EMI formula explained: how to calculate equal monthly instalments
Quick answer
EMI = P x r x (1 + r)^n / ((1 + r)^n - 1), where P is the loan amount, r is the monthly interest rate (annual rate / 12 / 100), and n is the number of monthly payments.
- 1Convert the annual rate to a monthly rate: r = annual rate / 12 / 100.
- 2Raise (1 + r) to the power of the number of months, n.
- 3Apply the EMI formula with P, r and n.
- 4Multiply EMI by n for the total payable, then subtract P for total interest.
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EMI stands for equated monthly instalment: a fixed monthly payment that covers both interest and principal, sized so a reducing-balance loan is paid off exactly at the end of its tenure. The formula below is the standard reducing-balance amortisation calculation used for most consumer loans.
The same formula explains why a longer tenure lowers the monthly payment but increases the total interest paid - a trade-off worth checking with real numbers before choosing a tenure.
How each input changes the EMI
| If you... | EMI | Total interest |
|---|---|---|
| Borrow more | Higher | Higher |
| Get a lower rate | Lower | Lower |
| Choose a longer tenure | Lower | Higher |
| Make a bigger down payment | Lower | Lower |
Step by step
Find the monthly rate
Divide the annual rate by 12, then by 100.
Raise 1 + r to the power of n
n is the total number of monthly payments (years x 12).
Work out total interest
Total paid = EMI x n; total interest = total paid - P.
Tips
- Compare loans by total interest paid, not only by the EMI. A low EMI over a very long tenure can cost far more overall.
- Ask whether the quoted rate is flat or reducing balance. The formula above is for reducing balance. Flat-rate loans cost more than the headline rate suggests.
- Add fees (processing, insurance) to the total cost when comparing offers.
- Part-prepayments reduce the principal, so they cut interest even if the EMI stays the same.
Common problems
My bank's EMI differs slightly from the calculator.
Banks may round differently, charge fees, or use a different day-count or rate type. Use the calculator for a close estimate, and the bank's schedule for the exact figure.
I only know the EMI and want the rate.
You need to solve the formula for r, which has no simple closed form. Try different rates in the calculator until the EMI matches.
Examples
Short loan: 100,000 at 12% for 12 months
r = 0.01, n = 12, (1.01)^12 = 1.126825. EMI = 100,000 x 0.01 x 1.126825 / 0.126825 = 8,884.88. Total paid is 106,618.55, so total interest is 6,618.55.
Longer loan: 500,000 at 9% for 5 years (60 months)
r = 0.0075, n = 60. EMI = 10,379.18. Total paid is 622,750.66, so total interest is 122,750.66.
Frequently asked questions
- What does EMI stand for?
- Equated Monthly Instalment (also written Installment). It is the fixed amount you pay each month to repay a loan, covering both interest and principal.
- Does a longer tenure lower the EMI?
- Yes, the monthly payment falls, but you pay more total interest over the life of the loan.
- Is EMI the same as the interest rate?
- No. The EMI is the monthly payment amount. The interest rate is one of the inputs used to calculate it.
Related related tools
- EMI CalculatorWork out your equated monthly instalment, and how much of the total is interest.
- Loan CalculatorFind the monthly payment on a loan, and see how much of it is interest rather than principal.
- Compound Interest CalculatorSee how savings grow when interest earns interest - with or without regular contributions.