Work out the equal monthly instalment on a reducing-balance loan from three numbers: the amount borrowed, the annual interest rate and the term in months.
This is for anyone comparing a quoted instalment with the arithmetic behind it, or testing how a different term or rate would change the total interest on a car loan, personal loan or mortgage. It assumes a fixed rate, equal monthly payments and interest charged on the reducing balance. All three figures use the same currency units, and nothing you type is sent to a server.
A mathematical estimate of a fixed-rate reducing-balance loan. It is general information, not financial advice, and it is not an offer or a quotation from any lender.
A reducing-balance loan charges interest each month on the balance still outstanding. The instalment stays the same, so its interest share falls as the balance falls and its principal share rises. The instalment that exactly clears the loan after n months is:
P is the amount borrowed, n is the term in whole months, and r is the monthly interest rate written as a decimal.
The monthly rate is the annual percentage divided by 1,200. A 9% annual rate becomes 9 ÷ 1,200 = 0.0075, which is 0.75% a month. This is simple proportional division, not a compounded conversion, which is how most lenders quote a nominal annual rate.
Total payment is the instalment multiplied by the number of months. Total interest is the total payment minus the amount borrowed, floored at zero so a rounding artefact cannot show as a negative figure. All three are displayed to two decimal places while the arithmetic keeps full precision, so adding up displayed numbers can differ from a displayed total by a fraction of a unit.
At a rate of zero the formula above divides by zero, so a separate branch splits the principal evenly: the instalment is P ÷ n. Entering 1,200 at 0% over 12 months returns an instalment of 100.00, a total payment of 1,200.00 and total interest of 0.00. That is correct for a genuinely interest-free loan, but few consumer offers are: a "0% finance" deal often carries a processing fee or a higher cash price, neither of which appears here.
Borrow 200,000 over 24 months at 9% a year. The monthly rate is 0.0075. The formula returns an instalment of 9,136.95, a total payment of 219,286.76 and total interest of 19,286.76.
The first two months show how the same instalment splits differently. Month one charges interest on the full 200,000: 200,000 × 0.0075 = 1,500.00. The rest of the instalment, 9,136.95 − 1,500.00 = 7,636.95, repays principal and leaves 192,363.05 outstanding. Month two charges interest on that smaller balance: 192,363.05 × 0.0075 = 1,442.72, so 7,694.23 goes to principal.
| Month | Opening balance | Interest | Principal | Closing balance |
|---|---|---|---|---|
| 1 | 200,000.00 | 1,500.00 | 7,636.95 | 192,363.05 |
| 2 | 192,363.05 | 1,442.72 | 7,694.23 | 184,668.83 |
Interest fell by 57.28 between the two months while principal rose by the same amount. Repeat that for 24 months and the closing balance reaches zero, which is what the formula solves for.
A longer term lowers the instalment but raises the total interest, because the balance stays large for longer. A higher rate raises both. All three rows below borrow 500,000.
| Annual rate | Term | Instalment | Total interest |
|---|---|---|---|
| 8.5% | 120 months | 6,199.28 | 243,914.13 |
| 8.5% | 240 months | 4,339.12 | 541,387.88 |
| 9.5% | 240 months | 4,660.66 | 618,557.43 |
Doubling the term from 120 to 240 months cuts the instalment by about 30% but more than doubles the interest. Adding one percentage point to the rate over 240 months costs 77,169.55 more in interest while the instalment rises by only 321.54 a month.
The result is the arithmetic of a fixed-rate reducing-balance loan and nothing more. A real repayment schedule from a lender will usually differ, for these reasons:
It also does not produce a full amortisation schedule, handle a grace or interest-only period, model part-prepayments, or compare offers on an annual percentage rate basis.
None in particular. The calculation is unit-free, so the output is in whatever currency you entered the loan amount in. Nothing is converted and no exchange rate is applied.
Probably both. Check the term in months first, then whether the quote includes insurance or a fee financed into the principal. If the inputs match and the gap is a few units, it is almost certainly the lender's rounding rule or its day-count convention, and the contract governs.
On a reducing-balance loan, yes, because interest is charged on the outstanding balance. This calculation cannot show the effect: it assumes the scheduled instalment is paid every month. Some agreements also charge a prepayment fee, which can offset part of the saving.
It returns an error rather than assuming zero. That is deliberate: an empty field is far more often an oversight than a genuinely interest-free loan, and silently treating it as 0% would understate the cost badly.