Enter the loan, the EMI and the tenure and this finds the annual interest rate that makes the EMI formula give that EMI: 10,00,000 repaid at 21,247 a month for 5 years is about 10%. It is the EMI calculator run backwards.
The formula
The EMI formula
EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)What is solved
r is found so that the formula gives your EMI; P is the loan and n the number of monthsAnnual and effective rate
annual rate = r × 12 · effective annual rate = (1 + r)¹² − 1The monthly rate cannot be written out as a formula, so the calculator narrows it down by repeatedly halving the range it must lie in, until it is exact. At the rate it finds, the EMI formula returns your EMI, and the result shows that as a check.
Worked example
An EMI of exactly 10,000 on 1,20,000 over 12 months pays back only what was borrowed, so the rate is 0%.
When to use it, and the mistakes to avoid
Use it to check what rate a loan really carries, to compare an EMI offer with a quoted rate, or to find the rate on a loan you took out where you remember the EMI but not the rate.
- Counting the tenure wrong. Use the number of monthly instalments: 5 years is 60, not 5.
- Including fees in the EMI. Insurance and charges rolled in raise the rate above the one quoted.
- Mixing flat and reducing rates. A flat rate applies to the whole loan the whole time; this is reducing balance.
- Comparing EMIs over different tenures. Compare the rate, not the EMI.
- Using a rounded EMI and expecting a round rate. An EMI rounded to the paisa gives a rate a hair off the round one.
FAQ
How do I find the interest rate from an EMI?
You need the loan amount, the EMI and the number of monthly instalments. There is no simple formula for the rate, so it is found by trial: try a rate, work out the EMI it gives, and adjust until it matches. This calculator does that to the last digit. A loan of 10,00,000 repaid at 21,247 a month for 5 years is at about 10% a year.
Is the rate shown the same as the one my lender quoted?
It should be close, if the lender uses a reducing balance with monthly instalments, which is how most loans work. If the rate here is clearly higher than the quoted one, the EMI probably includes other charges such as insurance or fees, or the lender's rate is a flat rate, which is much lower than a reducing-balance rate for the same cost. Ask for the annual percentage rate.
What is the effective annual rate?
The cost of a year of monthly compounding: (1 + monthly rate)¹² − 1. A nominal rate of 10% a year is 0.8333% a month, and compounded 12 times it is 10.47% a year. The effective rate is always a little higher than the nominal one, and the gap grows with the rate.
Why does a longer tenure at the same EMI give a higher rate?
Because more money is repaid for the same loan. At 21,247 a month, 60 payments total 12.7 lakh on 10 lakh borrowed. Seventy-two payments would total 15.3 lakh, so the interest, and therefore the rate, must be higher for that EMI. If you are comparing offers, a lower EMI over a longer tenure is not cheaper unless the rate is also lower.
Why does it refuse some numbers?
Two cases have no sensible answer. If the instalments add up to less than the loan, the rate would be negative, which means a figure is wrong. And if the EMI is so big that it implies more than 100% interest a month, it is almost certainly a typing mistake. An EMI that adds up to exactly the loan is an interest-free loan, a rate of zero.