The short answer
An equated monthly instalment is the one fixed payment that clears the loan exactly over the agreed number of months, with interest charged each month on whatever principal is still outstanding. Early instalments are mostly interest; later ones are mostly principal.
The standard reducing-balance formula is EMI = 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 12 and by 100.
This page is general information about the arithmetic, not financial advice. It does not take account of your circumstances, and the figures a lender quotes will include costs the formula leaves out.
Where the formula comes from
Each month, the lender adds interest of r × outstanding balance, then your payment is deducted. The instalment has to be large enough that this process reaches exactly zero on the last month and no sooner. Setting the present value of n equal payments equal to the amount borrowed and solving for the payment gives the expression above; the term (1 + r)n is simply the growth factor over the whole term.
- Convert the rate. An annual rate of 9% becomes a monthly rate of 9 ÷ 1200 = 0.0075. Dividing by 1200 does both jobs at once: per cent to decimal, and per year to per month.
- Count the payments. Five years is 60 monthly payments. Use months, not years, throughout.
- Raise the growth factor. (1.0075)60 = 1.56568103.
- Apply the formula. 500,000 × 0.0075 × 1.56568103 ÷ (1.56568103 − 1) = 10,379.18 per month.
- Find the totals. 10,379.18 × 60 = 622,750.66 paid in all, of which 122,750.66 is interest.
The calculator on this site evaluates the same expression in a numerically stable form, which matters only at very small rates, where raising a number very close to 1 to a high power loses precision. The answer is identical to the formula above.
Worked example: 500,000 over 5 years at 9%
With P = 500,000, an annual rate of 9% and n = 60, the instalment is 10,379.18 per month. Each month's interest is 0.75% of the opening balance, and whatever is left of the instalment reduces the principal.
| Month | Opening balance | Instalment | Interest | Principal | Closing balance |
|---|---|---|---|---|---|
| 1 | 500,000.00 | 10,379.18 | 3,750.00 | 6,629.18 | 493,370.82 |
| 2 | 493,370.82 | 10,379.18 | 3,700.28 | 6,678.90 | 486,691.93 |
| 3 | 486,691.93 | 10,379.18 | 3,650.19 | 6,728.99 | 479,962.94 |
| 59 | 20,527.14 | 10,379.18 | 153.95 | 10,225.22 | 10,301.91 |
| 60 | 10,301.91 | 10,379.18 | 77.26 | 10,301.91 | 0.00 |
Month 1 is 36% interest; month 60 is under 1% interest. That shift is the whole point of a reducing-balance loan, and it explains why paying off a loan halfway through does not halve the interest you have already paid — you front-loaded it.
The rows are rounded for reading, so adding two columns can land a cent away from a third. Lenders work to a fixed number of decimals internally and adjust the final instalment slightly so the balance ends at exactly zero.
Two more cases
A zero-interest loan
When the rate is 0, the formula divides by zero and must be replaced by plain division: EMI = P ÷ n. For 500,000 over 60 months that is 8,333.33 a month, with total interest of 0. The calculator handles this as a separate branch, so entering 0 as the rate returns a usable answer rather than an error. This case is worth checking on any "0% finance" offer: if the monthly payment is not the price divided by the number of months, there is a fee or an inflated price somewhere.
A larger, longer loan
For 1,200,000 over 20 years at 8.5% annual, the monthly rate is 8.5 ÷ 1200 = 0.00708333 and n = 240. The instalment is 10,413.88, the total paid is 2,499,330.91, and the interest is 1,299,330.91 — slightly more than the sum borrowed. On long terms at moderate rates, interest routinely exceeds the principal.
What a longer term really costs
Stretching a loan lowers the monthly payment and raises the total, and the trade is far from proportional.
| Term | Payments | Monthly instalment | Total paid | Total interest |
|---|---|---|---|---|
| 5 years | 60 | 10,379.18 | 622,750.66 | 122,750.66 |
| 10 years | 120 | 6,333.79 | 760,054.64 | 260,054.64 |
| 15 years | 180 | 5,071.33 | 912,839.93 | 412,839.93 |
| 20 years | 240 | 4,498.63 | 1,079,671.15 | 579,671.15 |
Doubling the term from 5 to 10 years cuts the instalment by about 39% but more than doubles the interest. Going from 15 to 20 years saves 572.70 a month and adds 166,831.22 in interest. The instalment flattens out as the term grows, because at a long enough term you are paying little more than the monthly interest; the total, meanwhile, keeps climbing.
What the formula leaves out
- Fees and charges. Processing or arrangement fees, documentation charges, valuation fees and prepayment penalties are not in the instalment and are often deducted from the amount you receive.
- Insurance. Credit life, property or payment-protection cover attached to a loan is usually billed alongside the instalment or added to the principal.
- Rate changes. A floating rate changes the instalment, the term, or both, part way through. The formula assumes one fixed rate for the whole term.
- Taxes and statutory levies that some jurisdictions apply to interest or fees.
- Day-count and compounding conventions. A lender may compound daily, use an actual-days basis, or charge interest from the disbursal date rather than a clean month start, all of which move the figures slightly.
- The first period. If the loan is drawn mid-month, the first instalment often covers a longer or shorter stretch of interest than a full month.
- Extra payments. Overpaying reduces the balance, so subsequent interest falls — a path the fixed-instalment formula does not model.
Because of all this, a lender's quoted annual percentage rate is usually higher than the nominal rate used here. Treat an EMI estimate as the floor, and ask for the full cost in writing.
Common mistakes
- Using the annual rate as the monthly rate. Putting 9 instead of 0.0075 into the formula gives a wildly wrong answer. Divide by 1200.
- Mixing years and months. n is a count of payments, so 5 years is 60, not 5.
- Multiplying the principal by the rate and the years. That is simple interest, and it understates a reducing-balance loan's early interest while overstating its total at long terms. The two methods are not comparable.
- Comparing instalments instead of totals. A lower monthly figure usually means a longer term and more interest.
- Assuming half the term means half the interest. As the amortisation table shows, interest is concentrated at the start.
- Forgetting rounding. A published instalment is rounded, so twelve of them will not exactly match a year's amortisation computed from the unrounded figure.
Check it yourself
Enter 500000, a rate of 9 and a term of 60 months in the loan EMI calculator. It reports Monthly EMI: 10379.18 | Total Payment: 622750.66 | Total Interest: 122750.66, in whatever currency you are thinking in — the arithmetic is currency-neutral. Set the rate to 0 and the same term returns 8333.33 with no interest.
The inputs it accepts are a loan amount above zero, a rate of zero or more, and a whole number of months above zero; anything else returns a message instead of a figure. To rebuild the amortisation table yourself, take 0.75% of the opening balance as the interest, subtract that from 10,379.18 to get the principal portion, and carry the remainder forward. The scientific calculator will raise 1.0075 to the power of 60 if you want to check step 3 by hand.
Related tools and guides
Reviewed October 1, 2026. Calculation methods and corrections.