Loan Calculator (EMI)

Every fixed-rate instalment loan uses one formula. The monthly payment is P·r·(1+r)ⁿ ÷ ((1+r)ⁿ − 1), where P is the amount borrowed, n is the number of monthly payments, and r is the monthly interest rate — the annual rate divided by twelve and then by a hundred.

That formula answers a specific question: what single fixed amount, paid every month for n months, exactly clears the debt including the interest that accrues along the way? Because interest is charged on whatever is still outstanding, the answer cannot be found by simple division. Early on the balance is large, so most of the payment is interest; as the balance falls, more of the same payment reaches the principal. The payment is constant, the split inside it is not.

A 6% annual rate becomes 0.5% per month here, which is how lenders quote and compute instalment loans in practice. Note that this is not the same thing as APR: APR is a disclosure figure that folds in fees, and it is deliberately designed to be comparable across offers. Two loans with the same nominal rate can carry different APRs, and the payment you actually make is driven by the nominal rate.

Interest-free loans are handled as the special case they are: with r at zero the formula divides by zero, so the balance is simply spread evenly across the term.

Take $240,000 borrowed at 6% over 30 years — 360 monthly payments. The formula gives a payment of $1,438.92, and the arithmetic over the full term is worth seeing laid out:

The total interest is the number most people have never seen. Borrowing $240,000 costs $278,011.65 in interest — you repay more than twice what you took. That is not a bad deal or a trick; it is simply what thirty years of compounding at 6% costs, and it is the figure worth knowing before signing rather than after.

The schedule the calculator prints shows every one of those 360 rows. It is the part lenders rarely present up front, and it is where the shape of the loan becomes obvious.

In the example above, the very first payment of $1,438.92 splits into $1,200.00 of interest and $238.92 of principal. Eighty-three per cent of it does nothing to reduce what you owe.

After a full year — twelve payments totalling $17,267.06 — only $2,947.23 has come off the balance. You have paid over seventeen thousand dollars and reduced the debt by under three. This surprises people, and it is the single most useful thing an amortization schedule teaches.

It follows directly from charging interest on the outstanding balance. At the start the balance is at its maximum, so the interest portion is at its maximum too. Every payment shifts the ratio slightly, but the shift is gradual. On this loan the principal portion does not exceed the interest portion until month 223 — year nineteen of thirty. For the first two thirds of the loan, most of what you pay is rent on the money.

Two practical consequences fall out of this. First, overpaying early is disproportionately powerful: an extra payment in year one removes principal that would otherwise have accrued interest for twenty-nine more years, whereas the same payment in year twenty-five saves comparatively little. Second, selling or refinancing early means you have built far less equity than the amount you have paid would suggest.

It also explains why the term matters more than most borrowers expect. The same $240,000 at 6% over fifteen years costs $2,025.26 a month rather than $1,438.92 — but the total interest falls from $278,011.65 to $124,546.15. An extra $586 a month saves $153,465 over the life of the loan.

It computes principal and interest, and nothing else. Real loan agreements commonly add origination or arrangement fees, and depending on the loan type may require insurance — payment protection, or on a mortgage the taxes and hazard insurance a lender collects alongside the payment. None of that is in the figure here, so treat this as the core cost rather than the whole cost.

It assumes the rate is fixed for the whole term. On a variable or tracker product the payment changes when the rate does, and on a fixed-then-variable deal the calculator only describes the fixed period. Model the reversion rate separately to see what happens afterwards.

It assumes payments are monthly and on schedule, with no overpayments, holidays or missed instalments. Fortnightly or weekly schedules, common in some markets, produce a slightly different total because interest accrues over shorter periods.

Small rounding differences from your lender's paperwork are normal — institutions differ in day-count conventions and in how they round each instalment, and here the final payment absorbs the accumulated rounding so the balance closes at exactly zero. The figures are accurate for comparing offers, and they are not a contractual quote. This is general information, not financial advice; confirm the exact numbers with the lender before committing.