How Loan EMI Is Calculated (Formula and Worked Example)
EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), where P is the loan amount, r is the yearly rate ÷ 12 ÷ 100, and n is the number of monthly instalments. For example, 500,000 at 10% a year for 5 years gives an EMI of about 10,624 and total interest of about 137,411. A longer tenure lowers the EMI but raises the total interest.
The EMI formula
EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)
- P = loan amount (principal)
- r = monthly interest rate = yearly rate ÷ 12 ÷ 100
- n = number of monthly instalments = years × 12
Worked example
Loan of 500,000 at 10% a year for 5 years:
- Monthly rate: r = 10 ÷ 12 ÷ 100 = 0.008333
- Number of instalments: n = 5 × 12 = 60
- (1 + r)ⁿ = 1.00833360 ≈ 1.6453
- EMI = 500,000 × 0.008333 × 1.6453 ÷ (1.6453 − 1) ≈ 10,624
- Total paid = 10,624 × 60 ≈ 637,411, so total interest ≈ 137,411
In the first month, interest is 500,000 × 0.008333 ≈ 4,167, so only about 6,457 of the EMI reduces the loan. Each month the interest part shrinks and the principal part grows.
How tenure changes the EMI
Same loan, same 10% rate, different lengths:
| Tenure | Monthly EMI | Total interest |
|---|---|---|
| 3 years | 16,134 | 80,809 |
| 5 years | 10,624 | 137,411 |
| 7 years | 8,301 | 197,250 |
Stretching the loan from 5 to 7 years cuts the EMI by about 2,300 a month but adds almost 60,000 of interest.
How the interest rate changes the EMI
| Yearly rate (5 years) | Monthly EMI | Total interest |
|---|---|---|
| 10% | 10,624 | 137,411 |
| 12% | 11,122 | 167,333 |
| 14% | 11,634 | 198,048 |
Every 2% adds roughly 30,000 of interest on this loan, which is why comparing offers matters.
The flat-rate trap
Some lenders quote a flat rate: interest on the full original amount for the whole term. At 10% flat for 5 years, interest is 500,000 × 10% × 5 = 250,000, and the EMI is 750,000 ÷ 60 = 12,500. That is the same cost as about 17.3% on a reducing balance. When you compare loans, always ask whether the rate is flat or reducing.
Prepayment: paying extra early
Using the same example, if you pay an extra 50,000 after 12 months and keep paying 10,624 a month, the loan ends about 6 months sooner and you pay roughly 22,700 less interest. Prepayments help most early in the loan, when the balance is highest. Check whether your lender charges a prepayment fee.
Try your own numbers
The EMI calculator applies this formula to any amount, rate and tenure, and shows a year-by-year repayment schedule. The figures here are rounded; your lender's statement may differ slightly because of fees and rounding.
Frequently asked questions
What does EMI stand for?
Equated monthly instalment: the same amount paid every month until the loan is repaid. Each payment covers that month's interest and repays part of the loan.
Why does most of my early EMI go to interest?
Interest is charged on the outstanding balance. At the start the balance is largest, so interest takes a bigger share; as the balance falls, more of each EMI repays the loan.
What is the difference between a flat rate and a reducing rate?
A flat rate charges interest on the full original amount for the whole term, even as you repay it. A reducing (diminishing) rate charges interest only on what you still owe. A 10% flat rate over 5 years costs about the same as a 17.3% reducing rate.
Does paying extra early really save money?
Yes. In the example in this guide, paying an extra 50,000 after one year and keeping the same EMI finishes the loan about 6 months earlier and saves roughly 22,700 in interest.
Is this formula used for car loans and personal loans too?
Yes, for any loan with a fixed rate on the reducing balance and equal monthly payments. Always ask your lender which method and which fees apply.