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Amortization and Sinking FundChapter 7
Sir Migo Mendoza
Basic Concepts in AmortizationLesson 7.1Sir Migo Mendoza
Do you know?
• One of the most important and most common applications of annuities in business is the repayment of interest-bearing debts:
1. Amortization; and
2. Sinking Funds.
Amortization• It is a financial arrangement whereby a lump-sum is incurred at compound interest now, such
as loan, and is liquidated or paid off or by a series of equal periodic payment for a specified amount of time (e.g. monthly, quarterly,
semiannually, annually, etc.)
Amortization of Loan• It is the repayment of a loan
by periodic payments, with the possible exception of the last payment, are equal in
size.
Note:• When the debt is paid on a series
of equal payments, pay the interest outstanding at the time the payments are made and also repay a part of the principal. As the principal gradually reduced
by periodic payments, the interest of the unpaid balance
decreases.
Amortization Period• It is the length of time
over which a loan is scheduled to be fully
repaid.
Amortization Schedule
• It is a list of several periods of payments showing the principal and the interest parts of those payments
and the outstanding balance (or principal) after
each payment is made.
Note:• After the two parties (lender and borrower) agreed on the amount of a loan, the rate of interest, and the repayment frequency, after of which the
amortization schedule will be established.
Note:• Majority of the financing
institutions provide the borrower with an
amortization schedule. The data on the amortization schedule are important to
the borrower for two reasons:
First:•the borrower
needs to know the total interest paid;
and
Second:•the borrower
needs the data if he/she is planning
paying off the loan early.
Computing the Present Value of an Amortization
Lesson 7.2Sir Migo Mendoza
Introduction:• With amortization, the original
amount of the loan (present value or obligation) is known; therefore we use the present
value formula for ordinary simple annuity.
Formula for Computing the Present
Value of an Amortization:
Note:• In our final computation, we will
include three significant decimal digits to generate a more
accurate result. Also, we will apply only the Ordinary Simple
Annuity.
Example 7.1• A loan of 7 quarterly
payments of P8,300.00 is to be made, to pay of a
loan at 10% compounded quarterly. Find the value of the loan and construct an
amortization schedule.
Answer:•The present
value of the loan is P52,699.942.
Question:•The example requested us to
construct an amortization
schedule, how can we do that?
Steps in Creating an Amortization Schedule
Lesson 7.2Sir Migo Mendoza
Step 1:•Build a strong
familiarization of the following variables
will be used in amortization schedule:
OPBI
•Outstanding Principal at Beginning of
Interval
POP
•Previous Outstanding
Principal
PRP
•Previous Repayment of Principal
IDEI
•Interest Due at the End of
Interval
RII
•Rate of Interest per
Interval
TPEI
•Total Payment of Principal at the End of Interval
RPEI
•Repayment of Principal
at the End of Interval
Step 2:•Construct an Amortization
Schedule Table with heading such as:
Columns• Column 1: Period
• Column 2: Outstanding Principal at the Beginning of Interval (OPBI)
• Column 3: Interest Due at the End of Interval (IDEI)
• Column 4: Total Payment at the End of the Interval (TPEI)
• Column 5: For Repayment of Principal at the End of Interval (RPEI)
The Amortization Schedule Table
Step 3:•Determine the value
of OPBI, IDEI, TPEI and RPEI for the first
period using the following formula:
Formula for Computing the
Outstanding Principal at the
Beginning of Interval (OPBI):
Formula for Computing the
Interest Due at the End of
Interval (IDEI):
Formula for Computing the
Total Payment at the End of
Interval (TPEI):
Formula for Computing the
Repayment of Principal at
the End of Interval (RPEI):
The Amortization Schedule Table
Step 4:•Compute for the OPBI, IDEI, TPEI, and RPEI for the next period up to the
nth period.
The Amortization Schedule Table
The Amortization Schedule Table
Computing the Periodic Payment of an Amortization
Lesson 7.3Sir Migo Mendoza
Introduction• Here, the formula for finding the
periodic payment for ordinary simple annuity given the present value will
be used to determine the periodic payment of an ordinary simple
annuity in amortization problem.
Formula Computing the
Periodic Payment of an
Amortization
Example 7.2• A Php30,600.00 loan at 15% compounded semiannually is to be amortized every 6 months for
3 years. Find the quarterly payment and construct an
amortization schedule.
Answer:•The amortization
payment is P6,519.174.
The Amortization Schedule Table
The Amortization Schedule Table
Basic Concepts in Sinking FundLesson 7.4
Sir Migo Mendoza
Introduction:• Annuities can also be applied in
business when a sum of money will be needed at some future
date, a good practice is to build up systematically a fund that will
equal the amount of money desired at the time it is needed.
Sinking Fund• A sinking fund is an interest-
earning account into which periodic payments are made
for the purpose of accumulating a specific
amount of money by a certain date or for the purpose of
saving for a future obligation.
Note:• The accumulated funds are typically used to acquire an asset requiring a substantial
capital expenditure, or to retire the principal amount of
a debt.
Note:• A sinking fund is also a
systematic means for a business or other organization
to accumulate funds for future project, or planned
capital expenditure like the replacement of equipment,
expansion of production facilities, or an acquisition.
Note:• The easiest sinking fund
arrangement requires equal periodic payments of a size
computed to accumulate the required amount of money by the
target date.
Note:• The sinking fund is
typically set up so that the interval between
contributions equals the compounding interval. The
periodic payments represent an ordinary
simple annuity.
Computing the Future Value of a Sinking Fund
Lesson 7.4Sir Migo Mendoza
Introduction• We will determine the future value of a sinking fund using the formula
for computing the future value of ordinary simple
annuity.
Note:
Note:• In our final computation,
we will include three significant decimal digits to generate a more accurate result. Also, we will apply only the Ordinary Simple
Annuity.
Example 7.3• Ms. Maia Dereguito invests
Php5,400.00 every 3 months at 16% compounded quarterly to accumulate
a fund. How much must the fund be in 1 year and 3 months, just after
the deposit due then is made? Construct a sinking fund schedule.
Answer:•The fund will accumulate to Php29,248.140.
Question:• In our example we are requested to construct a sinking fund schedule, how can we construct
that?
Steps in Constructing a Sinking Fund Schedule
Lesson 7.4Sir Migo Mendoza
Step 1:•Build a strong
familiarization of the following
variables will be used in sinking fund
schedule:
FBI
•Fund at the Beginning of
Interval
PBFEI
•Previous Balance in
Fund at the End of Interval
IRFEI
•Interest Received of Fund at the End
of Interval
RII
•Rate of Interest per
Interval
PFEI
•Payment of Fund at the End
of Interval
FEI
•Fund at the End of
Interval
Step 2:•Construct a Sinking Fund Schedule Table
with the following column headings:
Columns• Column 1: Payment Interval
• Column 2: In Fund at the Beginning of Interval (FBI)
• Column 3: Interest Received of Fund at the End of Interval (IRFEI)
• Column 4: Payment to Fund at the End of Interval (PFEI)
• Column 5: In Fund at the End of the Interval (FEI)
The Sinking Fund Schedule Table
Step 3:•Determine the
value of FBI, IRFEI, PFEI, and FEI for the first period
using the following formula:
Formula for Computing the
Fund at the Beginning of
Interval (FBI):
Formula for Computing the
Interest Received of Fund at the
End of Interval (IRFEI):
Formula for Computing the
Payment to Fund at the End of
Interval (PFEI):
Formula for Computing the In
Fund at the End of Interval
(FEI):
The Sinking Fund Schedule Table
Step 4:•Compute for the FBI, IRFEI, PFEI,
and FEI for the next period up to the nth payment interval.
The Sinking Fund Schedule Table
The Sinking Fund Schedule Table
Computing the Periodic Payment of a Sinking Fund
Lesson 7.5Sir Migo Mendoza
Introduction• Here, to calculate the value of
the periodic payment of a sinking fund we will do the
same method for finding the value of periodic payment of an ordinary simple annuity.
Formula Computing the
Periodic Payment of a Sinking
Fund
Example 7.4• The sum of Php14,000.00
will be needed at the end of 1 1/2 years. If money can
be invested at 12% quarterly, find the periodic payment and construct a
sinking fund schedule.
Answer:•The periodic
payment is P2,164.365.
The Sinking Fund Schedule Table
The Sinking Fund Schedule Table
Let’s PracticeLesson 7.5
Sir Migo Mendoza
Direction: Solve the following.1. Doctor Mike borrows a certain sum that bears
interest at 14% compounded quarterly for 2 years. He agrees to pay Php825.00 at the end of every 3 months to discharge his debt. Find the original debt and construct the amortization schedule.
2. Jeron Alvin Teng deposits Php5,880.00 in a commercial bank every month, in order to accumulate at the end of 6 months on educational fund for his eldest brother Jeric Allen Teng. What is the final amount in the fund if it is invested at 12% compounded monthly? Construct a sinking fund schedule.
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