How the EMI formula works
An EMI (equated monthly instalment) is a fixed payment that, over the whole tenure, repays the principal plus interest charged on the outstanding balance. The calculator uses the standard reducing-balance formula:
EMI = P × r × (1 + r)n / ((1 + r)n − 1)
Pis the loan amount.ris the monthly rate, which is the annual rate ÷ 12 ÷ 100. A 9% annual rate gives r = 0.0075.nis the number of monthly payments, which is the tenure in years × 12. The tenure field takes whole or decimal years, with a minimum of 1.
If the rate is 0, the tool simply divides the principal by the number of months. It then reports total payable as EMI × n and total interest as total payable − principal.
Worked example
For a loan of 10,00,000 at 9% for 20 years, r = 0.0075 and n = 240. The EMI works out to 8,997.26, so total payable is 8,997.26 × 240 = 21,59,342 and total interest is 11,59,342. In the first month the interest is 10,00,000 × 0.0075 = 7,500, so only about 1,497 of that first payment reduces the principal. Early payments are mostly interest, which is why prepaying early saves the most.
How tenure and rate change the result
| Loan 10,00,000 | EMI | Total interest |
|---|---|---|
| 9%, 10 years | 12,668 | 5,20,109 |
| 9%, 20 years | 8,997 | 11,59,342 |
| 9%, 25 years | 8,392 | 15,17,589 |
| 8%, 20 years | 8,364 | 10,07,456 |
Doubling the tenure from 10 to 20 years cuts the EMI by about 29% but more than doubles the interest. One percentage point of rate on the 20-year loan changes the EMI by about 633 a month and the lifetime interest by about 1.5 lakh.
Common mistakes and limits
- Flat rate versus reducing-balance rate. Some car and personal loans are quoted as a flat rate, where interest is charged on the full original principal. A 9% flat rate for 20 years would mean 18,00,000 of interest and an EMI of about 11,667, far above the figure here. Ask the lender which method is used. This calculator assumes reducing balance.
- Fees and insurance. Processing fees, insurance premiums and prepayment penalties are not included.
- Floating rates. If your rate is linked to a benchmark and resets, your EMI or tenure will change. The result is accurate only for a constant rate.
- First-payment timing. The formula assumes payments at the end of each month; a lender's actual schedule may differ slightly because of disbursal dates.
The calculator shows the EMI, total interest and total payable; it does not print a month-by-month schedule. For a yearly principal and interest breakdown, use the mortgage calculator, which uses the same payment formula. The guide on how EMI is calculated goes through the derivation, and the loan calculator is a general alternative.