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EMI formula explained, with a worked example
EMI = P × r × (1 + r)n ÷ ((1 + r)n − 1), where P is the loan, r the monthly rate and n the number of months. A ₹10 lakh loan at 10% a year for 10 years has an EMI of ₹13,215.07.
The formula
EMI = P × r × (1 + r)n ÷ ((1 + r)n − 1)
- P: loan amount (principal)
- r: monthly interest rate = annual rate ÷ 12 ÷ 100
- n: number of monthly EMIs = years × 12
Worked example: ₹10 lakh at 10% for 10 years
P = 10,00,000 · r = 10 ÷ 12 ÷ 100 = 0.008333 · n = 120. EMI = ₹13,215.07. Over 120 months you pay ₹15,85,809 in all, so the interest is ₹5,85,809.
How each EMI splits (the EMI list)
Early EMIs are mostly interest; later ones are mostly principal. The first three months:
| Month | EMI | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | ₹13,215.07 | ₹8,333.33 | ₹4,881.74 | ₹9,95,118.26 |
| 2 | ₹13,215.07 | ₹8,292.65 | ₹4,922.42 | ₹9,90,195.84 |
| 3 | ₹13,215.07 | ₹8,251.63 | ₹4,963.44 | ₹9,85,232.40 |
Prepayments and rate changes
A part-payment cuts the balance, so you can either lower the EMI or finish sooner. A rate change resets r from that month. Calcsend handles both and shows the full year-by-year and month-by-month EMI list, which you can send to a client as a PDF.
Results are estimates. A lender's figures can differ slightly because of fees, dates and rounding.
Questions
What is the EMI for a ₹10 lakh loan at 10% for 10 years?
About ₹13,215.07 a month, with total interest of about ₹5,85,809.
Why is most of my early EMI interest?
Interest is charged on the outstanding balance, which is highest at the start. As the balance falls, more of each EMI goes to principal.