Читать книгу Fundamentals of Financial Instruments - Sunil K. Parameswaran - Страница 116

The amortization process refers to the process of repaying a loan by means of regular installment payments at periodic intervals. Each installment includes payment of interest on the principal outstanding at the start of the period and a partial repayment of the outstanding principal itself. In contrast, an ordinary loan entails the payment of interest at periodic intervals, and the repayment of principal in the form of a single lump-sum payment at maturity. In the case of an amortized loan, the installment payments form an annuity whose present value is equal to the original loan amount. An Amortization Schedule is a table that shows the division of each payment into a principal component and an interest component and displays the outstanding loan balance after each payment.

Take the case of a loan which is repaid in N installments of $A each. We will denote the original loan amount by L, and the periodic interest rate by r. Thus this is an annuity with a present value of L, which is repaid in N installments.

The interest component of the first installment

The principal component

The outstanding balance at the end of the first payment

In general, the interest component of the ‘t’th installment is

The principal component of the ‘t’th installment is

and the outstanding balance at the end of the ‘t’th payment is