Workspace
The calculator's own fields, action and results arrive with the verified pack when you load it. Nothing is computed in this page.
Amortisation · level instalment
Level loan payment from principal, rate and term
Work out the level instalment on a mortgage or amortising loan from the principal, the annual rate, the term in years and payments per year.
Verified engine
What the engine returns
The instalment returned is the level amount that clears the balance exactly on the final payment. The intermediate figures show the periodic rate and the total payment count the calculation derived from your annual terms — check those first when an answer looks wrong, because that conversion is where hand-checks usually fail.
Inputs the result is built from
Principal
Annual rate
Term in years
Payments per year
How the result is derived
MethodThe annuity payment formula applied to a periodic rate derived from the quoted annual rate and the payment frequency, with the zero-rate case handled separately.
StandardStandard level-payment amortisation relation
GuardThe principal must be greater than zero — there is no instalment on nothing borrowed.
How the instalment moves with the rate
What the instalment is actually made of
A fully amortising loan is one where the instalment covers all the interest for the period and enough of the principal that the balance reaches exactly zero on the final payment. Nothing is left to refinance or settle at the end.
The quoted annual rate has to become a rate per payment period before it can be used, and the term in years has to become a count of payments. Dividing the annual rate by the number of payments per year is the convention this calculation uses — a nominal rate, not an effective one. It is what lenders quote and it is not the same as compounding the annual rate down.
Early instalments are mostly interest and late ones mostly principal, even though the instalment never changes. The instalment is level; its composition is not. That is why paying a little extra early moves the payoff date so much more than paying the same extra late.
A zero rate is handled as its own case rather than as a limit: with no interest, the instalment is the principal divided evenly across the payments. Treating that as a special case is deliberate — the general formula divides by the rate.
The annuity payment formula applied to a periodic rate derived from the quoted annual rate and the payment frequency, with the zero-rate case handled separately.
When this calculation is used
- Checking a quoted instalment against the principal, rate and term it was supposedly derived from.
- Comparing offers where the rate and the term differ, by reducing both to the instalment.
- Seeing what changing the payment frequency does at the same annual rate.
- Sizing an affordable borrowing amount by working backwards from an instalment you can meet.
Worked example
Take an ordinary amortising loan: a principal, a quoted annual rate, a term of several years and monthly instalments.
The instalment returned is the level amount that clears the balance exactly on the final payment. The intermediate figures show the periodic rate and the total payment count the calculation derived from your annual terms — check those first when an answer looks wrong, because that conversion is where hand-checks usually fail.
Now change only the payments per year, leaving the annual rate and the term alone. The instalment changes, and so does the total paid over the loan. That is the effect of a nominal rate convention, and it is a real difference between offers rather than an artefact.
What each input represents
Principal
The amount borrowed at the start — the balance the instalments have to clear. Fees rolled into the borrowing belong here; fees paid separately do not.
Annual rate
The nominal annual rate as a percentage, as quoted. It is divided by the number of payments per year to get the rate actually applied each period. Zero is permitted and gives an interest-free schedule.
Term in years
How long the loan runs, in years. Multiplied by the payments-per-year to get the total number of instalments. A term that is not a whole number of years is allowed.
Payments per year
How many instalments fall in a year — twelve for monthly, twenty-six for fortnightly, fifty-two for weekly. This drives both the periodic rate and the payment count, which is why changing it alone changes the instalment.
Assumptions and limits
- The rate is fixed for the whole term.
- Every instalment is the same amount and falls at the end of its period.
- The periodic rate is the annual rate divided by the payments per year — a nominal convention, not an effective annual rate compounded down.
- No fees, insurance, taxes or charges are included, so this is not an APR and not a total cost of credit.
- The balance reaches exactly zero on the final payment; there is no balloon or residual.
What the guards protect against
- The principal must be greater than zero — there is no instalment on nothing borrowed.
- The term must be greater than zero, and the payments per year must be at least one, so the payment count is a real count.
- The annual rate is bounded to a realistic range. A rate outside it is refused rather than answered, because the result would not describe any lending arrangement.
Provenance
Standard level-payment amortisation relation
The annuity payment formula applied to a periodic rate derived from the quoted annual rate and the payment frequency, with the zero-rate case handled separately.
Educational reference, not financial advice, and not an APR or total-cost-of-credit figure. The signed pack carries its own citation; the page reports the verification state of the release it mounted rather than asserting one.