Calculating an EMI by Hand, Step by Step
Published 13 October 2026 · 6 min read · Clean EMI Editorial
You do not need to calculate an EMI by hand to take a loan, but doing it once shows where each rupee goes. It is also useful for checking a figure a lender quotes. The formula is manageable with an ordinary calculator if you follow the steps in order. This guide works through how to calculate EMI manually for a ₹5 lakh loan over five years at an illustrative 8.5% rate, which is not a bank quote, and sets out the rounding rules.
Part of the Home Loan guide series.
The formula and what each part means
The EMI is P × r × (1 + r)^n ÷ ((1 + r)^n − 1). P is the loan amount. r is the monthly interest rate, found by dividing the annual rate by 100 and then by 12. n is the number of monthly instalments, which is the tenure in years multiplied by 12.
The term (1 + r)^n is the one that needs care. It grows quickly with the tenure, so keep several decimal places in it until the last step.
Step by step for ₹5 lakh over 60 months
- Convert the rate. 8.5 ÷ 100 = 0.085, then 0.085 ÷ 12 = 0.0070833, kept to seven decimal places.
- Count the months. Five years × 12 = 60.
- Raise (1 + r) to the power 60. (1.0070833)^60 is about 1.527301, rounded to six decimal places.
- Multiply the principal, the rate and that result: ₹5,00,000 × 0.0070833 × 1.527301 = ₹5,409.19.
- Work out the denominator: 1.527301 − 1 = 0.527301.
- Divide: ₹5,409.19 ÷ 0.527301 = ₹10,258.27, which rounds to an EMI of ₹10,258 a month.
Rounding rules to keep in mind
Keep at least six decimal places in intermediate steps and round only the final answer. Rounding the monthly rate early, for example to 0.007, can change the answer noticeably on a long loan. A lender's schedule usually rounds the EMI to the nearest rupee and adjusts the last instalment so the balance clears, so a small gap between your figure and the schedule is normal.
Check the answer and the first month
Multiply the EMI by the number of months to get the total paid: ₹10,258 × 60 = ₹6,15,480. Subtract the principal to get the interest: ₹6,15,480 − ₹5,00,000 = ₹1,15,480.
The first month shows how the split works. Interest for the first month is ₹5,00,000 × 0.0070833 = about ₹3,542, so about ₹6,716 of the first EMI goes to principal. As the balance falls, the interest part shrinks each month. The guide to reading a loan amortisation schedule shows the full pattern. For the general home loan steps, see the home loan page, and for the bank's details, see Canara Bank.
Use the calculator, but know the method
A calculator is faster for everyday use, and the EMI calculator runs the same steps for any amount. Doing the arithmetic by hand once helps you spot a wrong input or an unrealistic figure. Whatever figure you use for planning, the bank's sanction letter and schedule of charges set the actual EMI, and the final decision rests with the lending bank.
Frequently Asked Questions
Will my hand calculation match the bank's EMI exactly?
It should be close. Small differences can come from rounding, the exact day count or a rate that changes after sanction. Compare with the bank's schedule.
Why is most of the first EMI interest?
Interest is charged on the outstanding balance, which is highest at the start of the loan. Each month, more of the fixed EMI goes to principal as the balance falls.
Do I need to calculate every EMI this way?
No. A calculator is quicker. The hand method is most useful for checking a figure once and understanding how the loan works.
Useful free tools
- Free Credit Analyzer — Upload your CIBIL report and see which loans you may be eligible for, with an indicative EMI.
- Check my Loan Eligibility — Answer a few questions and see how your application would be routed to a PSU bank.
- Home Loan Balance Transfer Calculator — Compare your current EMI with a lower-rate loan over the same remaining tenure.
- Credit Score Enhancer — Practical steps to improve your CIBIL score before you apply for a loan.
Ready to check your eligibility?
No fee to apply. CIBIL score of 700 or above required.