How is an EMI (equated monthly instalment) calculated?
Short answer
An EMI is a fixed monthly payment that repays a loan’s principal and interest over its term. It is calculated from the loan amount, the monthly interest rate and the number of monthly instalments.
Most relevant for: भारत (India)
The formula
For a reducing-balance loan, where interest is charged on the outstanding balance, the EMI is:
EMI = P x r x (1 + r)^n / ((1 + r)^n - 1)
P = loan amount, r = annual rate / 12 / 100 (monthly rate as a decimal), n = number of monthly instalmentsA worked example
Illustrative arithmetic: a loan of 1,000,000 at 10% a year for 10 years (n = 120, r = 0.10 / 12) has an EMI of about 13,215.07. The total paid is about 1,585,809, so the interest cost is about 585,809. A different rate or term gives a different result.
What each payment contains
Early instalments contain mostly interest because the outstanding balance is highest; later ones contain mostly principal. A schedule that lists interest, principal and balance per month is called an amortisation schedule. Part-payments reduce the balance, and so reduce either the term or the EMI, depending on the lender’s terms.
Flat versus reducing rate
A flat rate charges interest on the original principal for the whole term, so a quoted flat rate is much higher in effect than the same number on a reducing-balance basis. Compare loans on an annual percentage rate or effective rate basis, and check fees, since processing charges also affect the real cost.