at exactly a 0% rate. For an interest-free loan, EMI simply equals the principal divided by the number of installments: EMI = P / n.
Is there a different formula for flat rate loans?
Yes — flat rate EMI is calculated as EMI = (P + P × annual rate × years) / n, which charges interest on the full original principal for the whole tenure instead of a shrinking balance. This produces a higher EMI than the reducing balance formula for the same stated rate.