An equated monthly instalment is the fixed payment that repays a loan, principal and interest together, over a set term. The term “equated” is the point: every instalment is the same amount, arranged so that the interest accruing each month is covered first and whatever remains reduces the balance. The loan is finished precisely on the final payment.
The design solves a problem lenders faced for centuries. Interest-only arrangements leave the borrower with the full principal to repay at the end; a constant payment smooths that obligation into something a household can budget for, at the cost of paying more interest overall than a faster repayment schedule would.
Because the instalment is level while the balance falls, the composition of each payment shifts steadily. Early instalments are mostly interest, late ones are almost entirely principal, and the crossover is invisible in a monthly statement that only shows one figure.
With P the loan amount, rate the nominal annual rate as a percentage and n the number of monthly payments:
monthly rate r = rate ÷ 1200
EMI = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
total paid = EMI × n total interest = total paid − P
The tool converts the term to months itself, so the years field is the loan's duration and the divisor 1200 is simply the annual percentage rate expressed as a monthly decimal. Term runs from 1 to 50 years and the rate field accepts up to 40 per cent.
One edge case matters in practice, because promotional finance is common: at an interest rate of exactly zero the annuity expression evaluates nought divided by nought. The tool handles that case directly, and an interest-free loan returns an instalment of P ÷ n — 500,000 over 240 months is 2,083.33 a month, with no interest at all. Enter 0 in the rate field and you will get that figure rather than an error.
500,000 at 4.5 per cent over 20 years:
The composition shift is worth seeing with real figures. Interest in the first month is 500,000 × 0.00375 = 1,875.00, leaving only 1,288.25 of the 3,163.25 to reduce the balance. By the final month the balance is down to about 3,151.43, interest is 11.82, and nearly the whole instalment is principal. The monthly payment never changed, but what it was doing changed completely.
Stretching the same loan to 25 years lowers the instalment to 2,779.16 — a saving of about 384 a month — and raises the total interest to 333,748.72, which is 74,568.68 more than the 20-year version. That is the central trade of loan selection: a lower monthly figure is bought with a larger total cost, and the exchange rate is rarely favourable.
P ÷ n directly. Promotional or subsidised zero-interest finance therefore works — but note that the total-paid figure then equals the principal, so the “interest saved” is the whole of what the rate column would otherwise have added.Because interest is charged on the balance for every month of the term, and at the start the balance is at its highest. Twenty years of charging roughly 4.5 per cent on a large outstanding sum accumulates to just over half the original loan. A shorter term charges for fewer months and on a faster-falling balance.
Yes, when the lower instalment is what makes the purchase affordable or preserves an emergency fund. Stretching a term is a liquidity decision, not an optimisation, and it should be made knowingly rather than by default.
Every extra unit goes entirely to principal, because the month's interest has already been covered. That shortens the term and removes the most expensive later years. This page will not compute it, but re-running with a smaller principal and a shorter term approximates the effect.
Not necessarily. The EMI formula uses a nominal monthly rate. An APR or effective annual rate folds in fees and the effect of intra-year compounding, which is why the APR on an offer is usually higher than the headline rate used for the instalment.
The Simple Interest page shows the flat-rate convention that makes car loans look cheaper than they are, which is the comparison worth making before signing. The Compound Interest page is the mirror image of this calculation, applied to money you are saving rather than repaying.