Power Corrupts essays

Power Corrupts essays Corruption is directly proportionate to the greed for power, and Napoleon, being a sly, selfish and witty pig, became more or less a despotic dictator of Animal Farm, who endorsed Lord Actons words, Power corrupts and absolute power corrupts absolutely. Through his use of actions, language and relationships, Napoleon became corrupt and started to take privileges for himself. He was able to disempower and dominate the animals of the farm, which only led to his increasing hunger for power. Through Napoleons actions, the discourse of power and control is evidently depicted by his use of tactics, which are features of a dictatorship, to assume his leadership and power. He took over the farm slowly by slowly, firstly privileging himself and his fellow pigs by convincing the other animals it was for their sake that the pigs ate most of the apples and drank most of the milk. We pigs are brain-workers. The whole management and organisation of this farm depends on us. Day and night we are watching over your welfare, and it is for your sake that we drink that drink and eat those apples. He did this through the use of Squealer who was a persuasive speaker, a follower and a liar. On Napoleons behalf, he told the animals that leadership was heavy responsibility, and therefore they should be thankful to Napoleon. This favoured Napoleons popularity and respect, and once he realised that the animals started listening to him, all the powers he had began to corrupt him. Napoleon also cunningly changed the commandments of Animal Farm to favour himself and ultimately gain more power. Napoleon became so corrupt in his actions he broke parts of the commandments to privilege himself and the other pigs. Nevertheless, some of the animals were disturbed when they heard that the pigs not only took their meals in the kitchen and used the drawing-room as a recreation room, but also s...

Pronouncing OE in French

Pronouncing OE in French Whether its an OE or a Å’, learning to pronounce this combination of French vowels is a little tricky. Thats because the sound can change from one word to the next, though there is a common pronunciation. This French lesson will help you navigate the complexities of OE in French words. How to Pronounce OE in French The letters OE  are usually combined into a single symbol in French: Å’ or Å“. When a pair of characters is used in such a way, it is called a digraph. The Å’ is pronounced more or less according to the same rules as EU. In general, if its in an open syllable, it sounds like the U in full: listen.  In a closed syllable, it is pronounced with the mouth just a little more open:  listen. There are quite a few exceptions to this, however. It is important to use a dictionary when trying to determine the pronunciation of any word with OE. You will also find Å’ in words that would otherwise begin with the combination EUI. It will look like this Å’IL and sounds like the OO in good followed by a Y sound. French Words With OE To practice your pronunciation of Å’, give these simple words a try. Click on the word to hear the correct pronunciation and try to repeat it. Å“uf  (egg)Å“ufs  (eggs)sÅ“ur  (sister) How to Type the Å’ When youre typing out French words, how do you type the digraph? There are a few ways to go about it and which you choose will depend on how often you use special characters on your computer. Your options include an international keyboard, which can be as simple as a setting in your operating system. If you use these characters on a very limited basis, your better option may be to  learn the ALT codes. To type Å“ or Å’, on a standard US-English keyboard, you will need the keyboard shortcut. For Windows, this is ALT 0156 for the lowercase and ALT 0140 for the uppercase.For Mac, it is typically ALT q and the shift key transforms it into upper case (OS Sierra may be slightly different).

Eng Essay Example | Topics and Well Written Essays - 750 words

Eng - Essay Example Campus learning has its own exclusive benefits which cannot be denied. In this paper I will argue that campus learning is very important for college students as compared to online learning, while keeping in view my own experience of college campus. When I joined my college, I met many other students; and thus, started socializing with my peers, which is an integral part of personality development. My personality has groomed a lot after I have joined my college. I know this when I compare myself to when I was in school. I believe that in campus learning, college students come to know how to behave in classrooms; how to show respect to teachers; how to deal with peers; and, how to show discipline while learning. This socializing is beneficial for them in both short and long terms because they learn how to deal with life and its problems and how to cope with relationships. I learned how to communicate with my teachers and friends, which benefitted me in my personal life as well. Hence, campus learning teaches effective relationship management which cannot be learned through online learning. Campus learning makes the students follow the deadlines in a better way, and they learn how to follow a set routine pattern for their studies. When I joined college, one of my friends who is an online student convinced me that college campus environment is very strict and makes the student follow the schedules forcibly. However, my experience has been different. I have been able to set my routine in a very effective manner. Online learning does not provide the students with these opportunities, because they tend to be relaxed since they do not have to confront teacher’s remarks and class fellows’ comments’ if they do not meet a deadline or are not dressed up neatly, and etcetera. Hence, campus learning teaches discipline in a much better way. I have learnt how to neatly dress up, how to convey my ideas face-to-face, and how to behave in groups and teams. I could never have learnt these important competencies in online learning. Moreover, communicating effectively is the key to success for me and for the rest of the world too. I did not join online learning because of communication barriers like slow internet speed and server breakdown between the teacher and students. I wanted to talk to my teachers and peers. For me, visual understanding of others’ feelings is very important. When I joined my college campus, I could freely share my ideas inside the classroom setting and discuss the concepts. Teachers came to know me personally. There is always an interactive atmosphere which enhances learning. In campus learning, there are hands-on labs in traditional classroom learning that are crucial for development of skill sets (Tabor 47). I am sure that I have made the right decision of joining college campus because online learning tends to isolate the students inside the territory of their homes, and so, they remain inside their study rooms for hours and hours, which creates a bad impact upon their personalities on the whole. This isolation leads to depression and anxiety in the individual leading to the development of negative behavior. Campus learning does not isolate the students in this way, and they can always share their problems with their peers which is an excellent way to ward off their depression. I have had very positive experience of

Global Intervention Essay Example | Topics and Well Written Essays - 250 words

Global Intervention - Essay Example US interventions, based on the imposition of democracy on unwilling nations during the Cold War, led to such entanglements as Vietnam. The intervention in Afghanistan may be justified in the light of the WTC attacks. However, the contemporary intervention in Uganda merely uses Kony and his Lord’s Resistance Army as pretext to appropriate control of Ugandan oil reserves. If US global intervention is justified, it logically follows that all other countries also have the right to intervene in the United States to protect their own economic or political interests. Of course, the US remains impervious to such retaliatory action because its status as a superpower, with unmatched military and economic might, puts it beyond the reach of most nations. This state of affairs is the cause of the growing resentment against the strong-arm tactics employed by America. Markets, investment opportunities, and natural resources are crucial to all nations. These do not constitute justifiable conditions for global interventions. The days of colonization and empire are irrevocably gone. It is time the United States realizes that assuming the role of a Global Policeman, wielding the big stick to impose its writ on reluctant nations, will not contribute to national interest. This is particularly relevant in these times of economic depression, when strong relationships with other nations, based on mutual respect of equal partners, will beast contribute to US

Five Things Your Fingers Tell About You Essay Example for Free

Five Things Your Fingers Tell About You Essay Purpose: To inform the audience about what their finger length tells about them. Theme: How to know more about yourself using your ring and index finger. Thesis Statement: Finger length cannot be an indicator of what or who you really are because it just informs us more about ourselves through our fingers length. Introduction: Hello there! Guys, did you know that your index finger is the best one to lose? Although it seems you need this finger more than any other, hand surgeons say that this is the best one to lose if you had a choice given by terrorists. But wait! Don’t lose it yet! Listen to me first and look at your fingers. Did you know that the length of your fingers can indicate how healthy you are, your sporting ability and even your sexuality? Body: It is thought that prenatal androgens affect the genes responsible for the development of fingers, toes and the reproductive system. High levels of androgens, such as testosterone increase the length of the fourth finger in comparison to the second finger. It is also important in the development of masculine characteristics such as aggression and strength. Evidence is growing that the length of your fingers can tell you a lot about yourself. So here are the five things your fingers say about you. Your sexuality. The most obvious thing the length of your finger tells you is your sexuality. Scientist from the University of California taught that higher levels of androgen in the womb influence both finger length and sexual orientation. According to the study, mens ring fingers are normally longer than their index fingers, while in women, ring fingers are normally shorter or tend to be the same length as their index fingers. A study also showed that lesbian women also tended to have more â€Å"masculine arrangement†-that is, they had shorter index fingers. Comparison between all men showed no differences. Only gay men with several older brothers had an unusually â€Å"masculine† finger ratio-in other words, they had significantly shorter index fingers. Homosexual men without older brothers had finger length ratios indistinguishable from heterosexual men, indicating that factors other than hormones-such as genetic influences-also contribute to sexual orientation. That you make a lot of money, or not. Researchers in Cambridge discovered that stock traders with long ring fingers made more up to 11 times their earnings than colleagues with shorter ring fingers. Again, this can be chalked up to higher testosterone, which can make men more assertive and likely to take risks. According to a new study, having a relatively long ring finger, augurs well for success in those high-stress financial arenas where fast thinking, good reflexes and good-old fashioned guts matter most. A long ring finger indicate greater exposure to testosterone in the womb which in turn gives â€Å"high-frequency† traders a biological leg up by encouraging the development of the right mix of mental attitude and physical skills for making money in a cutthroat business. How good you are at sports. Men and women whose ring fingers are longer that their index fingers are more likely to have an aptitude for sports. The correlation is particularly strong says finger expert Dr. John Manning, in middle and long distance runners. Those who have short index fingers may also do better in playing tennis and soccer and they are also more likely to be left-handed. That you are good at math. It has long been known that boys tend to do better on math tests while girls do better at writing, reading and verbal tests. Scientist behind this study suggests that measurement of finger length could help predict how well children will do in math and literacy. Scientist at the University of Bath found that children with masculine ring fingers- that is, long ring finger than their index fingers, do better in math tests than in literacy tests. Alternately, children whose second and fourth fingers are the same length perform better in literacy tests. Again, this is because of hormones called testosterone and estrogen. Testosterone lengthens ring fingers and is associated with greater math and spatial functions, while estrogen lengthens index fingers and is associated with greater verbal skills. If you are prone to arthritis. Researchers at the University of Nottingham have now discovered that arthritis could be connected to the hands. Having a ring finger longer than an index finger nearly doubles the chance of developing osteoarthritis in the knees and hips. And according to the study, the risk was grater in women than in men. Conclusion: Fingers are really significant to all of us and it is impossible for us to live without them. These things are facts gathered from the studies that can help us to know and inform ourselves better. But still, you yourself can define what or who you really are even without knowing these facts. These ideas that I have brought onto you are just guidelines. Your finger length differences won’t exactly define who you really are. Our health always depends on our lifestyle. Our future is the reward or the consequences of what we are doing in our present, it is in our hands not on our fingers. Let me end this speech with a quote by Fred Dehner, â€Å"The best helping hand that you would ever receive is the one at the end of your own arm.†

Analysis Of O. Henrys art And The Bronco :: essays research papers

Art and the Bronco summary O. Henry’s "Art and the Bronco" tells the story of Lonny Briscoe, a cowboy who is also an aspiring artist. It follows his quest to sell his first painting to the state legislature; to have it hung in the capital building. Lonny sees the sale of the painting as validation of his talent and worth as a painter. What he ends up learning is that the actual value of the painting turns out to be secondary to what other feel they can gain from it. The story takes place in San Saba, a place trying to shed its image of "†¦barbarism, lawbreaking, and bloodshed." It presents itself as a much more refined place now, one which is now safe for tourism and business. The Legislature was lending subsidy to the arts to enhance this image. Lonny’s painting is hanging in the capital building. It is a large painting "†¦one might even say panorama," depicting a cowboy and steer, hung in a gilt frame. At the capital, we are introduced to senators Kinney and Mullens, who only care about getting what they want from each other and getting re-elected. They see Lonny’s painting as a means to both ends. In the beginning, Kinney sees nothing of value in Lonny’s picture. In fact, he implies that it is awful, saying that he "†¦wouldn’t give six bits for the picture without the frame." Mullens agrees with Kinney’s assessment of the painting. He says that the painting is secondary to the artist—the grandson of Lucien Briscoe, a legendary local hero who is said to have "†¦carved the state out of the wilderness." The painting quickly fades to the background as both the senators see that pushing the state to give this hero’s grandson money is a quick way to gain public favor. Lonny’s cowboy friends ride into town to push the paintings merits as well, adding their admiration for the gilt frame, so big and beautiful. They are very simple and undereducated, as evidenced by Skinny Rogers’ act of leaping away from the painting yelling "†¦Jeeming Cristopher! Thought that rattler was a gin-u-ine one," and are not as concerned about the merits of the painting as they are with the idea of one of their own getting money for it. They always speak loudly when they think there might be someone around to whom their comments might be "†¦profitably addressed."

Education Insurance Awareness Essay

An Overview In 1965, Yarri proposed the use of life insurance to insure against lifetime uncertainty resulting for the mortality risk of individuals. Premature death of a family head can bring serious financial consequences for the surviving family members because the family head’s earnings are lost forever leaving unfulfilled financial obligations, such as dependents to support, children to educate, and a mortgage to repay. Life insurance allows individuals and families to share the risk of premature death with many others and to alleviate the financial loss from the premature death of the rimary wage earner (Garman & Forgue, 2006). The purchase of life insurance is one of the most important purchasing decisions for individuals and families (Anderson & Nevin, 1975) and it is a critical component of a long-term financial plan (Devaney & Keaton, 1994). 2). Introduction to Child Education Insurance Policy A child education policy is a life insurance product specially designed as a savings tool to provide an amount of money when a child reaches the age for entry into college normally 18 years old and above. The funds can be utilised to partly meet a child’s higher education expenses. Also, if purchaser opts for a payor benefit rider, an education policy provides the assurance that, in the event of an untimely demise of the parents or legal guardian, the child will have access to funds to help finance his or her education expenses. Under a child education policy, the child is the life assured, while the parent or legal guardian is the policy owner. 3). Types of child education policies available in life insurance market. There are two main types, i. . an endowment or investment-linked policy. The difference between the two lies in the structure as well as the nature of investments. 3. 1) Endowment policy is an endowment policy combines a savings component with protection coverage. Endowment policy may be either participating or non-participating. As the name implies, non-participating policy do not participate in the life insurance fund’s profits but all insurance benefits are fully guaranteed. On the other hand, for participating policy, a portion of insurance benefits are guaranteed. However, the ultimate amount of benefits at maturity is not guaranteed as these depend on the performance of the insurance company’s participating life insurance fund. 3. 2) Investment-linked policy is an investment-linked policy combines the elements of investment and protection based on your requirement as the policy owner. It offers flexibility as you are able to increase or top-up your monthly premium contribution as your income improves. If you wish to be more aggressive with the instruments of investment, an investment-linked policy will also allow you to choose the types of funds your money will be invested in. However, like any other similar investment, there are higher risks involved and there are no guarantees on the returns, which may be higher or lower than projected. 4). Research Background An increasing trend of education expenses to enter college or university nowadays, a lot of parents using financial sources such as Employee Providence Fund or rely on borrowing from Perbadanan Tabung Pendidikan Tinggi Negara to afford the study expenses of their son after leaving secondary school for a higher level of study. As an alternative source of financial protection against high education expenses, parents can purchase an education insurance starting from their children young age. Compare with withdrawal of lump sum of money from EPF (Employee Providence Fund) or make borrowing from PTPTN (Perbadanan Tabung Pendidikan Tinggi Negara), a parents just need to pay for a small amount of premium and parents as a payer can be covered by insurance in case death or total permanent disablement occurred by paying for an extra insurance rider in the particular education insurance policy. Therefore, this research carried out to examine the level of awareness among parents in Sibu Region towards education insurance provide by insurance companies in Malaysia. This thesis aims to examine both the type and amount of life insurance purchased by households. To this end, comprehensive models of households’ demand for life insurance were developed, which included demographic variables (age, education, employment status, health status, number of children, marital status, and race), economic and assets variables (income, homeownership, debts, as well as portfolio elements such as liquid assets, certificates of deposit, mutual funds, bonds, stocks, individual retirement accounts, annuities, other miscellaneous financial assets, and nonfinancial assets), and psychographic variables (attitude toward risk, attitude toward leaving a bequest, and one’s expected life expectancy). The effects of these factors on either term or cash value life insurance purchased by households were examined separately. Research Objective General objective To examine the parent’s awareness towards education insurance. Specific Objective 1). To investigate whether parents had purchase education insurance or not for their children at their young age. 2). To identify from which channel of information that made parents aware of education insurance. 3). To identify whether insurance industry playing an effective role in promoting education insurance in life insurance market. ). To examine parents interest towards education insurance products administered by insurance company in insurance market. 5). The main purpose of this study is to examine whether demographic factors influence the purchase of education insurance among parents in Sibu Region. Research question 1). Do you know there is education insurance product in insurance market? 2). Had you purchased any education insur ance from any insurance company for your children? 3). Had any insurance agent approach or introduce and give explanation to you regarding education insurance? 4). Are you willing to purchase any education insurance for your children? 5). what type sources of information you needed to enhance the knowledge regarding education insurance? Problem statement Financing child’s education is one of the major investments that any wise parent is prepared to undertake. A sound university education is not only among the basic requirements to establish a good career; it can also form the foundation of your child’s intellectual maturity for life. We all start learning since birth and the brief period of academic education in our lives represents another landmark in a life-long learning process. But given the high cost of education and the competition to enter well-known universities, it is necessary to have an investment plan to fund our children’s brief sting of three to four years in university. With the limited places available in local universities, many Malaysian students have wisely invested in university education abroad. Faced with the rising costs of overseas university education, how can parents save and invest to finance the tuition fees, let alone the living costs. The depegging of the ringgit from the U. S. dollar last year is a welcome move for many Malaysian parents because under the flexible exchange rate system, the ringgit is likely to appreciate over the long term. This will help Malaysians reduce the cost of overseas education in popular countries such as the U. K. , U. S. and Australia (Charles Goh, www. fimm. com. my/pdf/investor/articles/09). One of the biggest worries for parents nowadays is how to fund their children’s education, which does not come cheap. In addition, as with everything else, education expenses, is it in foreign and local colleges/universities, private primary and secondary schools are expected to trend upwards in future (Elaine Ang, http://thestar. com. my/ September 18, 2010). The trend is upwards as far as education costs are concerned. In predicting the future, we can only use assumptions such as cost and inflation factors in child education planning. The general increase for local studies is about 3% per year and foreign about 5% and this applies to a general business degree of three years (Mike Lee, CTLA Financial Planners Sdn Bhd managing director, 2010). An average increase of between 5% to 7% annually in education costs for studies locally and in countries such as Britain, United States, Australia, Canada and Singapore excluding foreign exchange rate fluctuations. Moreover, there are certain years where the increase can be in a lump sum instead of percentage depending on the circumstances. (Matthew Gan, E. T. Education Services Sdn Bhd managing director, 2010). Some of the common mistakes parents make when saving for their child’s education fund are starting too late, saving without investing and not considering foreign exchange fluctuations for those who aim to send their children overseas. It is important to determine what the education costs are in current value and identify a suitable savings and investment vehicle. Some parents don’t even have a clue how much education costs (Yap Ming Hui, Whitman Independent Advisors Sdn Bhd managing director, 2010). Save and invest your money as early as possible. Let your money grow with your child, school fees for primary and secondary education range from RM15,000 to RM17,000 per annum with an average 10% increase in fees every two years (Rina Thiagu-Kler, Marketing manager Sri KDU, 2010). Because of less study and difficulties to obtain data regarding education insurance demand in Sibu Region. A brief interview conducted with Mr. Ten Kim Loong, Unit Manager of Kumpulan Elite Ten from Etiqa insurance agency on 2nd December 2011 where he indicated that most of the insurance product demanded by household within Sibu region is medical card and personal accident policy, it is because the premium affordable by policyholder, moreover among the clients approached did not know what policy to purchase and how much sum insured should be enough for protection need†. A discussion session also conducted with Mohamad Faizuli Bin Abd Karim, a financial planner from Takaful Ikhlas Sdn Bhd reveal that among the prospects that approached by him saying that they are not interested in any of insurance products and they worried the premium payment can become an extra expenses as per we noticed the living standard and price of basic necessity good are very high nowadays. The Breakdown of Schooling Expenditure As shown in Table 2, the average cost of schooling overall was found to be RM1,782 per student per year. The cost in rural areas which averaged RM1,590 was about 22 per cent lower than urban areas.

Engineering Economics

Eng ineeri ng Economy Third Edition Leland T. Blank, P. E. Department of Industrial Engineering Assistant Dean of Engineering Texas A & M University Anthony J. Tarquin, P. E. Department of Civil Engineering Assistant Dean of Engineering The University of Texas at EI Paso McGraw-Hill Book Company New York S1. Louis San Francisco Auckland Bogota Caracas Colorado Springs Hamburg Lisbon London Madrid Mexico Milan Montreal New Delhi Oklahoma City Panama Paris San Juan Silo Paulo Singapore Sydney Tokyo Toronto 4 Level One 1. Define and recognize in a problem statement the economy symbols P, F, A, n, and i. 1. 6 Define cash flow, state what is meant by end-of-period convention, and construct a cash-flow diagram, given a statement describing the amount and times of the cash flows. Study Guide 1. 1 Basic Terminology Before we begin to develop the terminology and fundamental concepts upon which engineering economy is based, it would be appropriate to define what is meant by engineering economy . In the simplest terms, engineering economy is a collection of mathematical techniques which simplify economic comparisons. With these techniques, a rational, meaningful approach to evaluating the economic aspects of different methods of accomplishing a given objective can be developed. Engineering economy is, therefore, a decision assistance tool by which one method will be chosen as the most economical one. In order for you to be able to apply the techniques, however, it is necessary for you to understand the basic terminology and fundamental concepts that form the foundation for engineering-economy studies. Some of these terms and concepts are described below. An alternative is a stand-alone solution for a give situation. We are faced with alternatives in virtually everything we do, from selecting the method of transportation we use to get to work every day to deciding between buying a house or renting one. Similarly, in engineering practice, there are always seveffl ways of accomplishing a given task, and it is necessary to be able to compare them in a rational manner so that the most economical alternative can be selected. The alternatives in engineering considerations usually involve such items as purchase cost (first cost), the anticipated life of the asset, the yearly costs of maintaining the asset (annual maintenance and operating cost), the anticipated resale value (salvage value), and the interest rate (rate of return). After the facts and all the relevant estimates have been collected, an engineering-economy analysis can be conducted to determine which is best from an economic point of view. However, it should be pointed out that the procedures developed in this book will enable you to make accurate economic decisions only about those alternatives which have been recognized as alternatives; these procedures will not help you identify what the alternatives are. That is, if alternatives ,4, B, C, D, and E have been identified as the only possible methods to solve a Particular problem when method F, which was never recognized as an alternative, is really the most attractive method, the wrong decision is certain to be made because alternative F could never be chosen, no matter what analytical techniques are used. Thus, the importance of alternative identification in the decision-making process cannot be overemphasized, because it is only when this aspect of the process has been thoroughly completed that the analysis techniques presented in this book can be of greatest value. In order to be able to compare different methods for accomplishing a given objective, it is necessary to have an evaluation criterion that can be used as a basis Terminology and Cash-Flow Diagrams 5 for judging the alternatives. That is, the evaluation criterion is that which is used to answer the question â€Å"How will I know which one is best? Whether we are aware of it or not, this question is asked of us many times each day. For example, when we drive to work, we subconsciously think that we are taking the â€Å"best† route. But how did we define best? Was the best route the safest, shortest, fastest, cheapest, most scenic, or what? Obviously, depending upon which criterion is used to identify the best, a dif ferent route might be selected each time! (Many arguments could have been avoided if the decision makers had simply stated the criteria they were using in determining the best). In economic analysis, dollars are generally used as the basis for comparison. Thus, when there are several ways of accomplishing a given objective, the method that has the lowest overall cost is usually selected. However, in most cases the alternatives involve intangible factors, such as the effect of a process change on employee morale, which cannot readily be expressed in terms of dollars. When the alternatives available have approximately the same equivalent cost, the nonquantifiable, or intangible, factors may be used as the basis for selecting the best alternative, For items of an alternative which can be quantified in terms of dollars, it is important to recognize the concept of the time value of money. It is often said that money makes money. The statement is indeed true, for if we elect to invest money today (for example, in a bank or savings and loan association), by tomorrow we will have accumulated more money than we had originally invested. This change in the amount of money over a given time period is called the time value of money; it is the most important concept in engineering economy. You should also realize that if a person or company finds it necessary to borrow money today, by tomorrow more money than the original loan will be owed. This fact is also explained by the time value of money. The manifestation of the time value of money is termed interest, which is a measure of the increase between the original sum borrowed or invested and the final amount owed or accrued. Thus, if you invested money at some time in the past, the interest would be Interest = total amount accumulated – original investment (1. 1) On the other hand, if you borrowed would be Interest money at some time in the past, the interest (1. 2) = present amount owed – original loan In either case, there is an increase in the amount of money that was originally invested or borrowed, and the increase over the original amount is the interest. The original investment or loan is referred to as principal. Probs. 1. 1 to 1. 4 1. 2 Interest Calculations When interest is expressed as a percentage of the original amount per unit time, the result is an interest rate. This rate is calculated as follows: . Percent interest rate = interest accrued per unit time 00% .. I x 1 0 origma amount (1. 3) 6 Level One By far the most common time period used for expressing interest rates is 1 year. However, since interest rates are often expressed over periods of time shorter than 1 year (i. e. 1% per month), the time unit used in expressing an interest rate must also be identified and is termed an interest period. The following two examples illustrate the computation of interest rate. Example 1. 1 The Get-Rich-Quick (GRQ) Company invested $100,000 on May 1 and withdrew a total of $106,000 exactly one year later. Compute (a) the interest gained from the original investment and (b) the interest rate from the investment. Solution (a) Using Eq. ( 1. 1), Interest = 106,000 – 100,000 = $6000 (b) Equation (1. 3) is used to obtain Percent interest rate = 6000 per year 100,000 x 100% = 6% per year Comment For borrowed money, computations are similar to those shown above except that interest is computed by Eq. (1. 2). For example, if GRQ borrowed $100,000 now and repaid $110,000 in 1 year, using Eq. (1. 2) we find that interest is $10,000, and the interest rate from Eq. (1. 3) is 10% per year. Example 1. 2 Joe Bilder plans to borrow $20,000 for 1 year at 15% interest. Compute (a) the interest and (b) the total amount due after 1 year. Solution (a) Equation (1. 3) may be solved for the interest accrued to obtain Interest = 20,000(0. 15) = $3000 (b) Total amount due is the sum of principal and interest or Total due Comment = 0,000 + 3000 = $23,000 Note that in part (b) above, the total amount due may also be computed as Total due = principal(l + interest rate) = 20,000(1. 15) = $23,000 In each example the interest period was 1 year and the interest was calculated at the end of one period. When more than one yearly interest period is involved (for example, if we had wanted to know the amount of interest Joe Bilder would owe on Terminology and Cash-Flow Diagrams 7 the above loan after 3 years), it becomes necessary to determine whether the interest . payable on a simple or compound basis. The concepts of simple and compound interest are discussed in Sec. . 4. Additional Examples 1. 12 and 1. 13 Probs. 1. 5 to 1. 7 1. 3 Equivalence The time value of money and interest rate utilized together generate the concept of equivalence, which means that different sums of money at different times can be equal in economic value. For example, if the interest rate is 12% per year, $100 today (i. e. , at present) would be equivalent to $112 one year from today, since mount accrued = 100 =$112 Thus, if someone offered you a gift of $100 today or $112 one year from today, it would make no difference which offer you accepted, since in either case you would have $112 one year from today. The two sums of money are therefore equivalent to each other when the interest rate is 12% per year. At either a higher or a lower interest rate, however, $100 today is not equivalent to $112 one year from today. In addition to considering future equivalence, one can apply the same concepts for determining equivalence in previous years. Thus, $100 now would be equivalent to 100/1. 12 = $89. 29 one year ago if the interest rate is 12% per year. From these examples, it should be clear that $89. 29 last year, $100 now, and 112 one year from now are equivalent when the interest rate is 12% per year. The fact that these sums are equivalent can be established by computing the interest rate as follows: 112 100 = 1. 12, or 12% per year and 8~~~9 = 1. 12, or 12% per year The concept of equivalence can be further illustrated by considering different loan-repayment schemes. Each scheme represents repayment of a $5000 loan in 5 years at 15%-per-year interest. Table 1. 1 presents the details for the four repayment methods described below. (The methods for determining the amount of the payments are presented in Chaps. 2 and 3. ) †¢ Plan 1 a interest or principal is recovered until the fifth year. Interest accumulates each year on the total of principal and all accumulated interest. †¢ Plan 2 The accrued interest is paid each year and the principal is recovered at the end of 5 years. †¢ Plan 3 The accrued interest and 20% of the principal, that is, $1000, is paid each year. Since the remaining loan balance decreases each year, the accrued interest decreases each year. + 100(0. 12) = 100(1 + 0. 12) = 100(1. 12) 8 Level One Table 1. 1 Different repayment schedules of $5,000 at 15% for 5 years (1) End of year (2) = 0. 15(5) Interest for year (3) = (2) + (5) Total owed at end of year (4) Payment per plan (3) – (4) Balance after payment (5) Plan 1 0 1 2 3 4 5 Plan 2 0 1 2 3 4 5 Plan 3 0 1 2 3 4 5 Plan 4 0 1 2 3 4 5 $ 750. 00 862. 50 991. 88 1,140. 66 1,311. 76 5,750. 00 6,612. 50 7,604. 38 8,745. 04 10,056. 80 0 0 0 0 10,056. 80 $10,056. 80 $ $5,000. 00 5,750. 00 6,612. 50 7,604. 38 8,745. 04 0 $750. 00 750. 00 750. 00 750. 00 750. 00 $5,750. 00 5,750. 00 5,750. 00 5,750. 00 5,750. 00 $ 750. 00 750. 00 750. 00 750. 00 5,750. 00 $8,750. 00 $5,000. 00 5,000. 00 5,000. 00 5,000. 00 5,000. 00 0 $750. 00 600. 00 450. 00 300. 00 150. 00 $5,750. 00 4,600. 00 3,450. 00 2,300. 00 1,150. 00 $1,750. 00 1,600. 00 1,450. 0 1,300. 00 1,150. 00 $7,250. 00 5,000. 00 4,000. 00 3,000. 00 2,000. 00 1,000. 00 0 $750. 00 638. 76 510. 84 363. 73 194. 57 $5,750. 00 4,897. 18 3,916. 44 2,788. 59 1,491. 58 $1,491. 58 1,491. 58 1,491. 58 1,491. 58 1,491. 58 $7,457. 90 $5,000. 00 4,258. 42 3,405. 60 2,424. 86 1,297. 01 0 †¢ Plan 4 Equal payments are made each year with a portion going toward princi- pal recovery and the remainder covering the accrued interest. Since the loan balance decreases at a rate which is slower than in plan 3 because of the equal end-of-year payments, the interest decreases, but at a rate slower than in plan 3. te that the total amount repaid in each case would be different, even though each repayment scheme would require exactly 5 years to repay the loan. The difference in the total amounts repaid can of course be explained by the time value of money, since the amount of the payments is different for each plan. With respect to equivalence, the table shows that when the interest rate is 15% per year, $5000 at time 0 is equivalent to $10,056. 80 at the end of year 5 (plan 1), or $750 per year for 4 years and $5750 at the end of year 5 (plan 2), or the decreasing amounts shown in years 1 through 5 (plan 3), or $1,491. 8 per year for 5 years (plan 4). Using the formulas developed in Chaps. 2 and 3, we could easily show that if the payments in Terminology and Cash-Flow Diagrams 9 each plan (column 4) were reinvested at 15% per year when received, the total amount of money available at the end of year 5 would be $10,056. 80 from each repayment plan. Additional Examples 1. 14 and 1. 15 Probs. 1. 8 and 1. 9 1. 4 Simple and Compound Interest The concepts of interest and interest rate were introduced in Sees. 1. 1 and 1. 2 and ed in Sec. 1. 3 to calculate for one interest period past and future sums of money equivalent to a present sum (principal). When more than one interest period is involved, the terms simple and compound interest must be considered. Simple interest is calculated using the principal only, ignoring any interest that was accrued in preceding interest periods. The total interest can be computed using the relation Interest = (principal)(number of periods)(interest rate) = Pni (1. 4) Example 1. 3 If you borrow $1000 for 3 years at 14%-per-year simple interest, how much money will you owe at the end of 3 years? Solution The interest for each of the 3 years is = Interest per year 1000(0. 14) = $140 Total interest for 3 years from Eq. (1. 4) is Total interest = 1000(3)(0. 4)= $420 Finally, the amount due after 3 years is 1000 + 420 Comment = $1420 The $140 interest accrued in the first year and the $140 accrued in the second year did not earn interest. The interest due was calculated on the principal only. The results of this loan are tabulated in Table 1. 2. The end-of-year figure of zero represents th~ present, th at is, when the money is borrowed. Note that no payment is made by the borrower until the end of year 3. Thus, the amount owed each year increases uniformly by $140, since interest is figured only on the principal of $1000. Table 1. 2 Simple-interest (1) (2) computation (3) (4) (2) + (3) Amount owed (5) End of year 0 1 2 Amount borrowed $1,000 Interest Amount paid 3 $140 140 140 $1,140 1,280 1,420 $ 0 0 1,420 10 Level One In calculations of compound interest, the interest for an interest period is calculated on the principal plus the total amount of interest accumulated in previous periods. Thus, compound interest means â€Å"interest on top of interest† (i. e. , it reflects the effect of the time value of money on the interest too). Example 1. 4 If you borrow $1000 at 14%-per-year compound interest, instead of simple interest as in the preceding example, compute the total amount due after a 3-year period. Solution The interest and total amount due for each year is computed as follows: Interest, year 1 = 1000(0. 14) = $140 Total amount due after year 1 = 1000 + 140 = $1140 Interest, year 2 = 1140(0. 14) = $159. 60 Total amount due after year 2 = 1140 + 159. 60 = $1299. 60 Interest, year 3 = 1299. 60(0. 14)= $181. 94 Total amount due after year 3 = 1299. 60 + 181. 94 = $1481. 54 Comment The details are shown in Table 1. 3. The repayment scheme is the same as that for the simple-interest example; that is, no amount is repaid until the principal plus all interest is due at the end of year 3. The time value of money is especially recognized in compound interest. Thus, with compound interest, the original $1000 would accumulate an extra $1481. 54 – $1420 = $61. 54 compared with simple interest in the 3-year period. If $61. 54 does not seem like a significant difference, remember that the beginning amount here was only $1000. Make these same calculations for an initial amount of $10 million, and then look at the size of the difference! The power of compounding can further be illustrated through another interesting exercise called â€Å"Pay Now, Play Later†. It can be shown (by using the equations that will be developed in Chap. ) that at an interest rate of 12% per year, approximately $1,000,000 will be accumulated at the end of a 40-year time period by either of the Table 1. 3 Compound-interest (1) (2) computation (3) (4) = (2) + (3) (5) End of year 0 1 2 3 Amount borrowed $1,000 Interest Amount owed $1,140. 00 1,299. 60 1,481. 54 Amount paid $140. 00 159. 60 181. 94 $ 0 0 1,481. 54 Terminology and Cash-Flow Diagrams 11 – llowing investment schemes: †¢ Plan 1 Invest $2610 each year for the first 6 years and then nothing for the next 34 years, or †¢ Plan 2 Invest nothing for the first 6 years, and then $2600 each year for the next 34 years!! ‘ote that the total investment in plan 1 is $15,660 while the total required in plan _ to accumulate the same amount of money is nearly six times greater at $88,400. Both the power of compounding and the wisdom of planning for your retirement at he earliest possible time should be quite evident from this example. An interesting observation pertaining to compound-interest calculations in-olves the estimation of the length of time required for a single initial investment to double in value. The so-called rule of 72 can be used to estimate this time. The rule i based on the fact that the time required for an initial lump-sum investment to double in value when interest is compounded is approximately equal to 72 divided by the interest rate that applies. For example, at an interest rate of 5% per year, it would take approximately 14. 4 years (i. e. , 72/5 = 14. 4) for an initial sum of money to double in value. (The actual time required is 14. 3 years, as will be shown in Chap. 2. ) In Table 1. 4, the times estimated from the rule of 72 are compared to the actual times required for doubling at various interest rates and, as you can see, very good estimates are obtained. Conversely, the interest rate that would be required in order for money to double in a specified period of time could be estimated by dividing 72 by the specified time period. Thus, in order for money to double in a time period of 12 years, an interest rate of approximately 6% per year would be required (i. e. , 72/12 = 6). It should be obvious that for simple-interest situations, the â€Å"rule of 100† would apply, except that the answers obtained will always be exact. In Chap. 2, formulas are developed which simplify compound-interest calculations. The same concepts are involved when the interest period is less than a year. A discussion of this case is deferred until Chap. 3, however. Since real-world calculations almost always involve compound interest, the interest rates specified herein refer to compound interest rates unless specified otherwise. Additional Example 1. 16 Probs. 1. 10 to 1. 26 Table 1. 4 Doubling time estimated actual time from rule of 72 versus Doubling lime, no. of periods Interest rate, % per period 1 Estimated from rule 72 Actual 70 35. 3 14. 3 7. 5 2 5 10 20 40 36 14. 4 7. 2 3. 6 1. 8 3. 9 2. 0 12 Level One 1. 5 Symbols and Their Meaning The mathematical symbols: relations sed in engmeenng economy employ the following P = value or sum of money at a time denoted as the present; dollars, pesos, etc. F A n i = value or sum of money at some future time; dollars, pesos, etc. = a series of consecutive, equal, end-of-period month, dollars per year, etc. amounts of money; dollars per = number of interest periods; months, years, etc. = interest rate per interest period; percent per month, percent per year, etc. The symbols P and F represent single-time occurrence values: A occurs at each interest period for a specified number of periods with the same value. It should be understood that a present sum P represents a single sum of money at some time prior to a future sum or uniform series amount and therefore does not necessarily have to be located at time t = O. Example 1. 11 shows a P value at a time other than t = O. The units of the symbols aid in clarifying their meaning. The present sum P and future sum F are expressed in dollars; A is referred to in dollars per interest period. It is important to note here that in order for a series to be represented by the symbol A, it must be uniform (i. e. the dollar value must be the same for each period) and the uniform dollar amounts must extend through consecutive interest periods. Both conditions must exist before the dollar value can be represented by A. Since n is commonly expressed in years or months, A is usually expressed in units of dollars per year or dollars per month, respectively. The compound-interest rate i is expressed in percent per interest period, for example, 5% per year. Ex cept where noted otherwise, this rate applies throughout the entire n years or n interest periods. The i value is often the minimum attractive rate of return (MARR). All engineering-economy problems must involve at least four of the symbols listed above, with at least three of the values known. The following four examples illustrate the use of the symbols. Example 1. 5. If you borrow $2000 now and must repay the loan plus interest at a rate of 12% per year in 5 years, what is the total amount you must pay? List the values of P, F, n, and i. Solution In this situation P and F, but not A, are involved, since all transactions are single payments. The values are as follows: P = $2000 Example 1. 6 i = 12% per year n = 5 years If you borrow $2000 now at 17% per year for 5 years and must repay the loan in equal yearly payments, what will you be required to pay? Determine the value of the symbols involved. Terminology and Cash-Flow Diagrams 13 ~- ution = S2000 = ? per year for 5 years = 17% per year = 5 years – ere is no F value involved. – 1 In both examples, the P value of $2000 is a receipt and F or A is a disbursement. equally correct to use these symbols in reverse roles, as in the examples below. Example 1. 7 T you deposit $500 into an account on May 1, 1988, which pays interest at 17% per year, hat annual amount can you withdraw for the following 10 years? List the symbol values. Solution p = $500 A =? per year i = 17% per year n= 10 years Comment The value for the $500 disbursement P and receipt A are given the same symbol names as before, but they are considered in a different context. Thus, a P value may be a receipt (Examples 1. 5 and 1. 6) or a disbursement (this example). Example 1. 8 If you deposit $100 into an account each year for 7 years at an interest rate of 16% per year, what single amount will you be able to withdraw after 7 years? Define the symbols and their roles. Solution In this example, the equal annual deposits are in a series A and the withdrawal is a future sum, or F value. There is no P value here. A = $100 per year for 7 years F =? i = 16% per year n = 7 years Additional Example 1. 17 Probs. 1. 27 to 1. 29 14 Level One 1. 6 Cash-Flow Diagrams Every person or company has cash receipts (income) and cash disbursements (costs) which occur over a particular time span. These receipts and disbursements in a given time interval are referred to as cash flow, with positive cash flows usually representing receipts and negative cash flows representing disbursements. At any point in time, the net cash flow would be represented as Net cash flow = receipts – disbursements (1. 5) Since cash flow normally takes place at frequent and varying time intervals within an interest period, a simplifying assumption is made that all cash flow occurs at the end of the interest period. This is known as the end-of-period convention. Thus, when several receipts and disbursements occur within a given interest period, the net cash flow is assumed to occur at the end of the interest period. However, it should be understood that although the dollar amounts of F or A are always considered to occur at the end of the interest period, this does not mean that the end of the period is December 31. In the situation of Example 1. 7, since investment took place on May 1, 1988, the withdrawals will take place on May 1, 1989 and each succeeding May 1 for 10 years (the last withdrawal will be on May 1, 1998, not 1999). Thus, end of the period means one time period from the date of the transaction (whether it be receipt or disbursement). In the next chapter you will learn how to determine the equivalent relations between P, F, and A values at different times. A cash-flow diagram is simply a graphical representation of cash flows drawn on a time scale. The diagram should represent the statement of the problem and should include what is given and what is to be found. That is, after the cash-flow diagram has been drawn, an outside observer should be able to work the problem by looking at only the diagram. Time is considered to be the present and time 1 is the end of time period 1. (We will assume that the periods are in years until Chap. . ) The time scale of Fig. 1. 1 is set up for 5 years. Since it is assumed that cash flows occur only at the end of the year, we will be concerned only with the times marked 0, 1, 2, †¦ , 5. The direction of the arrows on the cash-flow diagram is important to problem solution. Therefore, in this text, a vertical arrow pointing up will indicate a positive cash flow. Conversely, an a rrow pointing down will indicate a negative cash flow. The cash-flow diagram in Fig. 1. 2 illustrates a receipt (income) at the end of year 1 and a disbursement at the end of year 2. It is important that you thoroughly understand the meaning and construction of the cash-flow diagram, since it is a valuable tool in problem solution. The three examples below illustrate the construction of cash-flow diagrams.  ° Figure 1. 1 A typical cash-flow time scale. Year 1 Year 5 r=;:;; r+;:;. I 1 2 Time o I I 3 4 I 5 Terminology and Cash-Flow Diagrams 15 + Figure 1. 2 Example of positive and negative cash flows. 2 3 Time Example 1. 9 Consider the situation presented in Example 1. 5, where P = $2000 is borrowed and F is to be found after 5 years. Construct the cash-flow diagram for this case, assuming an interest rate of 12% per year. Solution Figure 1. 3 presents the cash-flow diagram. Comment While it is not necessary to use an exact scale on the cash-flow axes, you will probably avoid errors later on if you make a neat diagram. Note also that the present sum P is a receipt at year 0 and the future sum F is a disbursement at the end of year 5. Example 1. 10 If you start now and make five deposits of $1000 per year (A) in a 17%-per-year account, how much money will be accumulated (and can be withdrawn) immediately after you have made the last deposit? Construct the cash-flow diagram. Solution The cash flows are shown in Fig. 1. 4. Since you have decided to start now, the first deposit is at year 0 and the [lith Comment deposit and withdrawal occur at the end of year 4. Note that in this example, the amount accumulated after the fifth deposit is to be computed; thus, the future amount is represented by a question mark (i. e. , F = ? ) Figure 1. 3. Cash-flow diagram for Example 1. 9. + P = $2. 000 i = 12% o 2 3 4 5 Year F= ? 16 Figure 1. 4 Cashflow diagram for Example 1. 10. Level One F= ? i = 17†³10 2 0 3 4 Year A=$1. 000 Example 1. 11 Assume that you want to deposit an amount P into an account 2 years from now in order to be able to withdraw $400 per year for 5 years starting 3 years from now. Assume that the interest rate is 151% per year. Construct the cash-flow diagram. Figure 1. 5 presents the cash flows, where P is to be found. Note that the diagram shows what was given and what is to be found and that a P value is not necessarily located at time t = O. Solution Additional Examples 1. 18 to 1. 20 Probs. 1. 30 to 1. 46 Additional Examples Example 1. 12 Calculate the interest and total amount accrued after 1 year if $2000 is invested at an interest rate of 15% per year. Solution Interest earned = 2000(0. 15) = $300 Total amount accrued = 2000 + 2000(0. 15) = 2000(1 + 0. 15) = $2300 Figure 1. 5 Cashflow diagram for Example 1. 11. A = $400 o 2 3 4 5 6 7 Year p=? Terminology and Cash-Flow Diagrams 17 Example 1. 13 a) Calculate the amount of money that must have been deposited 1 year ago for you to have $lOQO now at an interest rate of 5% per year. b) Calculate the interest that was earned in the same time period. Solution a) Total amount accrued = original deposit + (original deposit)(interest rate). If X = original deposit, then 1000 = X + X(0. 5) = X(l + 0. 05) 1000 = 1. 05X 1000 X=-=952. 38 1. 05 Original deposit = $952. 38 (b) By using Eq. (1. 1), we have Interest = 1000 – 952. 38 = $47. 62 Example 1. 14 Calculate the amount of money that must have been deposited 1 year ago for the investment to earn $100 in interest in 1 year, if the interest rate is 6% Per year. Solution Let a = a = = total amount accrued and b = original deposit. Interest Since a Interest Interest b b + b (interest rate), interest can be expressed as + b (interest rate) b =b = b (interest rate) $100 = b(0. 06) b = 100 = $1666. 67 0. 06 Example 1. 5 Make the calculations necessary to show which of the statements below are true and which are false, if the interest rate is 5% per year: (a) $98 now is equivalent to $105. 60 one year from now. (b) $200 one year past is equivalent to $205 now. (c) $3000 now is equivalent to $3150 one year from now. (d) $3000 now is equivalent to $2887. 14 one year ago. (e) Interest accumulated in 1 year on an investment of $2000 is $100. Solution (a) Total amount accrued = 98(1. 05) = $102. 90 =P $105. 60; therefore false. Another way to solve this is as follows: Required investment = 105. 60/1. 05 = $100. 57 =P $9? Therefore false. b) Required investment = 205. 00/1. 05 = $195. 24 =p $200; therefore false. 18 Level One (e) Total amount accrued = 3000(1. 05) = $3150; therefore true. (d) Total amount accrued = 2887. 14(1. 05) = $3031. 50 â€Å"# $3000; therefore false. (e) Interest = 2000(0. 05) = $100; therefore true. Example 1. 16 Calculate the total amount due after 2 years if $2500 is borrowed now and the compoundinterest rate is 8% per year. Solution The results are presented in the table to obtain a total amount due of $2916. (1) (2) (3) (4) = (2) + (3) (5) End of year Amount borrowed $2,500 Interest Amount owed Amount paid o 1 2 Example 1. 17 $200 216 2,700 2,916 $0 2,916 Assume that 6% per year, starting next withdrawing Solution P = you plan to make a lump-sum deposit of $5000 now into an account that pays and you plan to withdraw an equal end-of-year amount of $1000 for 5 years year. At the end of the sixth year, you plan to close your account by the remaining money. Define the engineering-economy symbols involved. $5000 A = $1000 per year for 5 years F = ? at end of year 6 i = 6% per year n = 5 years for A Figure 1. 6 Cashflow diagram for Example 1. 18. $650 $625 $600 $575 $ 550 $525 $500 $625 t -7 -6 -5 -4 -3 -2 -1 t o Year P = $2,500 Terminology and Cash-Flow Diagrams 19 Example 1. 1B The Hot-Air Company invested $2500 in a new air compressor 7 years ago. Annual income â€Å"-om the compressor was $750. During the first year, $100 was spent on maintenance, _ cost that increased each year by $25. The company plans to sell the compressor for salvage at the end of next year for $150. Construct the cash-flow diagram for the piece f equipment. The income and cost for years – 7 through 1 (next year) are tabulated low with net cash flow computed using Eq. (1. 5). The cash flows are diagrammed . Fig. 1. 6. Solution End of year Net cash flow Income Cost -7 -6 -5 -4 -3 -2 -1 0 1 Example 0 750 750 750 750 750 750 750 750 + 150 $2,500 100 125 150 175 200 225 250 275 $-2,500 650 625 600 575 550 525 500 625 1. 19 Suppose that you want to make a deposit into your account now such that you can withdraw an equal annual amount of Ai = $200 per year for the first 5 years starting 1 year after your deposit and a different annual amount of A2 = $300 p er year for the following 3 years. How would the cash-flow diagram appear if i is 14! % per year? Solution The cash flows would appear as shown in Fig. 1. 7. Comment The first withdrawal (positive cash flow) occurs at the end of year 1, exactly one year after P is deposited. Figure 1. 7 Cash-flow diagram for two different A values, Example 1. 19. A2 = $300 A, = $200 0 1 2 3 4 i = 14+% 5 6 7 8 Year p=? 20 Level One p=? j = 12% per year Figure 1. 8 Cash-flow diagram for Example 1. 20. F2 1996 1995 A = $50 A = $150 = $50 F, = $900 Example 1. 20 If you buy a new television set in 1996 for $900,. maintain it for 3 years at a cost of $50 per year, and then sell it for $200, diagram your cash flows and label each arrow as P, F, or A with its respective dollar value so that you can find the single amount in 1995 that would be equivalent to all of the cash flows shown. Assume an interest rate of 12% per year. Solution Comment Figure 1. 8 presents the cash-flow diagram. The two $50 negative cash flows form a series of two equal end-of-year values. As long as the dollar values are equal and in two or more consecutive periods, they can be represented by A, regardless of where they begin or end. However, the $150 positive cash flow in 1999 is a single-occurrence value in the future and is therefore labeled an F value. It is possible, however, to view all of the individual cash flows as F values. The diagram could be drawn as shown in Fig. . 9. In general, however, if two or more equal end-of-period amounts occur consecutively, by the definition in Sec. 105 they should be labeled A values because, as is described in Chap. 2, the use of A values when possible simplifies calculations considerably. Thus, the interpretation pictured by the diagram of Fig. 1. 9 is discouraged and will not generally be used further in this text. p=? j = 12% per year F. = $150 1. 9 A cash flow for Example 1. 20 considering all values as future sums. Figure 1996 1995 1997 1998 1999 F2 = $50 F3 = $50 F, = $900

Industrial Revolution, essays

Industrial Revolution, essays Before there were factories bustling with hard working men, women, and children there were farms scattered about among the countryside. This was so until the population began to soar upwards and nearly doubled in a few years. Then everybody started rushing into cities to join the rest of the farming community in the great factories of Britain. Even though housing conditions are horrible these days and workers have awful working conditions the Industrial Revolution is a huge leap ahead for Britain. The Industrial Revolution is wonderful because it gives everybody a job no matter what age or gender. Children are able to work so this gave them a chance to help out their families with paying the bills and making sure everybody has enough food to eat. With more and more trains and boats being built everyday the demand for coal shot up and this made many jobs for women, children, and men to do. As long as the coal mines held out everybody will have a job. The Industrial Revolution is a great opportunity for everybody who is properly educated to make great fortune in Britains new booming industries. With all the good chances that the Industrial Revolution is bringing us, bad conditions are also coming with it. Urbanization was becoming a huge problem with city dwellers. There isnt any proper waste disposal in the city for all of the shoddy housing developments that are being built for the factory workers. The sewage problem has grown out of hand because there is no sewer system to deal with all the waste that people are creating in the city. Diseases such as cholera, typhoid, and measles are quickly spreading and killing many. Children are working so hard in the factories that they cannot attend school to receive a proper education. Life expectancy in the city has gown down dramatically and many children are weak from working such long hours in the factories. Only the rich can afford to educate their children ...

Converting Cubic Meters to Liters (m3 to L)

Converting Cubic Meters to Liters (m3 to L) Cubic meters and liters are two common metric units of volume. There are three typical ways to convert cubic meters (m3) to liters (L). The first method walks through all the math and helps explain why the other two work; the second completes an immediate volume conversion in a single step; the third method demonstrates just how many places to move the decimal point (no math required). Key Takeaways: Convert Cubic Meters to Liters Cubic meters and liters are two common metric units of volume.1 cubic meter is 1000 liters.The simplest way to convert cubic meters to liters is to move the decimal point three places to the right. In other words, multiply a value in cubic meters by 1000 to get the answer in liters.To convert liters to cubic meters, you simply need to move the decimal point three places to the left. In other words, divide a value in liters by 1000 to get an answer in cubic meters. Meters to Liters Problem Problem: How many liters are equal to 0.25 cubic meters? Method 1: How to Solve m3 to L The explanatory way to solve the problem is to first convert cubic meters into cubic centimeters. While you might think this is just a simple matter of moving the decimal point of 2 places, remember this is volume (three dimensions), not distance (two). Conversion factors needed 1 cm3 1 mL100 cm 1 m1000 mL 1 L First, convert cubic meters to cubic centimeters. 100 cm 1 m(100 cm)3 (1 m)31,000,000 cm3 1 m3since 1 cm3 1 mL1 m3 1,000,000 mL or 106 mL Next, set up the conversion so the desired unit will be cancelled out. In this case, we want L to be the remaining unit. volume in L (volume in m3) x (106 mL/1 m3) x (1 L/1000 mL)volume in L (0.25 m3) x (106 mL/1 m3) x (1 L/1000 mL)volume in L (0.25 m3) x (103 L/1 m3)volume in L 250 L Answer: There are 250 L in 0.25 cubic meters. Method 2: The Simplest Way The previous solution explains how expanding a unit to three dimensions affects the conversion factor. Once you know how it works, the simplest way to convert between cubic meters and liters is simply to multiply cubic meters by 1000 to get the answer in liters. 1 cubic meter 1000 liters so to solve for 0.25 cubic meters: Answer in Liters 0.25 m3 * (1000 L/m3)Answer in Liters 250 L Method 3: The No-Math Way Or, easiest of all, you could just move the decimal point 3 places to the right. If youre going the other way (liters to cubic meters), then you simply move the decimal point three places to the left. You dont have to break out the calculator or anything. Check Your Work There are two quick checks you can do to make sure you performed the calculation correctly. The value of the digits should be the same. If you see any numbers that werent there before (except zeros), you did the conversion incorrectly.1 liter 1 cubic meter. Remember, it takes a lot of liters to fill a cubic meter (a thousand). A liter is like a bottle of soda or milk, while a cubic meter is if you take a meter stick (approximately the same distance as how far apart your hands are when you stretch your arms out to your sides) and put it into three dimensions. When converting cubic meters to liters, the liters value should be a thousand times more. Its a good idea to report your answer using the same number of significant figures. In fact, not using the right number of significant digits may be considered a wrong answer!

Foundation of lawwriter 1 Essay Example | Topics and Well Written Essays - 1500 words

Foundation of lawwriter 1 - Essay Example s (1953) 1 QB 401, display of goods is a willingness to conduct business or commence negotiations thus is considered as an invitation to make an offer (Mulcahy 2008). Mulcahy (2008) points out that the law of contract requires a valid offer and acceptance. An offer is an expression of willingness to enter in to a contract with the intention of creating legal obligations upon acceptance. An offer has to be communicated since there can be no ‘meeting of the minds’ the offer is not communicated. In this case, Harry has made an offer of  £1,000. According to mirror image’ rule, the acceptance by Paul must be done according to the terms of the offer. The case of Day Morris Associates v. Voyce (2003) clarified that acceptance by either words or conduct of the other party gives rise to the inference that the offeree assents to the offeror’s terms thus a valid acceptance must be done according to the terms of the offer for a legally binding contract to be formed (Mulcahy 2008). In this case, Paul has not accepted the offer from Harry since he asserts that he will accept  £1,500 thus he has made a counter-offer that extingui shes the original offer by Harry. In this case, Harry is required to make a valid acceptance that mirrors the terms of the offer from Paul. According to the court of appeal in the case of Butler machine v. Ex-cell-o (1979) 1 WLR 401, the ‘last shot’ or last offer wins the ‘battle of forms’ in instances where one party makes an offer and the other makes a counter-offer (Stone and Quinn 2007). Generally, silence is not deemed an acceptance, and thus Harry requests for three days to think about the acceptance. Although Harry has requested for three days to think about the offer, Paul has not cancelled the offer. Accordingly, the power of acceptance does not terminate if it is qualified in form, but not in substance. Paul’s offer can only be terminated through acceptance, rejection, lapse of time, counter offer and revocation. According