This document contains examples and explanations of compound interest calculations with varying compounding frequencies, including: - Example 1 shows how to calculate maturity value and interest for an amount compounded quarterly over 5 years. - Example 2 is a word problem asking to calculate the investment amount needed to reach $50,000 in 5 years at 5% compound interest. - The document also provides formulas, definitions, and a group activity with a table to practice various compound interest calculations.

1. REVIEW
What are the amounts of interest
and maturity value of a loan for
P150,000 at 𝟔
𝟏
𝟐
% simple interest
for 3 years?
ANSWERS: 𝑰𝒔 = 𝑷𝟐𝟗, 𝟐𝟓𝟎
𝑭 = 𝑷𝟏𝟕𝟗, 𝟐𝟓𝟎

2. PROBLEM
Ella and Thelma each invest P10,000 for two
years, but under different schemes. Ella earns 2%
of P10,000 the first year, which is P200, then
another P200 the second year. Thelma earns 2%
of P10,000 the first year, which P200, same as
Ella’s. But during the second year, she earns 2%
of the P10,000 and 2% of the P200 also.

3. COMPOUND INTEREST

4. OBJECTIVES
At the end of the lesson, the learner is able to:
a. compute interest, maturity value, and present
value in compound interest environment; and
b. solve problems involving compound interest.

7. EXAMPLE 1
Find the maturity value and the
compound interest if P10,000 is
compounded annually at an interest rate
of 2% in 5 years.

8. SOLUTION
Given: P= 10,000 r= 2%=0.02 t= 5 years
Find: (a) maturity value F (b) compound interest 𝑰𝒄
(a) 𝑭 = 𝑷(𝟏 + 𝒓)𝒕
= (𝟏𝟎, 𝟎𝟎𝟎)(𝟏 + 𝟎. 𝟎𝟐)𝟓
= 𝟏𝟏, 𝟎𝟒𝟎. 𝟖𝟏
(b) 𝑰𝒄 = 𝑭 − 𝑷 = 𝟏𝟏, 𝟎𝟒𝟎. 𝟖𝟏 − 𝟏𝟎, 𝟎𝟎𝟎 = 𝟏, 𝟎𝟒𝟎. 𝟖𝟏

10. EXAMPLE 2
What is the present value of P50,000
due in 7 years if money is worth 10%
compounded annually?

11. SOLUTION
Given: F= 50,000 r= 10%=0.1 t= 7 years
Find: P
𝐏 =
𝑭
(𝟏+𝒓)𝒕 =
𝟓𝟎,𝟎𝟎𝟎
(𝟏+𝟎.𝟏)𝟕 = 𝟐𝟓, 𝟔𝟓𝟕. 𝟗𝟏

12. GROUP ACTIVITY

13. -Accuracy of the answer 30 points
-Organization of the 10 points
ideas presented
-Delivery/ Presentation 10 points
TOTAL 50 points
RUBRICS

14. GROUP ACTIVITY
PRINCIPAL RATE (r) TIME (t) COMPOUND
INTEREST
MATURITY
10,000 8% 15 (1) (2)
3,000 5% 6 (3) (4)
50,000 10.5% 10 (5) (6)
(7) 2% 5 (8) 50,000
(9) 9.25% 2.5 (10) 100,000

15. PROBLEM
In order to have P50,000 in 5 years,
how much should you invest if the
compound interest is 5%?

16. PROBLEM
What are the amounts of interest and
maturity value of a loan for P20,000 at
6% compound interest for 3 years?

18. PROBLEM
Given a principal of P10,000, which of the
following options will yield greater interest after
5 years:
OPTION A: Earn an annual interest rate of 2% at
the end of the year, or
OPTION B: Earn an annual interest rate of 2% in
two portions- 1% after 6 months, and 1% after
another 6 months?

19. SOLUTION

22. COMPOUNDING MORE
THAN ONCE A YEAR

23. OBJECTIVES
At the end of the lesson, the learner is able to:
a. compute interest, maturity value, and present
value in compound interest environment; and
b. solve problems involving compound interest
when compound interest is computed more
than once a year.

24. DEFINITION OF TERMS

25. Note on rate notation: 𝒓, 𝒊𝒎
, 𝒋
Previously, 𝒓 was used to denote the interest
rate. Now that an interest rate can refer to two
rates (either nominal or rate per conversion
period), the symbols 𝒊𝒎
𝒂𝒏𝒅 𝒋 will be used
instead.

26. EXAMPLE 1

27. FORMULA

28. 𝑭 = 𝑷 𝟏 + 𝒋 𝒏
has the same structure as
𝑭 = 𝑷 𝟏 +
𝒊(𝒎)
𝒎
𝒎𝒕
where 𝒋 and
𝒊(𝒎)
𝒎
refer to the interest rate per conversion
period, 𝒏 𝒂𝒏𝒅 𝒎𝒕 refer to the number of times that is
compounded
YOU DO NOTE !

29. EXAMPLE 2
Find the maturity value and interest if P10,000 is
deposited in a bank at 2% compounded quarterly
for 5 years.

30. SOLUTION
Given: 𝑷 = 𝟏𝟎, 𝟎𝟎𝟎 𝒊𝟒
= 𝟎. 𝟎𝟐 𝒕 = 𝟓 𝒚𝒆𝒂𝒓𝒔 𝒎 = 𝟒
Find: (a) F (b) 𝑰𝒄
Compute for the interest rate in a conversion period by
𝒋 =
𝒊𝟒
𝒎
=
𝟎. 𝟎𝟐
𝟒
= 𝟎. 𝟎𝟎𝟓
Compute for the total number of conversion periods given
by
𝒏 = 𝒎𝒕 = 𝟒 𝟓 = 𝟐𝟎 𝒄𝒐𝒏𝒗𝒆𝒓𝒔𝒊𝒐𝒏 𝒑𝒆𝒓𝒊𝒐𝒅𝒔

31. Compute for the maturity value using
𝑭 = 𝑷 𝟏 + 𝒋 𝒏
= (𝟏𝟎, 𝟎𝟎𝟎) 𝟏 + 𝟎. 𝟎𝟎𝟓 𝟐𝟎
𝑭 = 𝟏𝟏, 𝟎𝟒𝟖. 𝟗𝟔
The compound interest is given by
𝑰𝒄 = 𝑭 − 𝑷 = 𝟏𝟏, 𝟎𝟒𝟖. 𝟗𝟔 − 𝟏𝟎, 𝟎𝟎𝟎 = 𝑷𝟏, 𝟎𝟒𝟖. 𝟗𝟔
SOLUTION

32. FORMULA

33. EXAMPLE 3
Find the present value of P50,000 due
in 4 years if money is invested at 12%
compounded semi-annually.

34. QUIZ
Fill in the blanks with the correct answers:
a. When money is compounded monthly, the frequency of
conversion is __________________.
b. When the annual interest rate is 16% compounded
quarterly the interest rate in a conversion period is
________________.
c. If the interest rate per conversion period is 1% and
money is compounded monthly, the nominal rate is
_______________.

35. QUIZ
d. When the term is 3 years and 6 months and money is
compounded semi-annually, the total number of
conversion periods is __________________.
e. When the total number of conversion periods is 12 and
the term is 6 years, the money is compounded
_______________________.

36. PRINCIP
AL
NOM
INAL
RATE
INTEREST
COMPOU
NDED
FREQUE
NCY OF
CONVE
RSION
INTER
EST
RATE
PER
PERIO
D
TIME IN
YEARS
TOTAL
NO. OF
CONVE
RSIONS
COMPO
UND
INTERE
ST
COMPO
UND
AMOU
NT
10,000 8% Semi-
annually
(1) (2) 15 (3) (4) (5)
3,000 5% quarterl
y
(6) (7) 6 years
and 3
months
(8) (9) (10)
(11) 12
%
monthly (12) (13) 10 (14) (15) 50,000