Amortization and Sinking Fund Chapter 7migomendoza.weebly.com/uploads/5/4/7/4/54745209/... · Amortization •It is a financial arrangement whereby a lump-sum is incurred at compound

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


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):


Interest Due at the End of

Interval (IDEI):


Total Payment at the End of

Interval (TPEI):


Repayment of Principal at

the End of Interval (RPEI):


Step 4:•Compute for the OPBI, IDEI, TPEI, and RPEI for the next period up to the

nth period.



Computing the Periodic Payment of an Amortization


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.



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


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


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:


Fund at the Beginning of

Interval (FBI):


Interest Received of Fund at the

End of Interval (IRFEI):


Payment to Fund at the End of

Interval (PFEI):

Formula for Computing the In

Fund at the End of Interval

(FEI):


Step 4:•Compute for the FBI, IRFEI, PFEI,

and FEI for the next period up to the nth payment interval.



Computing the Periodic Payment of a Sinking Fund


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.



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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Amortization and Sinking Fund Chapter 7migomendoza.weebly.com/uploads/5/4/7/4/54745209/... · Amortization •It is a financial arrangement whereby a lump-sum is incurred at compound