The document outlines essential learning competencies for mathematics, focusing on simple and compound interest calculations, maturity values, and annuities. It includes definitions, formulas, and practical examples to help students grasp these concepts, alongside sections on stocks, bonds, and business versus consumer loans. The content aims to enhance students' understanding of financial mathematics and its real-life applications.

1. GENERAL
MATHEMATICS

2. WEEK
1-2

3. Most Essential Learning Competencies
 Illustrates simple and compound interests.
M11GM-IIa-1
 Computes interest, maturity value, future value,
and present value in simple interest and
compound interest environment.
M11GM-IIa-b-1
 Solves problems involving simple and compound
interests.
M11GM-IIb-2

4. Objectives
At the end of this week the students will be
able to:
 Define simple and compound interest.
 Compute interest, maturity value future value,
and present value in simple interest and
compound interest environment
 Cite some importance usage of simple and
compound interest in real-life scenarios.

5. SIMPLE INTEREST

6. Lender or creditor
- person (or institution) who invests the money
or makes the funds available.
Borrower or debtor
- person (or institution) who owes the
money or avails of the funds from the lender.

7. Origin or loan date
 date on which money is received by the
borrower.
Repayment date or maturity date
 date on which the money borrowed, or loan
is to be completely repaid.

8. Time or Term (t)
 amount of time in years the money is borrowed or
invested, length of time between the origin and maturity
dates
Principal (P)
 amount of money borrowed or invested on the origin
date

9. Rate(r)
 annual rate, usually in percent, charged by the
lender, or rate of increase of the investment
Interest (I)
 amount paid or earned for the use of
money

10. Simple Interest
 Interest that is computed on the principal
and then added to it
Compound Interest
 Interest is computed on the principal and
also on the accumulated past interests.

11. Maturity value or future value (F)
 amount after t years that the
lender receives from the borrower
on the maturity date.

12. Formula in finding Simple Interest
Annual Simple Interest
𝑰 𝒔=𝑷𝒓𝒕
where
= simple interest
P = principal, or the amount invested or
borrowed
r = simple interest rate
t = term or time in years

13. Example
A bank offers 0.25% annual simple interest rate for
a particular deposit. How much interest will be
earned if 1,000,000 pesos is deposited in this
savings account for 3 year?
Given: P = 1,000,000 r = 0.25% = 0.0025
t = 3 year
Find:
Answer: The interest earned is P7,500.00

14. How much interest is charged when P50,000 is
borrowed for 9 months at an annual interest rate
of 10%?
Given: P = 50,000 r = 10% = 0.1
Find:
Answer: The simple interest charged is P3,750.00

15. Example 3
When invested at an annual interest rate of 0.22%,
the amount earned P25,700 of simple interest in 5
years. How much money was originally invested?
Given: r = t =
Find: Amount invested or principal P
Answer: The amount invested is

16. Example 3
When invested at an annual interest rate of 7%,
the amount earned P11,200 of simple interest in
two years. How much money was originally
invested?
Given: r = 7% = 0.07 t = 2 years
Find: Amount invested or principal P
Answer: The amount invested is P80,000.00

17. Example 4: If an entrepreneur applies for a loan
amounting to P500,000 in a bank, the simple
interest of which is P157,500 for 3 years, what
interest rate is being charged?
Given: P = 500,000 t = 3 years
Find: r
𝒓 =0.105=10.5 %

18. Example 5: How long will a principal earn
an interest equal to half of it at 5% simple
interest?
Given: P r= 5% = 0.05 t =?
Find: t
𝒕 =10 𝒚𝒆𝒂𝒓𝒔

19. Formula in finding Maturity Value
Maturity (Future) Value
where
F = maturity (future) value

20. Substituting by Prt gives F = P + PrT, = P (1 + rt)
Maturity (Future) Value
where
F = maturity (future) value
P =
Principal
t = term/

21. Example
Find the maturity value if 1 million pesos is
deposited in a bank at an annual simple
interest rate of 0. 25% after (a) 1 year ?
Given: P = 1,000,000 r= 0.25%=
0.0025
Find: (a) maturity of future value F after 1
year

22. Solution: (a) When t=1, the simple interest is given by
Method 1:
The maturity or future value is given by

23. Method 2
To direct solve the future value F,
Answer: The future or maturity value after 1 year is P1,002,500

24. Solved the following:
1.What are the amounts of interest and maturity
value of a loan for P 25,000 at 12% simple interest
for 5 years? Find the simple interest and maturity
value
2.How much money will you have after 4 years and 3
months if you deposited P 10,000.00 in a bank that
pays 0.5% simple interest? Find the maturity value

25. COMPOUND INTEREST

26. The following table shows the
amount at the end of each year if
principal P is invested at an annual
interest rate r compounded annually.
Computations for the example P=
100,000 and r = 5% are also
included.

27. YEAR
(t)
Principal = P
Int. rate = r, compounded
annually
Principal= P 100,000
Int. rate = 5% compounded
annually
Amount at the end of the year Amount at the end of the year
1
P x (1 + r ) = P (1 + r) 100,000 x 1.05 = 105,000
2
P (1 + r) x (1 + r ) = 105,000 x 1.05 = 110, 250
3
x (1 + r ) = 110,250 x 1.05 =115,762.5
4
121,550.63 x 1.05 = 121,550.63

28. Maturity (Future) Value and Compound Interest
where
F = maturity (future)
value at the end of the term
P = Principal
t = term/ time in years
The compound interest is given by

29. Example
Find the maturity value and the compound
interest if P10,000 is compounded annually at
an interest rate of 2% in 5 years.
Given: P = 10,000 r= 2% = 0.02 t= 5
years
Find: (a) maturity value F
(b) compound interest

30. Solution:

31. Answer: The future value F is P11,040.81 and the compound interest is P1,040.81.

32. PRESENT VALUE P AT COMPOUND
INTEREST
The present value or principal of the maturity
value F due in t years any rate r can be
obtained from the maturity value formula

33.  What is the present value of P50,000
due in 7 years if money is worth 10%
compounded annually?
Answer: The present value is P25,657.91

37. WEEK
3 - 4

39. Objectives
At the end of this week the students will be
able to:
 Define simple and general annuities.
 Computes for the future value and present value
of both simple annuities and general annuities.
Appreciate real life problems of simple and
general annuities

40. ANNUITY
 A sequence of payments made
at equal (fixed) intervals or
periods of time.

42. Term of an annuity, t
 time between the first payments interval
and last payment interval.

43. Regular or Periodic payment, R
the amount of each payment

44. Amount (Future Value) of an annuity, F
 Sum of future values of all the payments to be
made during the entire term of the annuity.
Present value of an annuity, P
 sum of present values of all the payments to be
made during the entire term of the annuity.

45. EXAMPLE 1
Mrs. Remoto likes to save 3,000 every month
₱
for 6 years in a fund that gives 9%
compounded monthly.
Solution:
The problem above, shows that the payment interval is
every month, while the interest period is compounded
monthly. Since the payment interval and the interest
period are the same, example 1 illustrates simple
annuity.

46. EXAMPLE 2
Cris started to deposit 1,000 monthly in a
₱
fund that pays 6% compounded quarterly for
15 years.
Solution: In this problem, the payment period is monthly,
and the interest period is compounded quarterly. If we
match the payment period to the interest period, the two
are different.Thus, this is an example of general annuity.

47. EXAMPLE 3
A teacher plans to save 5,000 every 6 months
₱
for 10 years in a bank that pays 0.25%
compounded monthly.
Solution: The example above, gives that the payment
period is at every 6 months, and the interest period is
compounded monthly. Comparing the two periods, we
can say that they are different. Therefore, it is general
annuity.

48. EXAMPLE 4
In order to save for her high school graduation,
Marie decided to save 2,000 at the end of each
₱
quarter. The bank pays 0.50% compounded
quarterly.
Solution: Example 4, presents that the payment
period is quarterly, and the interest period is
compounded quarterly. Since the two periods are
the same, this is simple annuity.

49. Given the following situations, illustrate and distinguish whether
it is simple annuity or general annuity.
1. Monthly payments of 3,000 for 4 years with interest rate of
₱
3% compounded monthly.
2. Semi-annual payments of 150,000 with intrest rate of 8%
₱
compounded annually for 10 years.
3. Annual payments of 20,500 with interest rate of 8.5%
₱
compounded semi-annually for 3 years.
4. Quarterly payment of 5,000 for 10 years with interest rate of
₱
2% compounded quarterly.
5. Quarterly payment of 15,000 for 10 years with interest rate of
₱
8% compounded annually.

60. Mr. Ribaya paid P200,000 as down
payment for a car. The remaining
amount is to be settled by paying
P50,000 at the end of each month for 4
years. If interest is 13.2% compounded
monthly, what is the cash price of his
car?

61. GENERAL ANNUITY
General Annuity- an annuity where the length
of the payment interval is not the same as the
length of the interest compounding period.
General Ordinary Annuity- a general annuity
in which the periodic payment is made at the end
of the payment interval

62. Examples of General annuity
Monthly installment payment of a
car, lot, or house with an interest
rate that is compounded annually.
Paying a debt semi-annually when
the interest is compounded
monthly.

64. The extra step occurs in finding j: the given interest
rate per period must be converted to an equivalent
rate per payment interval.

65. WEEK
4

66. STOCKS AND BONDS

67. ILLUSTRATING and DISTINGUISHING
STOCKS and BONDS
OBJECTIVES:
Illustrates problems related to stocks and bonds
Distinguishes between stocks and bonds
Appreciates the importance of illustrating and
distinguishing between stocks and bonds to real life
scenario.

68. History of Stocks and Bonds
The trading of goods began in the earliest civilizations.
Early merchants combined their money to outfit ships and
caravans to take goods to faraway countries. Some of these
merchants organized into trading groups. For thousand of years,
trade was conducted either by these groups or by individual
traders.
During the Middle Ages, merchants began to gather at
annual town fairs where goods from many countries were
displayed and traded. Some of these fairs became permanent,
year-round events.With merchants from many countries trading
at thee fairs, it became necessary to establish a money

69. One important annual fair took place in the city
of Antwerp, in present day Belgium. By the end of the
1400’s, this city had become a center of international
trade. A variety of financial activities took place there.
Many merchants speculated—that is, they bought goods
for certain prices and hoped that the prices would rise
later so they could make profits when they sold the
goods. Wealthy merchants or moneylenders also lent
money at high rates of interest to people who needed to
borrow it. They then sold bonds backed by these loans
and paid interest to the people who bought it.

72. Stocks
 are shares in the ownership of the
company.
Dividend
 is a share in the company’s
profit.

73. Dividend per share
 is a ratio of the dividends to the number of
shares.
Stock Market
 is a place where stocks can be bought or
sold. The stock market in the Philippines is
governed by the Philippine Stock Exchange
(PSE).

74. Market Value
 is the current price of a stock at which it
can be sold.
StockYield Ratio (current stock yield)
 is the ratio of the annual dividend per share and
the market value per share.

75. Par Value
 is the per share amount as stated on the
company’s certificate that is determined by the
company and remains stable over time.

76. Bond is the interest-bearing security
which promises to pay:
1.a stated amount of money on the maturity date
2.regular interest payments called coupon.

77. Coupon
 is periodic interest payment that the
bondholder receives during the time
between purchase date and maturity date
that is usually received semi-annually.

78. Coupon Rate (r)
 is the rate per coupon payment period.
Price of a bond (P)
 is the price of the bond at purchase time.
Fair Price of a bond
 is the present value of all cash inflows to
the bond holder.

83. Types of Bonds

84. Government Bonds
Bills: debt securities maturing in less than one year
Notes: debt securities maturing in one to 10 years
Bonds: debt securities maturing in more than 10 years

85. Municipal Bonds
 Municipal Bonds are the next
progression in terms of risk. Cities don’t
go bankrupt that often, but it can happen.
Often, the return is not taxable.

86. Corporate Bonds
 Corporate bonds are characterized by higher yields
because there is a higher risk of a company defaulting than
a government.
Zero-Coupon Bonds
 This a type of bond that makes no coupon
payments but instead is paid at the maturity of the
bond.

88. STOCKS

89. A certain financial institution declared
30,000,000.00 dividend for the common stocks. If
₱
there are a total of 700,000.00 shares of common
₱
stock, how much is the dividend per share?
Given:
Total Dividend = 30,000,000.00
₱
Total shares = 700,000.00
₱
Find:
Dividend per share

91. WEEK
5

92. BUSINESS AND
CONSUMER LOANS

93. SOLVING PROBLEMS ON BUSINESS
AND CONSUMER LOANS
OBJECTIVES
Recalls the basic concepts of business and consumer loans
Solves problems involving business and consumer loans
Chooses sensibly on the relevance of business or consumer
loan and its correct utilization

94. Identify whether the following is a
consumer or business loan.

95. 1. Mr. Agustin plans to have a barbershop.
He wants to borrow some money from the
bank in order for him to buy the equipment
and furniture for the barbershop.
2. Mr. and Mrs. Craig want to borrow money
from the bank to finance the college
education of their son.

96. 4. Mr. Alonzo wants to have some improvements
on their 10-year old house. He wants to build a
new room for their 13-year old daughter. He will
borrow some money from the bank to finance
this plan.
3. Mr. Alonzo wants to have some improvements
on their 10-year old house. He wants to build a
new room for their 13-year old daughter. He will
borrow some money from the bank to finance
this plan.

97. 5. Mr. Lim wants to have another branch for his
cellphone repair shop. He decided to apply for a
loan that he can use to pay for the rentals of a new
branch.
6. Mr. Trillas runs a trucking business. He wants to
buy three more trucks for expansion of his
business. He applied for a loan in a bank.

98. 7. Mrs. Alonzo decided to take her family for
a vacation. To cover the expenses, she
decided to apply for a loan.
8. Glenn decided to purchase a
condominium unit near his workplace. He got
a loan worth P2, 000,000.

99. Basic ideas of loans are very familiar to each
individual. Through loans, individuals,
businesspersons, entrepreneurs, and family
persons obtain support in addressing financial
constraints from different lending corporations.
Loans are not just borrowing money in a bank to
support business expansion. It also covers the use
of credit cards, amortizing appliances, and more.
Important: Once you get a loan, you should fulfill
the obligation by paying it regularly

100. Amortization method
 method of paying a loan (principal and interest) on
installment basis, usually of equal amounts at regular
intervals
Mortgage
 a loan, secured by a collateral, that the borrower is obliged
to pay at specified terms

101. Chattel mortgage
 a mortgage on a movable property
Collateral
 assets used to secure the loan. It may be a real estate or
other investments
Outstanding Balance
 any remaining debt at a specified time.

102. Business Loan
 money lent specifically for a business purpose. It may be used to
start a business or to have a business expansion.
Consumer Loan
 money lent to an individual for personal or family purpose
Term of the Loan
 time to pay the entire loan
Guarantor
 a person who guarantees that the person applying for a loan will
repay it.

103. mortgage
is a business loan or a consumer loan that is secured with a collateral. Collaterals
are assets that can secure a loan
If a borrower cannot pay the loan, the lender has a right
to the collateral. The most common collaterals are real
estate property. For business loans, equipment,
furniture, and vehicles may also be used as collaterals.
Usually, the loan is secured by the property bought. For
example,

104. if a house and lot is purchased, the purchased house and
lot will be used as a mortgaged property or a collateral.
During the term of the loan, the mortgagor, the borrower
in a mortgage, still has the right to possess and use the
mortgaged property. In the event that the mortgagor
does not make regular payments on the mortgage, the
mortgagee or the lender in a mortgage can repossess
the mortgaged property. The most common type of
mortgage is the fixed-rate mortgage wherein the interest
remains constant throughout the term of the loan.

111. Direction: Read and analyze the following situations and
do what is asked.Write your answers on your activity
sheets/activity notebook.
Loan 500,000, yearly interest 9%, payment monthly,
₱
payment period 10 years. Find the following: (Write
your answer on your activity sheets/activity notebook)
A. Periodic interest rate
B.Total number of periodic payments nt
C. Monthly amortization
D. Interest paid for the loan

112. BUSINESS LOAN
IMPORTANCE OF BUSINESS
LOAN
CONSUMER LOAN
IMPORTANCE OF
CONSUMER LOAN
Am I important to
you?
Directions: Write some important usage of business and consumer loans in your living,
how will it help you as an individual? This will serve as your performance output.

113. THANK YOU
JAMES A. PURGAS