The repayment schedule of a constant-annuity loan, in formulas
For a constant-annuity loan, Fiplan calculates a fixed monthly instalment, then, instalment after instalment, the interest on the outstanding principal and the principal repaid. Everything is calculated in whole cents, and the last instalment repays exactly the remaining principal.
Notation
- the amount borrowed (the principal)
- the annual rate, in per cent
- the periodic rate (monthly for monthly instalments)
- the number of instalments
- the constant monthly instalment (principal + interest)
- the outstanding principal after instalment , with
- the interest in instalment
- the principal repaid by instalment
- rounding to the cent, with half a cent rounded up
The monthly instalment
The monthly instalment is calculated without any intermediate rounding, then rounded only once.
Each instalment
(4): the last instalment repays all the outstanding principal; the principal repaid therefore adds up to exactly the amount borrowed, and the last instalment may differ from the others by a few cents. (6): a first instalment requested in the month of drawdown, or earlier, is moved to the following month — a loan is not repaid before it exists.
Numerical application · Boulangerie Dupont's loan
A loan of €40,000.00 at 4.5% over 5 years, drawn down in January 2027, repaid in monthly instalments.
The first instalment falls in February 2027, the month after drawdown:
The last instalment, in January 2032, repays the remaining €743.00, with €2.79 of interest: €745.79 instead of €745.72.
| Financial year | Instalments | Interest | Principal | Outstanding principal at 31 December |
|---|---|---|---|---|
| 2027 | 11 | 1,525.74 | 6,677.18 | 33,322.82 |
| 2028 | 12 | 1,343.95 | 7,604.69 | 25,718.13 |
| 2029 | 12 | 994.60 | 7,954.04 | 17,764.09 |
Over the full term, interest totals €4,743.27.
The journal entry
| Side | Account | Description | Amount |
|---|---|---|---|
| Debit | 550000 | Credit institutions — Current accounts | 40,000.00 |
| Credit | 173000 | Credit institutions — Debts on account | 40,000.00 |
| Side | Account | Description | Amount |
|---|---|---|---|
| Debit | 173000 | Credit institutions — Debts on account | 595.72 |
| Debit | 650000 | Debt charges — Interest, commissions and charges on debts | 150.00 |
| Credit | 550000 | Credit institutions — Current accounts | 745.72 |
| Side | Account | Description | Amount |
|---|---|---|---|
| Debit | 173000 | Credit institutions — Debts on account | 7,604.69 |
| Credit | 423000 | Amounts payable after more than one year falling due within one year — Credit institutions | 7,604.69 |
The principal comes from the repayment schedule, which the journal builds itself from the terms of the loan; the interest comes from the loan's companion line (650000), created at data entry with the same amounts (€1,525.74 in 2027). At year-end, the principal that will be repaid within twelve months — that of 2028, €7,604.69 — is moved to debt due within one year; the entry is reversed the following month.
Try it yourself
Change the loan: formulas (1) to (6) are recalculated
Drawdown in January 2027, monthly instalments, a plan from 2027 to 2029. The block calls echeancierEmprunt, the function behind the screen preview, which calls construireEcheancierCapital, the journal's function.
Source
Minimum standard chart of accounts (plan comptable minimum normalisé / minimumindeling van een algemeen rekeningenstelsel): accounts 173 (credit institutions, more than one year), 423 (debts payable after more than one year falling due within the year) and 650 (debt charges); reclassifying the portion falling due within the year follows from the format of the annual accounts (the Royal Decree implementing the Companies and Associations Code, CSA / WVV).
Fiplan conventions, declared in the code (echeancier-financement.ts): the constant-annuity formula, rounding of the monthly instalment and of each interest amount to the cent (half a cent up), the last instalment that clears the loan, the first instalment no earlier than the month after drawdown. The bank's loan agreement prevails: compare the schedule with the bank's repayment table.