What is Amortization?
Amortization: The process of gradually paying off a debt over time through regular (usually monthly) payments, where each payment covers both the interest owed and a portion of the original amount borrowed (the principal).
When you take out a loan , whether for a house, a car, or university , you don't repay it all at once. Instead, you make equal payments at regular intervals until the debt reaches zero. This is amortization.
The key idea is that each payment does two jobs at once:
- Pays off the interest that has accumulated since the last payment
- Reduces the principal (the remaining balance you still owe)
The amortization process each period follows these steps:
- Calculate the interest owed on the current balance
- Subtract that interest from your fixed payment
- Apply the remainder to reduce the principal
- The new (lower) principal becomes the starting balance for the next period
Because the principal decreases with every payment, the interest charged each period also decreases. This means that over time, more of each payment goes towards the principal and less towards interest , even though your payment amount stays the same.
Think of it like draining a bathtub that has a slow drip refilling it. The "drip" is the interest being added, and your payment is you scooping water out. At first, much of your scooping just keeps up with the drip. But as the water level (principal) drops, the drip slows too, and your scooping makes a bigger and bigger dent each time.
The Loan Payment Formula
To find the fixed regular payment required to fully repay a loan, we use the loan payment formula:
Where:
- = principal (the amount borrowed)
- = interest rate per payment period (e.g. annual rate ÷ 12 for monthly payments)
- = total number of payments
A very common mistake is using the annual interest rate directly in this formula. You must convert it to a rate per period. For monthly payments, divide the annual rate by 12. For quarterly payments, divide by 4, and so on.
This formula is derived from the present value of an annuity , the idea that a series of future payments has a calculable value today. You are not required to memorise or derive this formula for the IB exam.
The loan payment formula is NOT provided in the IB formula booklet. You must either memorise it or , more reliably in exam conditions , use your GDC's TVM (Time Value of Money) solver, which is the expected approach for IB Math AI SL.
The formula always gives a positive payment amount. In GDC solvers, payment (PMT) is often shown as negative because it represents money leaving your account. Keep sign conventions consistent when using technology.
