Lesson about market structures, cashflow, simple interest, and compound interest.

1. MARKET STRUCTURES
SIMPLE INTEREST
Prepared by:
Engr. Karl Kenneth S. Araojo / Engr. Karen Joi P. Beo
Course Instructor
ES6 – ENGINEERING ECONOMICS

8. SIMPLE INTEREST
Prepared by:
Engr. Karl Kenneth S. Araojo / Engr. Karen Joi P. Beo
Course Instructor
ES6 – ENGINEERING ECONOMICS

9. Where:
I = interest
i = rate of interest
n = number of interest period
P = principal or present worth
F = accumulated amount or future worth
𝐈𝐈 = 𝐏𝐏𝐏𝐏𝐏𝐏
𝐅𝐅 = 𝐏𝐏(𝟏𝟏 + 𝐢𝐢𝐢𝐢)
𝐅𝐅 = 𝐏𝐏 + 𝐈𝐈

11. Example 1:
Determine the ordinary simple interest
on P700 for 8 months and 25 days if the
rate of interest is 15%.

12. Example 1:
Determine the exact simple interest on
P500 for the period from January 10 to
October 28, 1996 at 16% interest.

13. Example 1:
Solution:

14. Example 2:
Solution:

15. Example 2:
Solution:

18. Republic of the Philippines
CATANDUANES STATE UNIVERSITY
Virac, Catanduanes
Prepared by:
Engr. Karl Kenneth S. Araojo / Engr. Karen Joi P. Beo
Course Instructor
ES6 – ENGINEERING ECONOMICS

19. Where:
I = interest
i = rate of interest
n = number of interest period
P = principal or present worth
F = accumulated amount or future worth
𝐈𝐈 = 𝐏𝐏𝐏𝐏𝐏𝐏
𝐅𝐅 = 𝐏𝐏(𝟏𝟏 + 𝐢𝐢𝐢𝐢)
𝐅𝐅 = 𝐏𝐏 + 𝐈𝐈

21. Republic of the Philippines
CATANDUANES STATE UNIVERSITY
Virac, Catanduanes
Prepared by:
Engr. Karl Kenneth S. Araojo / Engr. Karen Joi P. Beo
Course Instructor
ES6 – ENGINEERING ECONOMICS

22. Cash Flow Diagrams

23. Receipt (positive cash
flow or cash inflow)
Disbursement (negative cash
flow or cash outflow)
Cash Flow Diagrams
1 2 3 n

27. Example 1:

28. Five Types of Cash Flows

30. Where:
I = interest
i = rate of interest
n = number of interest periods
m = number of compounding periods
t = time
P = present worth
F = future worth
𝐅𝐅 = 𝐏𝐏(𝟏𝟏 + 𝐢𝐢)𝐧𝐧
𝐏𝐏 = 𝐅𝐅(𝟏𝟏 + 𝐢𝐢)−𝐧𝐧
𝐢𝐢 =
𝐫𝐫
𝐦𝐦
𝐧𝐧 = 𝐦𝐦 × 𝐭𝐭
Rate)
(Interest
interest)
accrued
All
(Principal
Interest +
=

32. Where:
i = interest rate per interest period
r = nominal interest rate
m = number of compounding periods
Where:
ER = effective rate
i = interest rate per interest period
r = nominal interest rate
m = number of compounding periods
𝐄𝐄𝐄𝐄 = 𝟏𝟏 +
𝐫𝐫
𝐦𝐦
𝐦𝐦
− 𝟏𝟏
𝐄𝐄𝐄𝐄 = (𝟏𝟏 + 𝐢𝐢)𝐦𝐦
−𝟏𝟏
𝐢𝐢 =
𝐫𝐫
𝐦𝐦

35. What is the effective annual
interest rate corresponds to a
nominal interest rate of 10%
compounded semi-annually.
𝐄𝐄𝐄𝐄 = 𝟏𝟏 +
𝐫𝐫
𝐦𝐦
𝐦𝐦
− 𝟏𝟏
Where:
ER = effective rate
i = interest rate per interest period
r = nominal interest rate
m = number of compounding periods
Example 2:
ER = (1 +
0.1
2
)2
- 1
ER = 0.1025 or 10.25%
Solution:

37. P = 𝑭𝑭 𝟏𝟏 +
𝐫𝐫
𝐦𝐦
−𝐦𝐦𝒕𝒕
Where:
i = interest rate per interest period
r = nominal interest rate
m = number of compounding periods
t = time
Example 2:
P = 𝑃𝑃𝑃𝑃𝑃 100,000 (1 +
0.12
2
)−2∗10
P = 𝑃𝑃𝑃𝑃𝑃 31,180.47
Solution:
How much should Engr. Cruz
deposit now, if after 10 years, this
will amount to Php100,000.
Interest rate is 12% compounded
semiannually?
P = 𝑭𝑭(𝟏𝟏 + 𝐢𝐢)−𝐧𝐧
𝐢𝐢 =
𝐫𝐫
𝐦𝐦
𝐧𝐧 = 𝐦𝐦 × 𝐭𝐭

41. Example 1:
Solution: