Loan amortisation schedule

A loan amortisation schedule is a table showing how each instalment on an amortising loan splits between interest and principal, and how the outstanding balance falls to zero by the final payment.

ByHoang TruongUpdated July 5, 2026

See it move

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Rovira Transport borrows €10,000 at 6% interest, repaid in three annual instalments of €3,741.10. Interest starts at €600.00 in year one, then falls to €411.53 and €211.76 as the balance shrinks, so the principal portion rises each year — €3,141.10, then €3,329.57, then €3,529.34 — bringing the balance to zero.

Where it fits

TopicTime Value of MoneyCoreSubjectCorporate FinanceCore

The formula

LaTeX

PMT = \dfrac{P \times r}{1-(1+r)^{-n}}

Variables

$P M T$: Fixed periodic instalment (€)
$P$: Original loan principal (€)
$r$: Periodic interest rate (decimal)
$n$: Number of instalments (periods)

Gives the fixed periodic instalment that fully repays a loan of principal P over n periods at periodic rate r.

LaTeX

I_t = B_{t-1} \times r, \quad P_t = PMT - I_t

Variables

$I_{t}$: Interest portion of the instalment in period t (€)
$B_{t - 1}$: Outstanding balance at the start of period t (€)
$r$: Periodic interest rate (decimal)
$P M T$: Fixed periodic instalment (€)
$P_{t}$: Principal portion of the instalment in period t (€)

Splits each instalment into its interest and principal components using the balance outstanding at the start of that period.

Check yourself

PracticeCORE

Nordic Freight borrows €20,000 at 8% annual interest, repayable in three equal annual instalments of €7,760.67. What is the outstanding loan balance immediately after the first instalment is paid?

Select an answer to check your understanding.