Amortization Schedule

An amortization schedule is a table that sets out every scheduled payment on a loan from the first instalment to the last. For each payment it shows the date, the total amount, how much goes towards interest, how much reduces the principal and the balance still owed afterwards. Lenders give schedules to borrowers of mortgages, car loans, personal loans and business term loans, and accountants use them to record interest expense and the split between short-term and long-term debt.

The schedule is the practical, payment-by-payment view of amortization, the gradual repayment of a debt over time. It applies to loans that are paid down in instalments, as opposed to those repaid in one sum at the end through a bullet repayment. In most consumer loans the payment is fixed and the interest share falls with each instalment, a pattern known as a level-payment or annuity-style schedule.

Think of an amortization schedule as a map of the journey from owing the full loan to owing nothing. Each line is one step: a payment is made, part of it pays the lender's charge for that month, and the rest knocks something off what is owed.

At the start, the amount owed is large, so the monthly interest charge is large too, and only a small part of each payment reduces the debt. As the debt shrinks, the interest charge shrinks with it, so more of the same payment goes towards the loan itself. Near the end almost the whole payment is reducing the debt. The schedule makes this visible, which helps borrowers see why paying a little extra early on saves a lot of interest.

For a loan with a fixed interest rate and equal payments, the payment per period is:

• $M$ is the payment made each period.
• $P$ is the principal, the amount borrowed.
• $r$ is the interest rate per period, written as a decimal (an annual rate divided by 12 for monthly payments).
• $n$ is the total number of payments.

Each row of the schedule is then built in three steps: interest equals the opening balance times $r$; principal repaid equals $M$ minus that interest; the closing balance equals the opening balance minus the principal repaid.

Take a loan of 10,000 at 12% a year, repaid monthly over one year. Here $r = 0.01$ and $n = 12$. The term $\left(1.01\right)^{12}$ is about 1.126825, so the payment is 10,000 times 0.01126825 divided by 0.126825, which is about 888.49. The first rows of the schedule are:

Total interest over the year comes to about 661.86. The final payment is a few cents lower because of rounding in earlier rows, which is normal in real schedules.

• Level payment. The same payment every period, as in the example. This is standard for mortgages and personal loans.
• Equal principal. The principal portion is fixed, so total payments start high and fall over time. This is common in business and project loans.
• Balloon. Payments are calculated as if the loan ran longer, leaving a large final sum, as described in balloon payments.
• Interest-only period. Only interest is paid for an initial period, after which amortization begins.
• Floating rate. When the rate is variable, the schedule is recalculated at each reset, so future rows are only estimates.

Borrowers use schedules to plan cash flow and to compare offers. The annual percentage rate on a consumer loan reflects the same payment stream plus fees. Business lenders use the schedule to test whether forecast cash flows can meet each payment, which is the basis of the debt service coverage ratio. Banks need the expected cash flows to estimate expected credit losses.

In accounting, loans held at amortised cost under IFRS 9 use the effective interest method, which spreads fees and costs over the loan's life. The resulting accounting schedule can differ slightly from the contractual payment table. The portion of principal due within 12 months is shown as a current liability on the balance sheet.

A schedule shows only what will happen if every payment is made on time and terms do not change. Prepayments, missed payments, rate resets, fees and compounding conventions all change the real outcome. Day-count rules also matter: a schedule that assumes equal months will differ slightly from one that charges interest on actual days elapsed.

• Consumer Financial Protection Bureau (CFPB)
• IFRS Foundation