Mathematics of Finance: Intended Learning Outcomes

ILOCOS SUR POLYTECHNIC STATE COLLEGE
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Mathematics of Finance
Intended Learning Outcomes

At the end of the chapter, the students are expected to:
1. Use mathematical concepts and tools in different financial transactions such
as investment on properties, savings and business,.
2. Support the use of mathematics in various aspects and endeavours in life,
3. Demonstrate appreciation on the importance of mathematics as a tool to
various financial applications; and,
4. Solve real life problems involving various financial transactions.
SCOPE AND SEQUENCE
5-1 Simple and Compound Interest

5-2 Credit Cards and Consumer Loans
5-3 Stocks, Bonds and Mutual Funds
5-4 Home Ownership
OVERVIEW (Time allotted for this chapter is 10 hours)
This chapter deals on how mathematics is used in finance. This chapter begins with a
discussion on how interests are computed in various financial transactions. Understanding on
this would entail wise decision – making. The chapter also discusses computations on monthly
amortization and pay – off amount on different acquisition such as appliance loan, car loan and
housing loan.
Specifically, this chapter deals with simple and compound interests, the use of credit
cards on the different investments thru stocks, bonds and mutual funds. Finally, this chapter
also discusses home ownership.
ESSENTIAL QUESTIONS
1. What makes mathematics an important tool in finance?

2. How can students determine the monthly amortization and pay – off amount on various
investments?
Course Code: GenEd103

Descriptive Title: Mathematics in the Modern World Instructor: Mrs. Joy C. Corres
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3. What are the ways to invest money and how do we evaluate a sound investment?
PERFORMANCE TASK
You are a financial adviser. Your work is to help individuals manage their finances by
providing them professional advice.
Mr. Raras, a retired employee, comes to your office to seek opinion or suggestion
because he wanted to ensure that his retirement benefits amounting to Php5, 000,000 would be
used wisely. Apart from this, Mr Raras receives a monthly pension of Php10, 000. However,
his family’s expense amount to Php15, 000 monthly. As such, Mr Raras want to find ways in
order for his monthly income to be higher than his monthly expenses.
In addition, Mr Raras wants to spend his retirement benefits to purchase a two-bedroom

unit for his children and a car for family use.
As financial adviser, you are to present your recommendations to Mr. Raras. The
recommendation should include a breakdown on how Mr Raras will use his retirement benefits
and a financial report in the next five years.
Below is the scoring rubrics or how will you be rated. Your report should be encoded.
SCORING RUBRICS
Criteria Excellent:4 Proficient:3 Progressing:2 Beginning:1
Practicality of Recommendatio Recommendatio Recommendatio Recommendati

Recommendatio ns suggest ns suggest good ns suggest good on suggest
ns wisest use of use of retirement use of retirement unwise use of
retirement benefits and benefits and retirement
benefits and takes into takes into benefits
takes into consideration all consideration
consideration all needs of Mr almost all needs
needs of Mr Raras of Mr Raras
Raras
Accuracy of All Most Some Most
computations computations computations computations computations
are accurate and are accurate and are accurate and are inaccurate
accompanied accompanied accompanied and are not
with logical with logical with logical accompanied
solutions and solutions solutions with solutions
explanations

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Authenticity of The data used The data used Some of the data Data are not
data are authentic are authentic. used are not authentic.
and updated. Data are taken authentic.
Data are taken from reliable
from reliable sources.
sources.
LESSON 5.1 Simple and Compound Interest

When you deposit money in a bank, either in a savings or current account, you are
permitting the bank to use your money. The bank has the right to lend the deposited amount to
their other costumers for different purposes such as housing loans, car loans, etc. The bank in
return, pays you a certain amount for the privilege of using your money. The amount paid to
you is called interest.
Definition 5.1: I nterest
 It refers to the fee paid on the borrowed money.
An interest may be either be simple or compound.
Definition 5.21: Simple Interest
 It is characterized by a fixed amount earned or paid over time. This means that only the
principal amount earns an interest.
The simple interest is calculated using the formula

I = PRT
where I is the interest, P is the principal amount, R is the interest rate and T is
the time period.
The amount deposited in a bank or borrowed from a bank is called the principal. The
amount of interest paid is usually given as a percent of the principal. The percent used to
determine the amount of interest is called the interest rates, unless stated otherwise. Since

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interest rates are generally given as percent, be sure to convert the interest rate as a decimal
when you do the computations.
EXAMPLE 5.1:
Calculate the simple interest earned in 6 months on a deposit of Php5,000 if the
interest rate is 5%.
6 1
Solution: P = 5000, R = 5% = 0.05, and T = =
12 2
I = PRT
1
I = 5000(0.05) ( 2 )
I = 125
The simple interest earned is Php125.
EXAMPLE 5.2:
Calculate the simple interest due on a 4 – month loan of Php10,000 if the interest rate
is 8%.
Solution: P = 10000, R = 8% = 0.08. Because the interest rate is an annual rate, the time must
be measured in years:
4 𝑚𝑜𝑛𝑡ℎ 𝑠 4 𝑚𝑜𝑛𝑡ℎ𝑠 4 1
T= = = =
1 𝑦𝑒𝑎𝑟 12 𝑚𝑜𝑛𝑡ℎ𝑠 12 3
Substitute these values to the simple interest formula.

1
I = PRT = 10,000 (0.08) ( ) = 266.67
3
The simple interest due is Php 266.67
EXAMPLE 5.3 :
Determine the simple interest rate if you earned Php3, 000 for depositing Php120, 000
in 10 months?
Solution: Using the simple interest rate formula I = PRT, the desired formula for the interest
rate is
𝐼
R=
𝑃𝑇
Substituting the given values to the interest rate formula

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3000 3
𝑅= 10 = = 0.03 = 3%
(120000 )( ) 100
12
Thus, the simple interest rate is 3%.
Maturity Value and Future Value
Definition 5.3: Maturity Value
 The total amount a borrower needs to pay its lender is called maturity value. The
maturity value is the sum of the principal amount and the interest.
Definition 5.3: Fut ure Value
 The future value is the sum of the principal amount and the interest when it is used for
investment.
The sum is calculated using the following maturity value or future value formula for
simple interest.
A = P+ I
where A is the amount after the interest P is the principal amount and I is the interest.
EXAMPLE 5.4
Jay Santos applied for a multi – purpose loan. If he intends to pay in 1 year the
Php200,000 loaned amount at 8% interest rate, what is his maturity value?
Solution:
Step 1: Solve for the interest.

I = PRT = (200000)(0.08)(1) = 16000
Step 2. Substitute these values to the maturity value formula
A = P + I = 200,000 + 16,000 = 216,000
Hence, the maturity value is Php216,000.

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EXAMPLE 5.5
Emmerson paid Php10,250 from Nueva Sgovia lending Firm for the Php10,000 he
borrowed with an interest rate of 5%. How long did it take him to pay the said amount?
Solution:
Step 1. Using the maturity value formula A = P + I, the desired interest can be obtained.
I = A – P = 10,250 – 10,000 = 250
Step 2. Using the simple interest rate formula I = PRT, derive a formula for the period of time
T.
𝐼 250 1
T= = = 𝑦𝑒𝑎𝑟 or 6 months
𝑃𝑅 (10,000)(0.05 ) 2
Therefore, Emmerson paid his loan in 6 months.
Compound Interest
For loans of 1 year or less, simple interest is generally used. However, for loans of more
than a year, compound interest is generally used. In simple interest, only the principal amount
earns an interest. However, in compound interest, the principal amount plus previous interest
earn an interest.
For instance, a principal amount of Php1, 000 earns Php50 using 5% simple interest
rate per annum. In succeeding years, the interest remains to be Php50 per year. However, in
compound interest, the succeeding interest is based on both the principal amount and previous
interest. In this case, the interest is based on Php1, 050 which is Php52.50. The interest each
year, using compound interest, keeps on increasing.
In this example, the interest is compounded annually. However, compound interest can
be compounded monthly, quarterly (every3 months) or semi-annually (every 6 months). The
frequency with which the interest is compounded is called compounding period. The compound
amount is calculated using the formula
𝑅 𝑁𝑇
𝐴 = 𝑃 (1 + )
𝑁

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where A is the compound amount, P is the amount of money deposited. R is the annual
interest rate. N is the number of compounding periods per year, and T is the number of
years.
EXAMPLE 5.6
Calculate the compound mount when Php25, 000 is deposited in an account earning 9%
interest, compound semi-annually for 5 years.
Solution: N = 2 since it is compounded semi-annually. P = Php25, 000, R = 0.09 and T = 5.

Substitute these values to the compound amount formula
𝑅 𝑁𝑇 0.09 (2)(5)
𝐴 = 𝑃 (1 + ) = 25,000 (1 + ) = 38,824.24
𝑁 2
Therefore, the compound amount is Php38,824.24.
EXAMPLE 5.7
Calcuate the future value of Php20,000 earning 6% interest, compounded monthly for 2 years.
Solution: N = 12 since it is compounded monthly. P Php20, 000, R = 0.06 and T = 2. Substitute

these values to the compound amount formula.
𝑅 𝑁𝑇 0.06 (12)(2)
𝐴 = 𝑃 (1 + ) = 20,000 (1 + ) = 22, 543.20
𝑁 12
EXAMPLE 5.8
How much interest is earned in 5 years on Php10,000 deposited in an account paying 8%
interest, compounded quarterly?
Solution: N = 4 since it is compounded quarterly. T = 5, P = Php10,000 and R = 0.08. Substitute

these values to the compound amount formula.
𝑅 𝑁𝑇 0.08 (12)(2)
𝐴 = 𝑃 (1 + ) = 10,000 (1 + ) = 14, 859.47
𝑁 4
But A = P + I, thus
I A – P = 14, 859.47 – 10,000 = 4, 859.47
Therefore, the interest is Php4, 859.47.

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To determine the due date of a loan, one needs to know the exact number of days each
month has. There are 31 days for the months of January, March, May, July, August, October
and December and there are 30 days for the remaining months except February which has 28
days and 29 days when it is a leap year. Using exact number of days in a month, there are 365
days in a year. However, when ordinary days are used, there are 30 days in each month. Thus
there are 360 days in each year.
EXAMPLE 5.9
Using exact number of days, find the due date of the following:
a. A 120 – day loan made on April 22, 2020
b. A 180 – day loan made on May 12, 2020
Answers:
a. There are 8 days from April 22 to April 30. For May to July, there are 31 + 30 + 31 = 92
days. And there are 20 days from August 1 to August 20, 2020. Thus the due date of a 120
– day loan made on April 22, 2020 is August 20, 2020.
b. There are 19 days from May 12 to May 31. For June 1 to October 31, there are 30 + 31 +31
+ 30 + 31 = 153 days. And there are 8 days from November 1 to November. Thus, the due
date of a 180-day loan made on May 12 is November 8, 2020.
PRESENT VALUE
The value of the investment before it earns any interest or the original principal invested
is called present value. This is used to determine how much investment is needed in order to
have a specific value in the future. The present value formula is
𝐴
𝑃=
𝑅 𝑁𝑇
(1 + )
𝑁
where P is the original principal invested, A is the compound amount, R is the annual interest
rate, N is the number of compounding periods per year, and T is the number of years.

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EXAMPLE 5.10
How much money should be invested in an account that earns 8% interest, compounded
quarterly, in order to have Php50, 000 in 3 years?
Solution: A = 50, 000, R = 0.08, N = 4, T = 3. Substitute these values to the present value
formula.
𝐴 30,000
𝑃= = = 23,654.80
𝑅 𝑁𝑇 0.08 4(3)
(1 + ) (1 + 4 )
𝑁
Therefore, the present value is Php 23, 654.80
EXAMPLE 5.11
How much money should be invested in an account that earns 6% interest, compounded semi-
annually, in order to have Php100,000 in 2 years?
Solution: A = 100, 000, R = 0.06, N = 2, T = 2. Substitute these values to the present value
formula.
𝐴 100,000
𝑃= = = 88,848.70
𝑅 𝑁𝑇 0.06 2(2)
(1 + 𝑁 ) (1 + 4 )
Therefore, the present value is Php 88,848.70.
Exercises
. Practice your Skill 5.1
Solve the following problems:

1. Calculate the simple interest earned in 9 months on a deposit of Php20, 000
if the interest rate is 6.5%
2. A php3, 000 is deposited at 5% simple interest rate. How long was it
invested if it earned an interest of Php75?
3. Determine the maturity value of a Php25, 000 loan at 7% interest and
payable in 9 months.
4. Calculate the compound amount when Php200, 000 is deposited in an
account earning 7.5% interest, compounded monthly for 5 years.
5. Using exact number of days, find the due date of a 90 – day loan made on
August 31, 2020.

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EXTEND YOUR KNOWLEDGE
Make an inquiry to at least three banks regarding interests. Using the information
obtained from these banks, determine when to use a simple interest and compound interest.
Also, compare which bank offers the lowest interest rates.
ESSENTIAL LEARNING
An interest is the fee paid on the borrowed money. A simple interest is characterized
by a fixed amount earned or paid over time. However, in compound interest, the principal
amount plus previous interest earn an interest. The frequency with which the interest is
compounded is called compounding period.
The total amount a borrower needs to pay its lender is called maturity value. When it is
used for an investment, it is called future value. Whereas, the value of the investment before
it earns any interest or the original principal invested is called present value.
ASSESSMENT
1. Calculate the simple interest earned in 3 months on a deposit of Php3, 000 deposit if the
interest rate is 8%
2. Determine the simple interest rate if you earn Php1,500 for depositing Php130, 000 in 6
months.
3. Lyca applied for a loan. If she intends to pay in 10 months the Php50, 000 loaned amount
at 4% interest rate, what is the maturity value for the loaned amount?
4. Calculate the compound amount when Php80, 000 is deposited in an account earning 6%
interest, compounded quarterly for 3 years.
5. Using exact number of days, find the due date of a 120 – day loan made on September
5, 2020.
6. How much money should be invested in an account that earns 8% interest, compounded
semi – annually, in order to have Php25, 000 in 3 years?
GO ONLINE
The following links are online calculators intended to solve simple and compound
interests. After solving the learning exercises found in this lesson, check your answers using
these online calculators.
a. http://www.webmath.com/simpleinterest.html
b. http://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php

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LESSON 5.2 Credit Cards and Consumer Loans

Credit Cards
A credit card is a plastic card that contains information and can be used to make
purchases. There are two types of credit cards – the bank cards and the travel and
entertainment cards.
If a consumer uses his credit card in making purchases, the customer is actually doing
a loan. As such, there is an added cost in the form of an annual fee or interest charges on
purchases. Finance charge is an amount paid in excess of the cash price, it is the cost to the
customer for the use of credit card.
Most credit card companies issue bills on a monthly basis. The due date on the bill is
usually 1 month after the billing date. No finance charge is given if the bill is paid in full on or
before the due date. However, if the bill is not paid in full by the due date, a finance charge is
added to the next bill.
The most common method of determining finance charges is the average daily balance, which
is calculated by dividing the sum of the total amounts owed each day of the month by the
number of days in the billing period.
AVERAGE DAILY BALANCE
Average daily balance is obtained by dividing the sum of the total amouts owed each
day of the month by the number of days in the billing period. To illustrate this, consider the
following examples.
EXAMPLE 5.12
Suppose an unpaid bill of Php4, 000 has a due date on October 15. After the due date,
the following transactions were made.
October 17 – Purchased grocery products worth Php1,500
October 20 – Paid Php1, 000
October 29 – Purchased 2 electric fans worth Php3, 000

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The next billing date is November 1. The interest on the average daily balance is 1.5%
per month. Find the finance charge on the November 15 bill.
Solution:
Prepare a table showing the unpaid balance for each purchase, the number of days the
balance is owed, and the product of these numbers. A negative sign in the Payments or Purchase
column of the table indicates that a payment was made on that date.
Date Payments or Daily Balance Number of Unpaid balance

Purchase Days until times number of
Balance days
changes
October 15 - 16 4,000 2 8,000
October 17 - 19 1,500 5,500 3 16,500
October 20 - 27 -1,000 4,500 7 31,500
October 28 - 3,000 7,500 18 135,000
Nov 14
Total 30 191,000
191,000
The average daily balance is = 6,366.67. To find the finance charge, use the
30
simple interest formula I = PRT = (6,366.67)(0.015)(1) = 95.50
Therefore, the finance charge on the November 15 bill is 95.50.
EXAMPLE 5.13
An unpaid bill of Php2, 850 has a due date on April 7. A purchase of Php1, 800 was
made on April 29, Php750 on May 2 and Php6, 225 was made on May 5. A payment of Php9,
000 was made on May 6. If the interest on the average daily balance is 1.5% per month, find
the finance charge on May 7.

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Solution:
Date Payments or Daily Balance Number of Unpaid balance

Purchase Days until times number of
Balance days
changes
April 7 - 28 2, 850 22 62, 700
April 29 – May 1, 800 4, 650 3 13, 950
1
May 2 - 4 750 5400 3 16200
May 5 6225 11625 1 11625
May 6 -9000 2625 1 2625
Total 30 107, 100
107 ,100
The average daily balance is = 3570. To find the finance charge, use the simple
30
interest formula I = PRT = (3570)(0.015)(1) = 53.55
Therefore, the finance charge on the May 7 bill is 53.55.
ANNUAL PERCENTAGE RATE
Annual Percentage Rate (APR), is the effective annual interest rate on which credit
payments are based. The idea behind the APR is that interest is owed only on the unpaid balance
of the loan.
For instance, a loan of Php30, 000 was made from a bank that advertises a 12% annual
interest. If you agree to pay the loan in 3 equal monthly payents, the interest due on the 3 –
month period is
3
I = PRT = (3000) (0.12) ( 12 ) = 900.
The total amount is
A = P + I = 30000 + 900 = 30, 900

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Since you agree to pay in 3 equal monthly payments, then your monthly payment is
30, 900 / 3 = Php10, 300
In your first monthly payment, Php10, 000 is a reduction for the principal amount while
the Php300 is for the interest. After the first monthly payment, you owe 30, 000 – 10, 000 =
20, 000. This is where the second monthly payment should be based. Thus, the interest is
1
I = PRT = (20, 000) (0.12) ( 12 )= 200
This means that of your Php10, 300 second monthly payment, Php10, 100 is a reduction
of the principal amount. Thus, the principal amount becomes
Php20, 000 – Php10, 000 = Php9 900
The purpose of these calculations is to show that the principal amount is decreasing not
by a constant amount. Thus, an interest rate for a loan must be calculated only on the amount
owed at a particular time, not on the original amount borrowed.
Approximate Annual percentage Rate (APR) Formula for a Simple

Interest Rate Loan
The annual percentage rate (APR) of a simple interest rate loan can be approximated
by
2𝑁𝑅
APR ≈ 𝑁+1
where N is the number of payments and R is the simple interest rate
EXAMPLE 5.14
Rosette purchased a 49 – inch TV originally priced at Php31, 000. She gave a Php5,
000 down payment and agreed to pay the balance in 6 equal monthly payments. Determine the
following if the finance charge of the balance is 6% simple interest.
a. Finance Charge
b. Annual Percentage Rate

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Solution:
a. Determine the amount financed. The amount financed will serve as the principal amount
31, 000 – 5 000 = 26, 000
Use the simple interest formula to determine the finance charge
I = PRT = (26, 000) (0.06) (6/12) = 780
Therefore, the finance charge is Php780.
b. Use the APR formula to determine the annual percentage rate
2𝑁𝑅 2 ( 6)( 0.06 )

APR ≈ = ≈ 0.1029 ≈ 10.29%
𝑁+1 6+1
Therefore, the annual percentage rate is Php10.29%
EXAMPLE 5.15
Raymond who is working on his thesis asked her mother to purchase a new continuous
printer. The printer costs Php8, 000. Raymond’s mother gave a 30% down payment and agreed
to pay the balance in 12 equal monthly payments. Determine the following if the finance charge
of the balance is 12% simple interest.
a. Finance Charge
b. Annual Percentage Rate
Solution:
a. Determine the amount financed. The amount financed will serve as the principal amount.
Since her mother gave a 30% down payment, then the balance is 70%.
(8,000)(0.7) = 5, 600
Use the simple interest formula to determine the finance charge.
I = PRT = (5, 600) (0.12) (1) = 672
b. Use the APR formula to determine the annual percentage rate

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2𝑁𝑅 2 ( 12)( 0.12)

APR ≈ 𝑁+1 = ≈ 0.2215 ≈ 22.15%
12 +1
Therefore, the annual percentage is 22. 15%
CONSUMER LOANS: CALCULATING MONTHLY PAYMENTS
The payment amount for these loans is given by Payment Formula for an APR Loan.
The payment for a loan based on APR is given by
𝑅
𝑁
𝑃𝑀𝑇 = 𝐴 ( 𝑅 −𝑁𝑇
)
1− 1+ )
(
𝑁
where PMT is the payment, A is the loan amount, R is the annual interest rate, N is the
number of payments per year, and T is the number of years.
EXAMPLE 5.16
An appliance center is offering those who will purchase their refrigerators an annual
interest rate of 10% for 30 months. If Cherry Pie purchases 1 refrigerator for Php18, 000, find
her monthly payment.
Solution:
Since the term is 30 months and there are 12 months in a year so T = 2.5 years, A = 18, 000, R
= 0.10, and N = 12.
𝑅
𝑃𝑀𝑇 = 𝐴 ( 𝑁 )
𝑅 −𝑁𝑇
1 − (1 + 𝑁)
0.10
𝑃𝑀𝑇 = 18, 000 ( 12 ) = 680.61
0.10 −(12)(2.5)
1 − (1 + )
12
CONSUMER LOANS: CALCULATING Loan Payoffs
There are instances where customers want to pay their loan before the end of the term.
For instance, a customer wants to pay his 10 year – housing loan in 8 years. For the remaining
2 years, it does not mean that monthly payment be multiplied to 24 to arrive at the payoff
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amount. Note that each payment includes both the principal and the interest. The only way to
do this, is to use the payment formula for an APR loan using the remaining principal amount.
APR Loan Payoff Formula
The payment amount for a loan based on APR is given by
𝑅 −𝑈
1 − (1 + 𝑁)
𝐴 = 𝑃𝑀𝑇 ( )
𝑅
𝑁
where A is the loan payoff, PMT is the payment R is the annual interest rate, N is the number
of payments per year, and U is the number of remaining (or unpaid) payments.
EXAMPLE 5.17
Mark wants to pay off his loan for a car that he has owned for 4 years. Mark’s monthly
payment is Php11, 000 on a 5 – year loan at an annual percentage rate f 8%. Find the payoff
amount.
Solution:
Because Mark has owned his car for 4 years in a 5 year loan, then he has 1 ear or 12
monthly payments remaining, U = 12, PMT = 11, 000, R = 8% or 0.08, N = 12. Substitute these
values to APR loan payoff formula.
𝑅 −𝑈
1 − (1 + )
𝑁
𝐴 = 𝑃𝑀𝑇 ( )
𝑅
𝑁
0.08 −12
1 − (1 + 12 )
𝐴 = 11, 000 ( ) = 126, 453.60
0.08
12
The loan payoff is Php126, 453.60

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CAR LEASES
Car Lease means a legal agreement that allows someone to use the car for a certain
period of time in return for a payment. This may result in lower monthly car payments because
ownership of the car reverts to the dealer. The dealer then can sell it as a used car and realize
the profit from the sale.
Residual Value of the car is the value of the car at the end of the lease term. This is the
amount the dealer thinks the car will be worth at the end of the lease period. It is based on a
percent of the manufacturer’s suggested retail price (MSRP) within 40% to 60% of the MSRP.
EXAMPLE 5.18
Determine the residual value of a car whose MSRP is Php625, 000 and the residual
value is 40%
Solution:
Residual value = (625,000) (0.4) = Php250, 000
Apart from the residual value of the car, net capitalized cost, the money factor, average
monthly finance charge, and average monthly depreciation are to be considered in the monthly
lease payment. The computation of the aforementioned factors are shown below.
NCC = negotiated price – Down Payment – Trade in Value
𝐴𝑛𝑛𝑢𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒

MF = 24
F = (NCC + residual value) (MF)
𝑁𝐶𝐶 −𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒

D=
𝑡𝑒𝑟𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑒𝑎𝑠𝑒 𝑖𝑛 𝑚𝑜𝑛𝑡ℎ𝑠
where NCC is the Net Capitalized Cost, MF is the Money Factor, F is the Average Monthly
Finance Charge and the D is the Average Monthly Depreciation.

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MONTHLY LEASE PAYMENT FORMULA
The monthly lease payment formula is given by
P = F + D,
where P is the monthly lease payment, F is the average monthly finance charge, and D
is the average monthly depreciation of the car.
EXAMPLE 5.19
Suppose you decide to lease a car for 3 years. Suppose the annual interest rate is 7%,
the negotiated price is Php900, 000, there is no trade – in, and the down payment is Php200,
000. Find the monthly lease payment. Assume that the residual value is 40% of the MSRP of
Pjp1, 200,000.
Solution:
Step 1. Solve for Net Capitalized Cost (NCC), Residual Value and Money Factor (MF).
NCC = negotiated price – downpayment – tradein value
NCC = 900,000 – 200,000 – 0 = 700, 000
Residual Value = (1,200,000) (0.4) = 480, 000
𝐴𝑛𝑛𝑢𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 0.07

MF = = = 0.0029
24 24
Step 2. Use the computed values to solve for Average Monthly Finance Charge (F) and the
Average Monthly Depreciation (D).
F = (NCC = Residual Value) (MF)
F = (700, 000 + 480, 000) (0.0029)
F = 3, 422
𝑁𝐶𝐶 −𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 700,000−480,000

D = 𝑡𝑒𝑟𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑒𝑎𝑠𝑒 𝑖𝑛 𝑚𝑜𝑛𝑡ℎ𝑠 = 36
D = 6, 111.11
Step 3. Use the computed values in step 2 for the monthly lease payment (P)

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P=F+D
P = 3, 422 + 6, 111.11
P = 9, 533.11
Exercises
.
Practice your Skill 5.2

1. Suppose an unpaid bill of Php6, 000 has a due date on March 20. After
the due date, the following transactions were made
March 28 – Paid Php4, 900
April 7 – Purchased grocery products worth Php2, 100
April 17 – Purchased clothes worth Php3, 250
April 19 – Purchased electric oven worth Php1, 500
The next billing date is April 20. The interest on the average daily balance
is 2% per month. Find the finance charge on the April 20 bill.
2. Edna purchased a sofa bed originally priced at Php 25, 000. She gave a
Php5, 000 down payment and agreed to pay the balance in 3 equal monthly
payments. Determine the following if the finance charge of the balance is
5% simple interest.
a. Finance charge
b. Annual Percentage rate
Make an inquiry to at least three credit card providers. Using the information obtained
(interest rate, annual fee, finance charge, etc.) from these credit card providers, answer the
following questions:
a. Which among these credit card providers offer the lowest charges?
b. Is it advisable to use credit card? Why or why not?

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ESSENTIAL LEARNING
A credit card is a plastic card that contains information and can be used to make
purchases. There are two types of credit cards – the bank cards and the travel and
entertainment cards. Finance charge is an amount paid in excess of the cash price. It is the
cost to the customer for the use of credit.
Consumer loans include cash loan, appliance loan, car loan, etc. Car lease means a
legal agreement that allows someone to use the car for a certain period of time in return for a
payment. Residual value of the car is the value of the car at the end of the lease term. This is
the amount the dealer thinks the car will be worth at the end of the lease period.
ASSESSMENT
1. Rica purchased a home theatre for Php45, 000. If it has an annual interest rate of 8% and
a payable in 3 years, find his monthly payment.
2. Gerald wants to pay off his loan for a car that he has owned for 42 months. Gerald’s
monthly payment is Php12, 000 on a 5 – year loan at an annual rate of 7.5%. Find the payoff
amount.
GO ONLINE
Credit Card use must be accompanied with wise decision making. To help you with this,
read the article “Worried about Debt? Tips on Managing Your Loans” which can be accessed
thru this link http://www.wisebread.com/worried-about-debt-tips-on-managing-your-loans.
After reading the article, write a reflection paper

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LESSON 5.3 Stocks, Bonds, and Mutual Funds

Stocks
One of the challenges a growing business is facing, is how to raise enough money to
finance the expansion. Apart from lending money from the bank, the company may opt to sell
some of their stocks.
Stocks represent ownership in the company. Stock is measured in shares. Shares of

stock in a company is a certificate that indicates partial ownership in the company. The owners
of the certificates are called stockholders or shareholders. The stockholders share profits or
losses of the company. The profits or losses are distributed to its shareholders in the form of
dividends on per-share basis
EXAMPLE 5.20
An annual dividend of Php45 per share is to be distributed to its stockholders.
Determine the amount paid to a stockholder who own 500 shares of the company’s stocks.
Solution:
(500)(45) = Php22, 500
The dividend yield, which is used to compare companies’ dividends, is the annual
dividend per share divided by current stock price and is expressed as percent. This is used to
measure the investments productivity.
EXAMPLE 5.21
What is the dividend yield on the copany’s stocks which pays Php15 per share in annual
dividends, if the current stock price is Php200?
Solution:
15
Dividend yield = 200 = 0.075 = 7.5%

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The market value of the shares of stocks is the price for which the stockholders are
willing to sell and the buyers are willing to purchase. A brokerage firm facilitates a transaction
between the buyer and the seller. However, the brokers in the firm charge commissions for
their service.
BONDS
If stock represent ownership in the company, bonds represent debt. When a company
issues bond, the company is borrowing money from the bondholders. A bondholder lends
money to a corporation. The terms of the bond determine the given interest rate (coupon),
maturity date and payment schedule. The price paid for the bond is called face value. The
payments are calculated using the simple interest formula where the face value, coupon and
maturity date, represent principal amount, interest rate and time period respectively.
EXAMPLE 5.22
A bond with a Php50, 000 face value has a 2.5% coupon and a 3 – year maturity date.
Determine the interest payments to be paid to the bondholder.
Solution: I = PRT = (50, 000) (0.025) (3) = Php3, 750.
Stocks reflect the company’s success. This means that stockholders are not guaranteed
of earnings. However, the bonds are referred to as fixed income securities because it has fixed
interest rate. This makes bonds less risky than stocks.
In case of bankruptcy, the bondholders get paid first before the stockholders. However,
if the company does well, the bondholders do not share in the company’s profits.
Bonds can be classified according to maturity – treasury bills (T-bills) and

Treasury bond (T-bonds). Treasury Bills refer to debt investments with maturity of less than
a year. There are three maturity periods of treasury bills, the 91 – day, 182 – day and 364-day.
On the other hand, treasury bonds refer to debt investment with more than one year. There
are five maturity periods of treasury bonds, 2 years, 5 years, 7 years, 10 years and 20 years.

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Moreover, bonds can also be classified according to issuer – treasury securities,

government bonds, municipal bonds and corporate bonds.
If the issuer is the Bureau of Treasury, the bond is known as treasury securities. This
type of bond is ideal for big corporations. However, if the issuer is government agency, the
bond is known as the government bond. This type of bond is ideal for individual investments.
If the issuer is the local government, the bond is known as municipal bond. If the bond is
issued by large corporations, the bond is known as corporate bond.
MUTUAL FUNDS
A mutual fund is an investment company that pools together savings of different

investors and invests them in a common financial goal. The mutual fund company do not
manufacture products but purchase stocks and bonds with the hope that their value will
increase.
The mutual funds in the Philippines are categorized as equity funds, bond funds, money
market funds and balanced funds. Equity funds are for those who want long-term capital
growth. Bond funds are for those whose goal is stability and reasonable growth. Money-
market funds are for those who wants short-term investment and earn from it and balanced –
fund are for those who want medium to long term investments.
The investments within a mutual fund are called the fund’s portfolio. The investors in
a mutual fund proportionality share the fund’s profits or losses from the investments in a mutual
fund. Their job includes conducting research and evaluating stocks.
Mutual funds are made up from different investments. Each share of the funds owns a
fractional interest of the companies. The value of a share in the fund depends on the stock
performance on a daily basis. It is called net asset value of the fund (NAV). It is calculated
using the formula:
𝐴−𝐿
NAV = 𝑁
where A is the total fund assets, L is the total fund liabilities nd N is the number of
outstanding shares.

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EXAMPLE 5.23
A mutual fund has Php500, 000, 000 worth of stocks. Php50, 000, 000 worth of bonds
and Php100, 000, 000 in other assets. The fund’s liabilities is Php10, 000, 000. There are 4,
000, 000 outstanding shares. You invest Php2, 000, 000 in this fund.
a. Calculate the NAV.
b. How many shares will you purchase?
Solution:
a. The total assets is the sum of the worth of stocks, worth of bonds and other assets. Thus, the
total assets is 500, 000, 000 + 50, 000, 000 + 100, 000, 000 = Php650, 000, 000. Use this value
together with the total liabilities and outstanding shares to solve for the NAV.
𝐴−𝐿 650 ,000 ,000 −10,000 ,000

NAV = = = 160
𝑁 4,000 ,000
b. Divide the amount invested with NAV. Thus, you can purchase 2, 000, 000 ÷ 160 = 12, 500
shares
EXAMPLE 5.24
A mutual fund has Php800, 000, 000 worth of stocks. Php100, 000, 000 worth of bonds
and Php50, 000, 000 in other assets. The fund’s liabilities is Php75, 000, 000. There are 5, 000,
000 outstanding shares. You invest Php2, 000, 000 in this fund.
a. Calculate the NAV.
b. How many shares will you purchase?
Solution:
a. The total assets is the sum of the worth of stocks, worth of bonds and other assets. Thus, the
total assets is 800, 000, 000 + 100, 000, 000 + 50, 000, 000 = Php950, 000, 000. Use this value
together with the total liabilities and outstanding shares to solve for the NAV.
𝐴−𝐿 950,000,000−5,000 ,000

NAV = = = 189
𝑁 5,000,000

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b. Divide the amount invested with NAV. Since 2, 000, 000 ÷ 189 = 10, 582.01 is not a whole
number, round down the result to the nearest whole number. Thus, you can purchase 10, 582
shares.
Exercises
.

1. An annual dividend of Php30 per share is to be distributed to its stockholders.
Determine the amount paid to the stockholder who own the following shares of
the company’s stocks.
a. 1200 shares
b. 3500 shares
2. What is the dividend yield on the company’s stocks which pays Php22 per
share in annual dividends, if the current stock price is Php350?
In order to protect your investment, be sure you are investing in a recognized and
profitable company. List the top 5 mutual fund companies in each of the four categories: equity
funds, bond funds, money market funds and balanced funds. Be sure ranking is based on the
return of investments (ROI) and is published in Philippine Fund Association (PIFA).
ESSENTIAL LEARNING
Stocks represent ownership in the company and is measured based on shares. Shares
of stock in a company is a certificate that indicates partial ownership in the company. The
owners of the certificates are called stockholders or shareholders.
The dividend yield is used to measure the investment’s productivity. The market value
of the shares of stock is the price for which the stockholders are willing to sell and the buyers
are willing to purchase.

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Bonds represent debt. When a company issues a bond, the company is borrowing
money from the bondholders. A bondholder lends money to a corporation. The price paid for
the bond is called face value.
A mutual fund is an investment company that pools together savings of different

investors and invests them in a common financial goal. Equity funds are for those who want
long-term capital growth. Bond Funds are for those whose goal is stability and reasonable
growth. Money-market funds are for those who wants short-term investment and earn from it
and balanced – funds are for those who want medium to long term investments. The value of
a share in the fund depends on the stock performance on a daily basis. It is called net asset
value.
ASSESSMENT
1. A bond with a Php60, 000 face value has a 2.5% coupon bond and a 3-year maturity
date. Determine the interest payments paid to the bondholder.
2. A mutual fund has Php180, 000, 000 worth of stocks, Php20, 000, 000 worth of bonds
and Php17, 000, 000 in other assets. The fund’s total liabilities is Php1, 500, 000. There are
2, 400, 000 outstanding shares. If you invested Php1, 000, 000 in this fund, calculate the
NAV. How many shares will you purchase?

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LESSON 5.4 Home Ownership
In purchasing a house and lot, a 10% to 30% down payment is usually required. The
remainder may be availed either thru bank financing or thru the Home Development Mutual
Fund (HDMF) or better known as PAGIBIG Housing Loans. The amount borrowed to purchase
real property is known as mortgage. As such, mortgage is the difference between the selling
price and the down payment.
Mortgage = Selling price – Down Payment
EXAMPLE 5.25
Determine the mortgage in a Php1, 200, 000 two bedroom bungalow housing unit if
30% down payment is required.
Solution:
Step 1. A 30% down payment is required. Thus, the down payment is
(1, 200, 000)(0.3) = Php360, 000
Step 2. Subtract the down payment from the selling price to obtain the mortgage.
1, 200, 000 – 360, 000 = Php840, 000
Thus, the mortgage is Php840, 000.
Alternate Solution.
Since a 30% down payment is required, then the mortgage is 70% of the selling price, that is
100% - 30% = 70%. Thus the mortgage is (1, 200, 000) (0.70) = Php840, 000.
EXAMPLE 5.26
Determine the selling price of a housing unit is a 25% down payment is required and
the mortgage is Php1, 350, 000.
Solution: Since 25% down payment is required, then the mortgage is 75% of the selling price.
(0.75) (selling price) = mortgage

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𝑚𝑜𝑟𝑡𝑔𝑎𝑔𝑒 1,350,000
selling price = = = 1, 800, 000
0.75 0.75
Thus, the selling price is Php1, 800, 000.
Apart from the down payment, there are other expenses associated with housing
purchase. These expenses called closing costs include attorney’s fees, processing fee and title
searches. Apart from these, there may be also a loan origination fee. This fee is usually
expressed in points where one point is equal to 1% of the mortgage.
EXAMPLE 5.27
The purchase price of a housing unit is Php2, 100, 000. A 25% down payment is made.
The bank charges Php20, 000 in other fees plus 2 points. Determine the sum of down payment
and closing costs.
Solution:
Step 1. The down payment is (0.25) (2, 100, 000) = Php525, 000
Step 2. Determine first mortgage.
Mortgage = 2, 100, 000 – 525, 000 = Php1, 575, 000
Then, calculate the charge for points.
(0.02) (1, 575, 000) = Php31, 500
Step 3. The sum of the down payment and closing costs is
525, 000 + 31, 500 = Php556, 500
EXAMPLE 5.27
The purchase price of a housing unit is Php1, 300, 000. A 20% down payment is made.
The bank charges Php15, 000 in other fees plus 1.5 point. Determine the sum down payment
and closing costs.
Solution:
Step 1. The down payment is (0.20) (1, 300, 000) = Php260, 000

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Step 2. Determine first mortgage.
Mortgage = 1, 300, 000 – 260, 000 = Php1, 040, 000
Then, calculate the charge for points.
(0.15) (1, 040, 000) = Php15, 600
Step 3. The sum of the down payment and closing costs is
260, 000 + 15, 600 = Php275, 600
MORTGAGES
When a bank agrees to provide you with a mortgage, you are given a contract. Be sure
you understand all the terms and conditions, before you sign the contract. The contract contains
the payment terms and interest rate, among others. If you fail to follow the contract, the bank
has the right to foreclose your property. This means that the bank has the right to sell your
property.
For home buyers, there are two types of mortgages available. These are adjustable rate
mortgages (ARMS) and fixed rate mortgages or conventional mortgages.
The interest rate applied on ARMs is based on the outstanding balance. This means that
the mortgage agreement specifies exactly by how often and by how much the interest rate can
change. Whereas, the interest applied to a fixed rate mortgage is fixed or constant. It means
that the interest rate won’t change during the duration of the loan.
The mortgage payment varies depending upon the terms applied. Usually, the terms are
in 10 years, 15 years, 20 years and 25 years. The mortgage payment is calculated as follows:
𝑅
𝑃𝑀𝑇 = 𝐴 ( 𝑁 )
𝑅 −𝑁𝑇
1 − (1 + 𝑁)
where 𝑃𝑀𝑇 is the monthly mortgage payment, A is the amount of the mortgage,
R is the annual interest rate, N is the number of payment per year, and T is the number of
years.

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EXAMPLE 5.29
Helen purchases a housing unit and secures a loan of Php1, 500, 000 for 15 years at an
annual interest rate of 5.5%
a. Find the monthly mortgage payment.

b. What is the total of the payments over the life of the loan?
c. Find the amount of interest paid on the loan over the 10 years?
Solution:
a. A = 1, 500, 000, R = 0. 055, N = 12 and T = 15. Substitute these values,
𝑅
𝑃𝑀𝑇 = 𝐴 ( 𝑁 )
𝑅 −𝑁𝑇
1 − (1 + )
𝑁
0.055
𝑃𝑀𝑇 = 1, 500, 000 ( 12 )
0.055 −(12)(15)
1 − (1 + 12 )
= Php12, 256.25
b. To determine the total payments, multiply the monthly mortgage payments with the number
of payment. Since the term is 15 years, so there are (15) (12) = 180 monthly payments.
Thus, the total payments is (12, 256.25) (180) = Php2, 206, 125.
c. To determine the amount of interest paid, subtract the mortgage from the total payments.
Thus, the amount of interest is 2, 206, 125 – 1, 500, 000 = Php706, 125.
EXAMPLE 5.3 0
Rolando, an Overseas Filipino Worker (OFW), applied for a housing loan at a certain
bank amounting to Php1, 000, 000 payable in 10 years at an annual rate of 6%.
a. Find the monthly mortgage payment.

b. What is the total of the payments over the life of the loan?
c. Find the amount of interest paid on the loan over the 10 years?

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Solution:
a. A = 1, 000, 000, R = 0. 06, N = 12 and T = 10. Substitute these values,
𝑅
𝑃𝑀𝑇 = 𝐴 ( 𝑁 )
𝑅 −𝑁𝑇
1 − (1 + 𝑁)
0.06
𝑃𝑀𝑇 = 1, 000, 000 ( 12 )
0.06 −(12)(10)
1 − (1 + 12 )
= Php11, 102.05
b. To determine the total payments, multiply the monthly mortgage payments with the number
of payment. Since the term is 10 years, so there are (10) (12) = 120 monthly payments.
Thus, the total payments is (11,102.05) (120) = Php1, 332,246.
c. To determine the amount of interest paid, subtract the mortgage from the total payments.
Thus, the amount of interest is 1, 332, 246 – 1, 000, 000 = Php332, 246.
The monthly payment is a reduction both of the principal amount and the interest. For
instance, in example 5.30, the interest on the first month is
1
I = PRT = (1, 000, 000) (0.06) (12 ) = 5, 000.
Thus, of the Php11, 102.05, the Php5, 000 is a payment for the interest while the remaining
Php6, 102. 05 is a reduction of the principal amount owed.
Upon approval of the loan, the bank will prepare an amortization schedule. This is a list
containing the payment number, mortgage payment, interest payment, amount applied toward
the principal and resulting balance.
Using an amortization schedule, one will notice that the amount of the mortgage
payment that is an interest payment decreases and the amount applied toward the principal
increases.
The partial amortization schedule of example 5.30 is shown as follows. The

amortization schedule shows the first 12 monthly mortgage payments.

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Amortization Schedule of Rolando
Payment Mortgage Interest Principal Balance

Number Payment Payment Reduction
1 11, 102.05 5000.00 6102.05 993897.95
2 11, 102.05 4969.49 6132.56 987765.39
3 11, 102.05 4938.83 6163.22 981602.17
4 11, 102.05 4908.01 6194.04 975408.13
5 11, 102.05 4877.04 6225.01 969183.12
6 11, 102.05 4845.92 6256.13 962926.98
7 11, 102.05 4814.63 6287.42 956639.57
8 11, 102.05 4783.20 6318.85 950320.72
9 11, 102.05 4751.60 6350.45 943970.27
10 11, 102.05 4719.85 6382.20 937588.07
11 11, 102.05 4687.94 6414.11 931173.96
12 11, 102.05 4655.87 6446.18 924727.78
EXAMPLE 5.3 1
Using the partial amortization schedule of Rolando, how much of the loan has been
paid in a year?
Solution:
The total payment in a year is the difference between the original principal amount and
the outstanding balance after the 12th payment. Thus, the total payment is 1, 000, 000 – 924,
727. 78 = Php75, 272. 22. The total payment in a year may also be computed using the sum of
the principal reduction. It will yield similar results.
EXAMPLE 5.3 2
You purchase a housing unit for Php2, 200, 000 and obtain a 20 –year, fixed – rate
mortgage at 7.5%. After paying a down payment of 20%, how much of the second payment is
the interest and how much is applied toward the principal?
Solution:
Step 1. Determine the down payment. The down payment is 20% of the selling price. Thus,

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(0.20) (2, 200, 000) = Php440, 000.
Step 2. Determine the mortgage value. The mortgage value is
2, 200, 000 – 440, 000 = Php1, 760, 000
Step 3. Use the mortgage payment formula to determine the monthly payment where A = 1,
760, 000, R = 0.075, N = 12 and T = 20. Thus, the monthly mortgage payment is
𝑅
𝑃𝑀𝑇 = 𝐴 ( 𝑁 )
𝑅 −𝑁𝑇
1 − (1 + 𝑁)
0.075
𝑃𝑀𝑇 = 1, 760, 000 ( 12 )
0.075 −(12)(20)
1 − (1 + 12 )
= Php14, 178.44
Step 4. Determine the interest and the reduction to the principal of the monthly payment. The
interest of the first month payment is
1
I = PRT = (1, 760, 000) (0.75) (12 ) = Php11, 000.
of the Php14, 178.44 first month payment, Php11, 000 goes to the interest and the remaining
Php3, 178.44 is a reduction to the principal. Thus, the new principal amount is
1, 760, 000 – 3, 178.44 = Php1, 756, 821.56
Step 5. Determine the interest and the reduction to the principal of the second monthly payment
using the new principal amount. Thus,
1
I = PRT = (1, 756, 821.56) (0.75) ( ) = Php10, 980.13.
12
of the Php14, 178.44 second month payment, Php10, 980.13 goes to the interest and the
remaining Php3, 198.31 is a reduction to the principal.
When a homeowner wants to pay the loan before the term expires, then the homeowner
must pay the remaining loan balance. To calculate that balance, we can use the APR loan payoff
formula:

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𝑅 −𝑈
1 − (1 + 𝑁)
𝐴 = 𝑃𝑀𝑇 ( )
𝑅
𝑁
where A is the loan payoff, PMT is the mortgage payment R is the annual interest rate, N is the
number of payments per year, and U is the number of remaining (or unpaid) payments.
EXAMPLE 5.3 3
A homeowner has a monthly mortgage payment of Php11, 500 on a 20 – year loan at
an annual interest rate of 8%. After making payments for 5 years, the homeowner decides to
sell the house. What is the payoff for the mortgage?
Solution:
The term of the loan is 20year or 240 months. However, the homeowner has only paid 5 years
or 60 monthly payment. Thus, there are 240 – 60 – 180 months unpaid. U = 180, R = 0.08, N
= 12 and PMT = 11, 500.
𝑅 −𝑈
1 − (1 + )
𝑁
𝐴 = 𝑃𝑀𝑇 ( )
𝑅
𝑁
0.08 −180
1 − (1 + 12 )
𝐴 = 11, 500 ( ) = 𝑃ℎ𝑝1, 203, 366.81
0.08
12
The loan payoff is 𝑃ℎ𝑝1, 203, 366.81.
Aside from the monthly mortgage payment, there are other ongoing expenses
associated with home ownership. These include property tax, insurance and utility expenses
such as water and electricity.

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Exercises
.

1. You purchase a home worth Php1, 800, 00. If 20% down payment is
required, find the following:
a. Amount of the down payment; and
b. Mortgage amount
2. Determine the selling price of a housing unit a 30% down payment is
required and the mortgage is Php1, 500, 000
3. The purchase price of a housing unit is Php1, 200, 000. A 25% down
payment is made. The bank charges Php10, 000 in other fees plus 1 point.
Determine the sum of down payment and closing costs.
4. A homeowner has a monthly mortgage payment of Php15, 000 on a 15 –
year loan at an annual interest rate 6%. After making payments for 12 years,
the homeowner decide to sell the house. What is the payoff for the
mortgage?
A housing loan may be availed thru Home Development Mutual Fund (HDMF) or
popularly known as PAG – IBIG housing loans. To better understand how to avail on the said
loan, read the article found in this link http://www.pagibigfund.gov.ph/benpro.aspx.
ESSENTIAL LEARNING
The amount borrowed to purchase a real property is known as mortgage. The mortgage
may be availed either thru bank financing or thru HDMF.
Apart from the down payment, there are other expenses associated with housing
purchases. These expenses called closing costs include attorney’s fees, processing fees and
title searches. Apart from these, there may also be a loan origination fee. This fee is usually
expressed in points where one point is equal to 1 % of the mortgage.

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Aside from the monthly mortgage payment, there are other on-going expenses
associated with home ownership. These include property tax, insurance, and utility expenses
such as water and electricity.
ASSESSMENT
1. You purchase a house worth Php2, 100, 00. If 30% down payment is required, find the
amount of the down payment and mortgage payment.
2. A homeowner has a monthly mortgage payment of Php17, 000 on a 10 – year loan at an
annual interest rate 7.5%. After making payments for 9 years, the homeowner decide to sell
the house. What is the payoff for the mortgage?
GO ONLINE
Suppose you availed of a housing loan worth Php1, 500, 000 payable in 10
years. Prepare an amortization schedule using any of the amortization schedule
calculators found in the internet. Afterwards, determine the total principal reduction
after the 100th payment.
CHAPTER CHALLENGE
I. Identify what is described or referred to in each item.
1. The total amount the borrower needs to pay its lender.
2. Value of the investment before it earns any interest.
3. Cost to the customer for the use of credit card.
4. Amount the dealer thinks the car will be worth at the end of the lease period.

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5. Represents ownership in the company.
6. Used to measure the investment’s productivity.
7. Investment Company that pools together savings of different investors and invests them in a
common financial goal.
8. Holders of certificate that indicates partial ownership of the company.
9. Amount borrowed that is used to purchase real property.
10. Legal agreement that allows someone to use the car for a certain period of time in return
for a payment.
II. Solve the following completely.
1. Joy has Php2, 00, 000. If she invested 60% of her money in account paying 6% simple
interest and the remaining amount is invested in account paying 5% simple interest. How much
is the total interest for the investments after 10 months?
2. Mario is planning to invest Php1, 000, 000. He received the following offers from the three
banks:
Bank A – 8% interest compounded semi – annually
Bank B – 6% interest compounded quarterly
Bank C – 4% interest compounded monthly
Which bank offers the best deal? By how much?
3. A newly – wed couple has a combined monthly take home pay of Php40, 000. They decided
to purchase a housing unit and secures a loan of Php1, 200, 000 for 15 years at an annual
interest rate of 6%. On top of this, the other monthly expenses is Php17, 000. What is the
maximum amount the newly – wed couple can save on a monthly basis?
4. A mutual fund has Php160, 000, 000 worth of stocks, Php15, 000, 00 worth of bonds and
Php25, 000, 00 in other assets. The fund’s total liabilities is Php5, 000, 000. There are 2, 000,
000 outstanding shares. If you invested Php1, 500, 000, how many shares will you purchase?


Mathematics of Finance: Intended Learning Outcomes

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Mathematics of Finance: Intended Learning Outcomes

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ILOCOS SUR POLYTECHNIC STATE COLLEGE

Sta. Maria Campus

Intended Learning Outcomes

SCOPE AND SEQUENCE

5-1 Simple and Compound Interest

OVERVIEW (Time allotted for this chapter is 10 hours)

1. What makes mathematics an important tool in finance?

Course Code: GenEd103

Sta. Maria Campus

In addition, Mr Raras wants to spend his retirement benefits to purchase a two-bedroom

Criteria Excellent:4 Proficient:3 Progressing:2 Beginning:1

Practicality of Recommendatio Recommendatio Recommendatio Recommendati

Course Code: GenEd103

Sta. Maria Campus

LESSON 5.1 Simple and Compound Interest

Definition 5.1: I nterest

 It refers to the fee paid on the borrowed money.

An interest may be either be simple or compound.

Definition 5.21: Simple Interest

The simple interest is calculated using the formula

Course Code: GenEd103

Sta. Maria Campus

The simple interest earned is Php125.

Substitute these values to the simple interest formula.

The simple interest due is Php 266.67

Substituting the given values to the interest rate formula

Sta. Maria Campus

Thus, the simple interest rate is 3%.

Maturity Value and Future Value

Definition 5.3: Maturity Value

Definition 5.3: Fut ure Value

Step 1: Solve for the interest.

Course Code: GenEd103

Sta. Maria Campus

I = A – P = 10,250 – 10,000 = 250

Therefore, Emmerson paid his loan in 6 months.

Course Code: GenEd103

Sta. Maria Campus

Solution: N = 2 since it is compounded semi-annually. P = Php25, 000, R = 0.09 and T = 5.

Therefore, the compound amount is Php38,824.24.

Solution: N = 12 since it is compounded monthly. P Php20, 000, R = 0.06 and T = 2. Substitute

Solution: N = 4 since it is compounded quarterly. T = 5, P = Php10,000 and R = 0.08. Substitute

I A – P = 14, 859.47 – 10,000 = 4, 859.47

Therefore, the interest is Php4, 859.47.

Course Code: GenEd103

Sta. Maria Campus

a. A 120 – day loan made on April 22, 2020

b. A 180 – day loan made on May 12, 2020

Course Code: GenEd103

Sta. Maria Campus

Therefore, the present value is Php 23, 654.80

Therefore, the present value is Php 88,848.70.

Solve the following problems:

Course Code: GenEd103

Sta. Maria Campus

EXTEND YOUR KNOWLEDGE

Course Code: GenEd103

Sta. Maria Campus