The ABC of Amortization

When we apply for loans or any financial agreement, we sign a contract with all the terms and conditions.  The loan amount, interest rate and payment period are the most important parts of this contract.  The loan needs to be repaid periodically, or, to be more technical, the loan needs to be amortized.  Amortization is the gradual reduction of a loan, through equal payments, in order to fully repay the loan and outstanding interest.  In this article I will explain how to understand each part of amortization, as well as how to understand what an amortization schedule means.

An amortization schedule is simply a table with the following information for each payment: payment number, payment amount (usually equal amounts), interest paid component, principle paid (capital) component and outstanding capital (or an ending balance).  We can use the following example to explain how an amortization schedule works.  Let’s assume we borrow $100 000 over a period of 24 months.  The annual effective interest rate is fixed at 12% and compounded monthly.  The amortization schedule for this loan, would be:

It is important to calculate the monthly installment first.  The formula is very simple:

where i is the interest rate per period and n is the number of periods.  In our example, the monthly installment would be:

To calculate the interest per period, we simply multiply the opening balance of that period with the interest rate per period.  In the first month, this would be $100 000 x 0.01 = $1 000.  Please note that the interest paid decreases every month.  This will be explained later.

The part of the monthly installment that goes towards decreasing the outstanding capital, is called “Principle Paid”.  It is simply the difference between the monthly installment and the amount of interest paid.  Because the interest paid decreases as the months go by, the amount that goes towards paying the outstanding capital increases every month.  This can be seen in the graph below:

Lastly, the end balance is simply the opening balance minus the principle paid during that period.  The end balance decreases every month until the loan is fully repaid.  This implies why the interest paid amount is getting smaller every month.  You are paying interest on a smaller amount of outstanding capital every month.  As time goes on, every installment will have a smaller interest paid component and will contribute more towards the principle and decreasing the outstanding capital balance.  At the end of the 24 months, the outstanding capital balance is zero and the loan is fully amortized.

It is important to be able to understand an amortization schedule.  Let’s take period 15 for example.  We know the installment is the same for every month.  However, the amount of interest that you have paid on an outstanding balance of $44 584.22 (balance at end of period 14), would be $445.85.  The amount that you have actually paid towards decreasing your loan, is $4 261.50.  At the end of period 15, your outstanding balance is the opening balance of period 15, minus the principle paid, which is $44 584.72 - $4 261.50 = $40 323.22.

Amortization can get more complex if you borrow money at a floating interest rate.  In the example above, we had a fixed interest rate throughout the entire period, which simplified the schedule.  These schedules are important for accounting purposes.  When compiling the balance sheet, the accountant needs to know the outstanding balance and also the total capital you have paid towards reducing the outstanding capital balance.  They also calculate the amount of interest you have paid during the financial year, for the income statement.  It is important to know the exact amount of interest that you have paid, as interest is tax deductible. Understanding the basics of an amortization schedule can help with understanding any loan and why it is important to do proper research before considering a specific loan.