Amortization
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+? −?
? = 100,000
0.025
1− 1+0.025 −8
A= P 13,946.73
Example
John borrowed P 400,000 at 6% interest compounded monthly for the additional working capital of his business. He settled his debt by making equal payments at the beginning of each month for 3 years. How much was his monthly payment?
Answer:
P=400,000
r=0.06
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+? −?
? = 100,000
0.025
1− 1+0.025 −8
A= P 13,946.73
Example
John borrowed P 400,000 at 6% interest compounded monthly for the additional working capital of his business. He settled his debt by making equal payments at the beginning of each month for 3 years. How much was his monthly payment?
Answer:
P=400,000
r=0.06