This document outlines the topics and concepts covered in the CE 213 Engineering Economics course. It includes 17 topics related to engineering economic analysis such as simple and compound interest, annuities, depreciation, present worth analysis, and rate of return. The introduction defines engineering economy as the analysis and evaluation of economic factors that affect the success of engineering projects to ensure capital is best utilized. The document then provides detailed explanations and formulas for simple interest, discount rates, and sample problems.

1. CE 213 – ENGINEERING
ECONOMICS

2. COURSE OUTLINE
1. Simple Interest
2. Compound Interest
3. Continuous compounding
4. Annuities
5. Ordinary Annuities
6. Annuity Due
7. Equivalent Annual Cost
8. Deferred Annuity
9. Rate of Return
10. Uniform Gradient Series
11. Bonds
12. Depreciation
13. Present Worth Method
14. Annual Cost analysis
15. Capitalized Cost
16. Break even analysis
17. Perpetuity

3. INTRODUCTION
Engineering economy is the analysis and evaluation
of the factors that will affect the economic success
of engineering projects to the end that a
recommendation can be made which will insure the
best use of capital.

4. I. INTEREST AND MONEY-TIME
RELATIONSHIP
Interest
• is the amount of money paid for the use of borrowed capital or
the income produced by money that has been loaned.
• The amount of money paid for the use of money is called the
capital for a certain period of time.

5. SIMPLE INTEREST
• the interest to be paid which is proportional to the length of
time the principal is used.
• In practice, simple interest is paid on short-term loans in which
the time of the loan is measured in days.
• Principal – the amount of money used on which interest is
charge.
• Rate of Interest – the amount earned by one unit of principal
during a unit of time.
• Ordinary Simple Interest – computed on the basis of 12
months 0f 30 days each or 360 days a year.

6. SIMPLE INTEREST
• Exact Simple Interest – based on the exact number of days in a
year, 365 days for ordinary year and 366 days for a leap year.
• 1 interest period = 365 or 366 days.
Other terms:
• Discount – is the difference between the future worth and its
present worth.
• Rate of Discount – the discount on one unit of principal per unit
of time.

7. SIMPLE INTEREST
• Where: 𝐼 = interest
• 𝑃 = principal
• 𝑛 = number of interest periods
• 𝑖 = rate of interest in decimal
• 𝐹 = total amount
• FORMULAS FOR SIMPLE INTEREST
• 𝐼 = 𝑃𝑟𝑡
• 𝐹 = 𝑃 + 𝐼
• 𝐹 = 𝑃 + 𝑃𝑟𝑡
• 𝑤ℎ𝑒𝑛 𝑡 = 1 𝑎𝑓𝑡𝑒𝑟 𝑜𝑛𝑒 𝑦𝑒𝑎𝑟 , 𝐹 = 𝑃 (1 + 𝑟)

8. FORMULAS
RATE OF DISCOUNT
• 𝑑 = 𝐹 − 𝑃1
• 𝑑 = 1 −
1
( 1+𝑖)
• 𝑑 =
𝑖
1+𝑖
• Where: d = rate of discount
EQUIVALENT RATE OF INTEREST
• 𝑑 =
𝑖
1+𝑖
• 𝑑 + 𝑑𝑖 = 𝑖
• 𝑖 − 𝑑𝑖 = 𝑑
• 𝑖 1 − 𝑑 = 𝑑
• 𝑖 =
𝑑
1−𝑑
• Where: 𝑖 = rate of interest

9. SAMPLE PROBLEMS
1. A man borrowed 𝑃2,000 from a bank and promise to pay the
amount in one year. He received only the amount of 𝑃1,920 after the
bank collected an advance interest of 𝑃80.00. What was the rate of
discount and the rate of interest that the bank collected in advance?
2. A bank charges 12% simple interest on a 𝑃300.00 loan. How much
will be repaid if the load is paid back in one lump sum after three
years?
3. A deposit of 𝑃110,000 was made for 31 days. The net interest after
deducting 20% withholding tax is 𝑃890.36. Find the rate of return
annually.
4. 𝑃5,000 is borrowed for 75 days at 16% per annum simple interest.

10. 5. An Engineer Promised to pay 36,000 pesos at
the end of 90 days. He was offer a 10%
discount if he pays in 30 days. Find the rate of
interest.
6. Eng’r. Paloma borrowed money from a bank.
He received from the bank P1,340 and
promised to pay P1,500 at the end of nine
months. Determine the simple interest rate
and the corresponding discount rate or often
referred to as the “Bankers discounts”.

11. ASSIGNMENT
1. If you borrowed money from your friend with a simple interest of 12 %, find the present worth
of 𝑃50,000; which is due at the end of 7 months.
2. A price tag of 𝑃1200 is payable in 60 days but if paid within 30 days it will have a 3% discount.
Find the rate of interest.
3. It is the practice of almost all banks in the Philippines that when they grant a loan, the interest
for one year is automatically deducted from the principal amount upon release of money to a
borrower. Let us, therefore, assume that you applied for a loan with the bank and the
𝑃80,000.00 was approved at an interest rate of 14% of which 𝑃11,200.00 was deducted and you
were given a check of 𝑃68,800.00. Since you have to pay the amount of 𝑃80,000.00 one year
after, what then will be the effective interest rate?
4. A businessman wishes to earn 7% on his capital after the payment of taxes. If the income from
an available investment will be taxed at an average rate of 42%, what minimum rate of return,
before payment of taxes, must the investment offer be justified?
5. A 𝑃4,000 is borrowed for 75 days at 16% per annum simple interest. How much will be due at
the end of 75 days?

12. ASSIGNMENT
6. Agnes Abanilla was granted a loan of 𝑃20,000 by her employer CPM Industrial Fabricator and
Construction Corporation with an interest of 6% for 180 days on the principal collected in
advance. The corporation would accept a promissory note for 𝑃20,000 non-interest for 180
days. If discounted at once, find the proceeds on the note.
7. Kathy buys a television set from a merchant who asks for 𝑃1,250.00 at the end of 60 days (cash
in 60 days). Kathy wishes to pay immediately and the merchant offers to compute the cash
price on the assumption that the money is worth 8% simple interest. What is the cash price
today?
8. Find the amount due at the end of 15 months whose present value is 𝑃2000 at a 5% simple
discount.
9. What simple interest rate is equivalent to the simple discount rate of 6% in discounting an
amount of 𝑃1000 due at the end of 3 months?
10. Mr. Almagro made a money market placement of 𝑃1,000,000 for 30 days at 7.5% per year. If
the withholding tax is 20%, what is the net interest that Mr. Almagro will receive at the end of
the month?

13. • https://www.youtube.com/watch?v=mQq14QcJng4&t=1198s
• Please view this link it might help you fully understand simple interest