Amortization

Objectives
At the end of the discussion, students shall be able to:  Describe the nature of amortization  Find the size of each payment  Determine the outstanding liability  Describe amortization with irregular payment  Prepare an amortization schedule

Nature of Amortization
Amortization  Refers to the process of liquidating by installment the payments (at a regular interval) of a loan or debt, including the interest charges  By the process of amortization, the principal and the interests are reduced by a series of installment payments made either at the beginning or at the end of the payment interval  Implies that the amount regularly paid to discharge an obligation is of equal size Note: in finding the size of the periodic payment, one of the most important factors to consider is whether the loan is due now or later

 The concept of amortization is applicable if the loan or

financial obligation due now

Finding the Size of Each Payment
The size of the periodic payment to settle a debt is highly dependent on the time the payment is made.  For ordinary annuity ������ ������ = ������ 1 − 1 + ������ −������  For annuity due ������ ������ = ������ 1 − 1 + ������ −������ 1 + ������  For deferred annuity ������ 1 + ������ ������ ������ = ������ 1 − 1 + ������ −������

Example
The cash price of a shopping equipment was P 120,000. Alex bought it with a down payment P 20,000 and the balance was payable at the end of every quarter for two years. If money was worth 10% compounded quarterly, how much did Alex pay at the end of every quarter?
Given:

P= 100,000 f=4 t=2 r=0.10 A=?

Since the periodic payment is made at the end of the payment interval, the concept of ordinary annuity will apply

Answer:
 ������ =
������ ������ 1− 1+������ −������ 0.025 1− 1+0.025 −8

 ������ = 100,000

 A= P 13,946.73

Example
John borrowed P 400,000 at 6%