An EMI (equated monthly instalment) is the fixed amount you pay every month on a reducing-balance loan. Banks will quote you a number. With one formula, you can check it yourself. To skip the arithmetic, use the EMI Calculator.
The formula
EMI = P × r × (1 + r)^n ───────────────── (1 + r)^n − 1
| Letter | Meaning | How to get it |
|---|---|---|
| P | principal, the amount borrowed | e.g. 1,000,000 |
| r | monthly interest rate, as a decimal | annual rate ÷ 12 ÷ 100 |
| n | number of monthly instalments | years × 12 |
The most common mistake is using the annual rate for r. A 12% annual rate is r = 0.01 per month, not 0.12.
Worked example
Loan of 1,000,000 (say NPR 10 lakh) at 12% a year for 5 years.
P = 1,000,000r = 12 ÷ 12 ÷ 100 = 0.01n = 5 × 12 = 60(1 + r)^n = 1.01^60 = 1.816697- Top:
1,000,000 × 0.01 × 1.816697 = 18,166.97 - Bottom:
1.816697 − 1 = 0.816697 - EMI = 18,166.97 ÷ 0.816697 = 22,244.45
Over 60 months you pay 22,244.45 × 60 = 1,334,667. Total interest: 334,667.
You'll need a calculator with a power key (xʸ) for step 4. In a spreadsheet, =PMT(12%/12, 60, -1000000) gives the same answer.
Where each payment goes
Every month, interest is charged on what you still owe. The rest of the EMI pays down the principal.
| Month | Opening balance | Interest (1%) | Principal | Closing balance |
|---|---|---|---|---|
| 1 | 1,000,000.00 | 10,000.00 | 12,244.45 | 987,755.55 |
| 2 | 987,755.55 | 9,877.56 | 12,366.89 | 975,388.66 |
| 3 | 975,388.66 | 9,753.89 | 12,490.56 | 962,898.10 |
The EMI stays the same, but the split shifts each month: less interest, more principal. That's why prepaying early saves far more interest than prepaying late.
How tenure changes the total
Same 1,000,000 at 12%:
| Tenure | EMI | Total interest |
|---|---|---|
| 3 years | 33,214 | 195,715 |
| 5 years | 22,244 | 334,667 |
| 7 years | 17,653 | 482,830 |
| 10 years | 14,347 | 721,651 |
Going from 5 to 10 years cuts the EMI by about a third and more than doubles the interest.
How the rate changes the EMI
Same 1,000,000 over 5 years:
| Annual rate | EMI |
|---|---|
| 10% | 21,247 |
| 12% | 22,244 |
| 14% | 23,268 |
Each 2 percentage points adds roughly 1,000 a month here, or about 60,000 over the loan. That's why it's worth negotiating the rate, not just the fee. (If "percentage points" vs "percent" is fuzzy, see Percent vs Percentage Points.)
Things the formula doesn't include
- Processing fees and insurance, which raise the real cost.
- Floating rates. Many loans, including most home loans in Nepal and India, are linked to a base rate that can change. When it does, the bank changes your EMI or your tenure.
- Flat-rate loans. Some vehicle and personal loans charge interest on the original amount for the whole term. The formula above doesn't apply, and the real rate is much higher. See Flat Rate vs Reducing Balance.
Quick checklist before you sign
- Is the rate reducing balance or flat?
- Is it fixed or floating, and what is it linked to?
- What are the processing fee and prepayment charges?
- Does your EMI calculation match the bank's within a rupee or two?