Ozymandias C. Despair Essays - Fiction, Literature, Imagination

Ozymandias C. Despair Ozymandias C. Despair changed from the feeling that the greatness statue would inspire despair in others through fear but it did the opposite, the passers by feel despair for the statue in it wrecked stat, it is situational irony. Hardness scale D. These lines are a description of a specific event between woman and her husband or lover. The specific event is a symbol for the entire relationship between the man and the woman. The man goes off and is irresponsible in this situation and in life and get's into trouble mostly because of drink, and then uses the woman to help him. He tries to smooth over his taking advantage of her by using words of praise but only tends to harden the woman emotions. LV C. The allusion in the first line is that the person in the poem will eventually rise to judge and be judged in an almost biblical sense, of the ultimate judgement of life. Last poem D. This line tells of how wildmen cherish the sun for what it is but only learned how important it really is when it leaves. This symbolizes the choice of man throughout history, the idea is that people celebrate what they have but rarely totally understand the significance of what they have until its gone or leaving. This is a lesson for man to look at what they have understand it's important and truly appreciate all we have. Poetry Essays

The 5 Easiest AP Exams to Self-Study

The 5 Easiest AP Exams to Self-Study SAT / ACT Prep Online Guides and Tips Once you’ve decided to self-study for an AP, you’ll need to choose an exam that’s right for you. With dozens of potential choices, it might seem overwhelming. I can demystify the choice for you. First, I’ll give you four important things to consider when you make your choice. Then, I’ll list the five easiest APs toself-study. After that, I’ll touch on some other solid self-study choices, and wrap up with a few AP exams you should NOT try to study for on your own. How to Choose WhichAP Exam to Self-Study There are four things to consider when selecting whichAP exam you want to prepare for on your own. Consideration 1: What's the Course Workload? The less material covered by the course, the less you will need to study to ace the exam. It makes sense to choose an AP that is narrower in scope instead of a behemoth. Let’s say you want to self-study a science AP; all things being equal, it’s going to be better for you to choose a comparatively content-light course like AP Environmental Science than a content-heavy class like AP Chemistry. (Also, don’t self-study AP Chemistry. More on this later.) If you aren’t sure how much work is involved in learning all the material for a given AP, ask friends, ask the internet, ask teachers...you get the idea. You can also look on the College Board’s individual AP course pages. On each â€Å"Course Overview† page, you’ll find a link to a document that describes the general scope of the course as well as the format of the exam. Consideration 2: How Conceptual Is The Material? Does the exam involve applying a lot of abstract and theoretical concepts, or is it primarily based on memorization? Memorization can be kind of tedious, but it’s often easier to learn this kind of material on your own than to teach yourself to understand, say, particle physics. So try to look for APs that are not overly conceptual. This is why I generally don’t advise people to self-study for math APs, with the possible exception of statistics. Generally, a course weighted more towards memorization as opposed to complex concepts is probably better for self-study. Weighing the options. Consideration 3: How Full Is Your Schedule? You probably already thought aboutyour course schedule when you first considered self-studying for an AP exam to make sure you would have enough time for the extra work. This is all well and good, but you shouldalso consider your schedule whenchoosing the actual exam to self-study. There are a few AP exams that might overlap with your high school coursework even if you aren’t in that specific AP class. You might consider self-studying one of these: One notable example of this is biology. If you are in an honors biology class, you might consider self-studying for AP biology because you will onlyneed to supplement what you are learning in class with any additional competencies necessary for the AP exam. (See the College Board’s helpfulcourse and exam description for AP Biology.) Another common course to take the AP for when you are taking the honors class is US History. Again, you’ll need to learn additional information, but you’ll be learning a lot of the material anyways in your non-AP US History class. You’ll just need to learn some extra information and do some dedicated exam prep. (This is what I did, and I got a 5 on APUSH without a crazy amount of outside studying.) If you are a particularly strong student in English, you might also consider self-study in one or both of the English APs while you are in an honors English class (I did this with AP Language and Composition). This could be a little trickier because it’s very important to be able to get feedback from a knowledgeable person about any practice essays you are writing, but if you have a supportive teacher or mentor, it can definitely work. Consideration 4: What Are Your Strengths? If you are going to self-study for an exam, it makes the most sense to choose a subject you are good at and enjoy. If you rock at social studies, choose a social studies AP. If science is your jam, choose a science AP (but not AP Chemistry or AP Physics! Don’t do it.) And so on.It will help you stay motivated if you actually like the subject. Don’t try to self-study an exam in a subject you hate, even if the exam has a reputation for being an easy self-study choice. If you already have a special skill tested by an AP examforeign languages and computer science come to mindit might make sense to self-study for that AP. You will need to make sure you fill any gaps in your knowledge and are prepared for the exam format, but it’s a good way to make the most of your own personal resources and skills. With these four factors in mind, we can move on to my recommendations for the best five AP exams for relatively painless self-study. The best self-study choice will be almost as easy as pie! But less delicious. 5 Best AP Exams To Self-Study Let's go through a few of the easiest APs to self-study. AP Environmental Science AP Environmental Science is a hugely popular self-study option, and with good reason. The test is considered to be fairly easy, and the coursework assumes no prior knowledge in any environmental sciences, so the material is not particularly advanced. There is some course material about experimental design, some basic statistics for reading charts and tables, and some historical/environmental trend information. Many questions on the test focus on cause-effect relationships. This is going to be a solid choice for anyone who is good at science or history and needs something relatively quick and easy. AP Human Geography This is another popular self-study exam with a reputation for fairly easy material that’s limited in scope. The test is on the short side, clocking in at only 2 hours and 15 minutes with 75 multiple choice questions and 3 â€Å"constructed responses.† Human Geo is essentially a soft-sciences course about how societies develop; think anthropology. To be successful, you’ll need to do some memorization of facts/dates/etc., perform some analysis/synthesis of how cultures came to be and how they might develop, and learn some specialized vocab. AP Psychology This test is a self-study home run.If you want to self-study AP Psychology, you’ll need to learn some psychological concepts and memorize details about some notable scientists in the field as well assome seminal experiments. You’ll also need to learn some discipline-specific vocab. The test is short, tooonly 2 hourswith 100 multiple-choice and two free-response questions. Free-response questions are known for being fairly straightforward. AP US Government and Politics and AP Comparative Government and Politics Both the politics exams are decent self-study APs. You probably already have some background knowledge in US Government and Politics from years of US History coursework, plus the exam is fairly narrow in scope. Comparative Government is a little harder to self-study for just because there’s likely to be more material you aren’t familiar with, but it’s still pretty manageable. The rare self-studying jellyfish, exploring the ocean on her own. Other Good AP Exams to Self-Study Some exams aren’t quite universal self-study slam dunks, but if you have a proclivity for a certain subject, a particular interest, or some prior knowledge, they canstill be good choices for you. This is particularly true if, for whatever reason, the thought of self-studying Psychology, Environmental Science, Human Geography, or Government and Politics is tedious and repugnant to you. AP Economics Exams: AP Macroeconomics and AP Microeconomics Macroeconomics deals with overall economics systems while Microeconomics examines the economy from the perspective of smaller actors within the system. You will need to learn concepts for this course, and there is some basic math, but they are often seen as good self-study options because each exam has a fairly limited scope, and there is some overlap in material. Especially if you took the class for one, you might consider self-studying for the other. Additionally, self-study students found it fairly easy to prepare for the FRQs by looking at old tests. AP Biology The general consensus is that taking onAP Biology self-study with no previous bio coursework is not a good idea, but that if you have taken or are taking honors biology, it can be a solid choice. There’s definitely a lot of content to cover and a lot to memorize, but if it’s a subject you are very gifted in/are very interested in, it could be worth it. AP US History Self-studying for APUSH is considered easier than self-studying for most of the other history APs because most American students will already have some background knowledge in US history. The scope of information is also narrower than AP European or AP World History, so there’s less to learn! It’s going to be more content-heavy than something like AP Environmental Science, but definitely doable. AP English Language and Composition and AP English Literature and Composition If you have a particular proclivity for English, one (or even both) of the English APs could be a good self-study choice for you. The most important skill you will need to work on is timed analytical essay writing, so your self-study way will be much smoother if you have a teacher or other knowledgeable person willing to look over your practice essays. You don't have to self-study in an empty stadium...unless you want to. Do Not Try To Self-Study These AP Exams There are three AP subject areas in particular that are not very well-suited to self-study. These are the APs that are the both very conceptual AND content-heavy in nature. In these cases, having an instructor and a structured class tends to be very important for learning and understanding. I strongly advise you not to self-study for any of the following exams: AP Calculus AB andBC Calculus is hard to learn. This is because it introduces concepts that are very different fromany math class that comes before it; in a lot of ways it involves a massive recalibration of your brain’s understanding of math. It is likely that, in the course of learning calculus concepts, you will get very confused, and this is why it is essential to have a good teacher. In the immortal words of the Legend of Zelda:it’s dangerous to go alone. You will be very frustrated if you try to self-study AP Calculus. AP Chemistry The AP Chemistry class is known for having a high workload, and it'sanother course where the guidance of a good teacher is very important. In addition to there being a lot of content to learn, you will need to understandlots of concepts and problem-solving methods to do well on the exam. Having a class to keep you on track and a teacher to explain material you don’t understand is going to be essential for most people to succeed on the exam. AP Physics AP Physics is a double-whammy, with a lot of math and science concepts to learn. The exams (there are four!) themselves are known for being particularly difficult, even for those who do well in a structured course. Self-studying for this exam is not an efficient use of your time.Even if you were able to do well, you would most likely need to self-study for many more hours than you would in a guided course to achieve the same level of mastery. It's dangerous to go alone! Here, take this. And an AP class. Look, I don’t want to tell you what you can and can’t do. Maybe you’re the next Isaac Newton, and you’ve been learning derivatives since you were a wee child; maybe Richard Feynman was your grandpa, and he taught you physics in the cradle. In that case, self-study for one of these APs if you feel you must. For most people, however; even very smart people, the entire experience of learning these subjects will be much more pleasant and effective, not to mention more efficient time-wise, if you learn it in a classroom and not by yourself. Also, the intensity of these classes makes them a bonding experience! The people in my Calculus BC crew became some of my favorite high school classmates. Key Takeaways What makes an AP exam easy to self-study will vary somewhat from person to person, but, in general, AP exams with a narrower scope, without too many complex concepts, and insubject areas where you have special interests or talents will be the best choices for self-study. The five easiest exams for self-study, in general, are AP Environmental Science, AP Human Geography, AP Psychology, AP US Government and Politics, and AP Comparative Government and Politics. A number of other exams may also be good choices depending on your situation. However, you should NOT try to self-study for AP Calculus AB or BC, AP Chemistry, or any of the AP Physics exams! If you keep these tips in mind, you will be able to choose the right AP exam to self-study for with ease! What's Next? When you're ready to start self-studying, see my article on how to self-study for an AP exam. If you'd really like to take an accredited AP course, but you can't make it workwith your schedule, or your school doesn't offer it, consider AP online courses- we can guide you in the right direction, towards the best and worst online AP classes. Taking the ACT or SAT? Let us revealthe secret to getting a perfect score. Did you know the SAT haschanged? Check out our complete guide to the new SAT. Want to improve your SAT score by 160 points or your ACT score by 4 points?We've written a guide for each test about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:

LEVEL 4 VTCT BEAUTY THERAPY Essay Example | Topics and Well Written Essays - 750 words

LEVEL 4 VTCT BEAUTY THERAPY - Essay Example e salon is a safe place for all, and that by default the practices in the salon will not lead to accidents or pose health, safety and security risks to customers and employees. These are   fundamental to business practice The justifications for such recommendations and proposals stem from the need to secure the salon and to make it safe, primarily because accidents and harm to customers can result in lawsuits, loss of trust, the tarnishing of the image of the salon, and even business closure and loss of revenues.    Compliance with the law ensures that practices relating to safety, security and health meet legal standards and regulatory standards. This is good business practice that can protect the salon from lawsuits and regulatory fines and problems. What can happen when regulations and the law are not followed is that the salon can be subjected to lawsuits and legal problems that can hamper operations. Also, these translate to shortcomings that can be used against the salon by customers in cases of legal and regulatory disputes. A good way to manage improvements is to benchmark processes versus a checklists of compliance targets, and those targets must meet minimum legal and regulatory standards for such points of compliance. The checklists must be strict and that post-implementation measures to measure compliance must be put in place to gauge whether the compliance activities led to adequate compliance with such minimum standards. The regular evaluation of salon health, security and safety measures acts as a kind of regular audit of how well the salon is implementing procedures and measures to ensure those, and how well the work processes of the salon meet minimum regulatory and legal standards for compliance. As well, the idea is to exceed those minimum standards. This acts as a kind of health check for the salon, to make sure that it does not slide downwards in terms of its security, health and safety standards and practices. Written communication modes

Assignment (Economics) Example | Topics and Well Written Essays - 250 words - 7

(Economics) - Assignment Example The ban of a product hurts the consumer markets especially if the good was used by a lot of people. When vendors smuggle the goods and bring them to the marketplace illegally society benefits because these goods are providing a utility that is needed for the consumers. I believe that US citizens should boycott companies that abuse its workers in less developed countries. The only way for these companies to stop these unethical practices is for the customers to take proactive action to boycott these types of establishments. A full boycott of an item that is offered at much lower prices might hurt consumers that cannot afford to pay higher prices. Due to the different in opinions of customers it would be hard to implement a full boycott. Country A should produce toys, while country B should produce pineapples. Country A must trade toys for pineapples and country B must trade pineapples for toys. In general country A produces less toys or pineapples than country B. Their competitive advantage is in toys because country B can produce more than twice the amount of pineapples than country A. Since country B can produce 900 pineapples per day this country should concentrate on producing pineapples. The competitive advantage of country B in pineapples is 2.25 to

Essay on Correction Techniques Example | Topics and Well Written Essays - 2000 words

On Correction Techniques - Essay Example Probation, pardon and parole are some kind of the most common corrective measures implemented by criminal justice system to test the behaviour of the criminals who are sentenced. These mechanisms are normally performed to evaluate the success of the correction measures. This paper evaluates the differences between parole and probation and the extent to which probation is successful in correcting a criminal. Hertfordshire printer Frederic Rainer, a volunteer with the Church of England Temperence Society (CETS), writes to the society of his concern about the lack of help for those who come before the courts. He sends a donation of five shillings (25p) towards a fund for practical rescue work in the police courts. The CETS responds by appointing two "missionaries" to Southwark court with the initial aim of "reclaiming drunkards". This forms the basis of the London Police Courts Mission (LPCM), whose missionaries worked with magistrates to develop a system of releasing offenders on the c ondition that they kept in touch with the missionary and accepted guidance (Timeline: A history of probation) The history of probation started from England as explained above. Probation conditions have been changed or modified periodically based on the feedbacks received from the experiences. Many people do not have awareness about the differences between probation and parole. ... On the other hand, a criminal on probation may have less supervision from the probation officers. Parole and probation are granted based on the Pre-Sentence Investigation report (PSI) prepared by a probation officer. The practice of preparing PSI has started in 1920. â€Å"Its original purpose was to provide information to the court on the defendant’s personal history and criminal conduct in order to promote individualized sentencing† (The History of the Pre-sentence Investigation Report, p.1). This report normally contains the background information of the criminal such as his crime history, crime tendency, family history, juvenile adjudications, description of the crime, the defendant's work history, marital status, financial status, length of residence in the community, educational background, medical history, substance abuse history, etc. Based on these information probation officers decide about the corrective measures needed for the criminal. For example, a crimin al who has the history of series of criminal activities may normally get parole whereas first time criminals may normally get probation. Probation is the most liberal corrective mechanism. A judge can decide about the probation of the criminal after reviewing the nature of the crime and the character of the criminal. Fresh criminals may get probation in most of the cases. â€Å"A violation of probation gives rise to a hearing on whether or not probation should be revoked† (Kaman). If a criminal violates the conditions of probation, the judge or the probation officer has the right to withdraw the probation. In such cases, the criminal may get sentencing. On the other hand, parole is granted at the end of a prison term or in between the

Prior (2004) Sydney Gay Saunas 1967-2000 Book Analysis

Prior (2004) Sydney Gay Saunas 1967-2000 Book Analysis Farzan Babaei S5030791 Article name: Sydney Gay Saunas 1967-2000: Fight for Civic Acceptance and Experiences Beyond the Threshold Article Source: PhD thesis, School of Sociology and Anthropology, The University of New South Wales Article Author and Year: Jason Hugh Prior (2004) Citation: Prior, J. H. (2004). Sydney gay saunas 1967-2000: Fight for civic acceptance and experiences beyond the threshold (Doctoral thesis). School of Sociology and Anthropology, The University of New South Wales, New South Wales, Australia. Introduction and Research Questions Jason Prior is an established researcher particularly in the field of spatial governance and its relation to sexuality, religion, and health and wellbeing. In his PhD thesis titled Sydney Gay Saunas 1967-2000: Fight for Civic Acceptance and Experiences Beyond the Threshold (year), he attempts to shed light on Sydneys gay saunas through two key questions. The first relates to how the gay sauna transitioned from a clandestine operation to a legally recognized and accepted institution considered important within particular environs of the city. The second concerns how the dynamic public domain of the gay sauna contributed to the development of gay culture in the city by fostering the opportunity of collective and individual homosexual expression. Part 1 of Study Methodology and Results In the first part of the study, utilizing his background in urban sociology, planning, and legal geography, Prior draws heavily upon the works of Knopp (1995,1998) and Castells (1983) as a conceptual framework. He uses empirical examination and analysis of documents (including development applications, archival documents, legal records, civic authority records, government gazettes, law reports, records of police raids, government acts, newspaper and magazine articles, and twenty-nine in-depth interviews) as a research methodology, to understand the process of acceptance of gay saunas in Sydneys civic society. Using these data, he traces the history of these establishments from 1967 to 2000. The first gay saunas existed through subterfuge and public charades by disguising themselves from the largely homophobic society as gyms and fitness centres. Through the years that followed, change in legislation which led to the decriminalisation of homosexuality set the stage for the emergence o f the gay sauna into public view and their partial acceptance by civic authorities. Although the emergence of AIDS added a layer of complexity to the process, it led to new alliances between the gay community, medicine and the state government. These alliances played a major role in the eventual acceptance of the gay sauna by civic authorities, judiciary, and citizens as not just social but also sexual institutions. Prior argues that this transformation was possible through the conjunction of greater understanding and acceptance of homosexuality by the general community, the mobilisation of gay activists and the broader radicalism of the 1960s and 70s, and the emergence of enlightened processes by council bureaucracies and the judiciary. Part 2 of Study Methodology and Results Priors background in architecture comes into use in the second part of the study where he examines through an empirical analysis (analysis of the material features of the built form, and twenty-nine in-depth interviews), how the evolving social spaces of Sydneys gay saunas allowed men to develop and experience individual and collective sexual identities and practices. In describing the dynamic nature of these spaces Prior identifies three stages of evolution. The first and most basic/rudimentary stage started with the establishment of the the Bondi Junction Steam Bath, Sydneys first gay sauna. Here the aim was to providing a safe space where men could temporarily escape from the city outside, with a focus on the threshold to protect patrons from the largely homophobic world outside. The second involved the shift of focus from the threshold to the development of the domain, into the creation of a space that was more socially, sexually, and psychology enabling for the expression of hom osexuality. This golden age of the saunas aligned with the gay liberation movement. The last stage focuses on the redesign of the domain into a safe sex venue to cope with the new experience of sexuality that AIDS awareness evoked. These stages involved changes to the physical realm of the saunas, which in turn affected the type of sexual activity that took place. Critical Review/ Contextualization within other works Priors well-structured and comprehensive study fills a gap in the existing literature by adding to the largely unexplored realm of gay bathhouses in the Australian context. In describing the history of these establishments, he continually draws parallels between the United States and Australia which provides readers with a broader perspective, and highlights the uniqueness of this particular context. The first part of the study which deals with the sexualisation of urban space is contextualized within the body of works of Foucault (1990), Castells, and Knopp, while the second part of the study which concerns how designed sexual environments affect sexual practises fits within the works of Brodsky (1993), Rubin (1991), and Tattelman (1999). Priors work also contributes to the broader topic of studies specifically on gay saunas. The latter includes ethnographies particularly in the american context (Weinberg Williams, 1975; Styles, 1979; Chauncey, 1994), the study of saunas from a more architectural perspective where alternate design possibilities and concepts of queer space are explored (Tattelman, 2000; Betsky, 1997), and more recently, studies on AIDS prevention research (Bolton, Vincke, Mak, 1994; Binson Woods, 2003; Lyons, Smith, Grierson, Doussa, 2010). Link to my Research The inter-relation between sexual culture, the built-form, and the social/sexual relations that forms the core of Priors work, is a theme that I want to carry forward and build onto in my research. Specifically, I am interested in looking at how social and sexual relations have changed in the bathhouse due to technologies in the 21st century such as PrEP, internet, and dating apps and how this in turn has affected the physical and social environs of the baths. The main aim of the authors research was to examine the social and political forces which contributed to the acceptance of gay saunas by Sydneys civic society. To answer this research question, he provides an in-depth description of the material (and immaterial) aspects of gay saunas in Sydney from the first gay sauna in 1967 to the year 2000, outlining distinct stages of evolution in the form/use of these structure. This data will form an important benchmark for my research which will explore the possible formation of a new architectural typology in the 21st century. The fact that this study, along with the work of Richters (2007), is one of the few literary works offering a detailed description of Sydneys baths, including floor plans and advertisements in the gay press, makes it the single most important source for my research. References Betsky, A. (1997). Queer Space: Architecture and Same-Sex Desire (1st edition). New York: William Morrow. Binson, D., Woods, W. J. (2003). A Theoretical Approach to Bathhouse Environments. Journal of Homosexuality, 44(3-4), 23-31. Bolton, R., Vincke, J., Mak, R. (1994). Gay Baths Revisited: An Empirical Analysis. GLQ: A Journal of Lesbian and Gay Studies, 1(3), 255-273. Brodsky, J. I. (1993). The Mineshaft: A Retrospective Ethnography. Journal of Homosexuality, 24(3-4), 233-252. Castells, M. (1983). The City and the Grassroots: A Cross-cultural Theory of Urban Social Movements. London: Edward Arnold. Chauncey, G. (1995). Gay New York: Gender, Urban Culture, and the Making of the Gay Male World, 1890-1940 (unknown edition). New York: Basic Books. Foucault, M. (1990). The History of Sexuality, Vol. 1: An Introduction. (R. Hurley, Trans.) (Reissue edition). New York: Vintage. Knopp, L. (1995). Sexuality and Urban Space: A Framework for Analysis. In David Bell and Gill Valentine (Eds.), Mapping Desire: Geographies of Sexualities (pp. 149-161). London and New York: Routledge. Knopp, L. (1998). Sexuality and Urban Space: Gay Male Identity Politics in the United States, the United Kingdom, and Australia. In Ruth Fincher and Jane M. Jacobs (Eds.), Cities of Difference (pp. 149-176). New York: The Guilford Press. Lyons, A., Smith, A. M. A., Grierson, J. W., Doussa, H. von. (2010). Australian mens sexual practices in saunas, sex clubs and other male sex on premises venues. Sexual Health, 7(2), 186-192. Prior, J. H. (2004). Sydney gay saunas 1967-2000: Fight for civic acceptance and experiences beyond the threshold (Doctoral thesis). School of Sociology and Anthropology, The University of New South Wales. Richters, J. (2001). The Social Construction of Sexual Practice: Setting Sexual Culture and the Body in Casual Sex Between Men. University of Sydney, Sydney, NSW, Australia. Rubin, G. (1991). The Catacombs: A Temple of the Butthole. In Mark Thomson (Ed.), Leatherfolk: Radical Sex, People, Politics, and Practice (pp. 119-141). Boston: Alyson Publications. Styles, J. (1979). Outsider/Insider: Researching Gay Baths. Urban Life, 8(2), 135-152. Tattelman, I. (1999). Speaking to the Gay Bathhouse: Communicating in Sexually Charged Spaces. In W. L. Leap (Ed.), Public Sex/ Gay Space (pp. 71-94). New York: Columbia University Press. Tattelman, I. (2000). Presenting a Queer (Bath) House. In J. A. Boone, M. Dupuis, M. Meeker, K. Quimby, C. Sarver, D. Silverman, R. Weatherston, Queer Frontiers: Millennial Geographies, Genders, and Generations (pp. 222-258). Madison: University of Wisconsin Press. Weinberg, M. S., Williams, C. J. (1975). Gay Baths and the Social Organization of Impersonal Sex. Social Problems, 23(2), 124-136.

Time Value of Money and Present Value

Date: 14/11/2012 52. Annuities: You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $23,000 per year per child, payable at the beginning of each school year. The annual interest rate is 5. 5 percent. How much money must you deposit in account each year to fund your children’s education? Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume four years of collegeSolution: Cost of 1 year at university = 23,000 N=4 I=5. 5% PMT=23,000 CPT PV = 80,618. 45 For the first child the PV = 80,618. 45/ (1. 055) ^14 = $38,097. 81 For the second child the PV = 80,618. 45/ (1. 055) ^16 = $34,229. 07 Therefore the total cost today of your children’s college expense will be the addition of the 2 = $72,326. 88 This is the present value of my annual savings, which are an annuity, so to get the amount I am supposed to save each year would be: PV=72,326. 88 N=15 I=5. 5 CPT PMT = 7,205. 6 57. Calculating Annuity Values: Bilbo Baggins wants to save money to meet three objectives.First, he would like to be able to retire 30 years from now with retirement income of $25,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $350,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $750,000 to his nephew Frodo. He can afford to save $2,100 per month for the next 10 years. If he can earn an 11 percent EAR before he retires and an 8 percent EAR after he retires, how much will he have to save each month in years 11 through 30? Solution:First we get the FV of the 2,100 savings over 10 years Bilbo Baggins can afford to save $2,100 dollars per month for the next 10 years therefore at 10 years he would have saved: PMT = 2,100 I = 10. 48 / 12 = 0. 873 N = 10 x 12 = 120 CPT FV = $442,201. 15 So after 10 years he would be able to purchase his yacht at the price of $350,000, and he would be left with a balance of $92,201. 15 This $92,201. 15 will be our current PV at year 10. At year 30, the year when Bilbo retires, the $92,201. 15 would become 92,201. 15*(1. 11) ^20 = $620,283. 23 Second we have to find out how much the inheritance of 750,000 would be at year 30: 750,000/1. 8^20= $160,911. 16 Third In order for him to be able to withdraw a sum of 25,000 per month for the next 20 years after his retirement, we should now calculate this annuity’s present value: N= 20 x 12 = 240 I= 7. 72 / 12 = 0. 643 PMT= 25,000 CPT PV = $3,052,135. 26 Adding up the PV’s of the $750,000 and the annuity, we will get $3,213,046. 32 We will subtract the future value at year 30 of the $92,201. 15 ($620,283. 23) which we saved at year 10 from $3,213,046. 32 to get $2,592,763. 09 We are now left with an annuity that pays $2,592,763. 09 at year 30, and a time period of 20 years (yr11-30) To calculate the yearly PMT, we haveFV= $2,592,763. 09 I= 10. 48 / 12 = 0. 873 N= 20 x 12 = 240 CPT PMT = 3,207. 33 Therefore the monthly PMT Bilbo would have to save each month through years 11-30 would be = $3,207. 33 34. Valuing bonds: Mallory Corporation has two different bonds, currently outstanding. Bond M has a face value of $20,000 and matures in twenty years. The bond makes no payments for the first six years, then pays $1,200 every 6 months over the subsequent eight years, and finally pays $1,500 every 6 months over the last years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes n coupon payments over the life of the bond.If the required return on both these bonds is 10% compounded semiannually, what is the current price of bond M? Of bond N? Solution: The price of a bond is equal to PV of ex pected future cash flows Bond M: Face value 20,000 Present value of 20,000 = 20,000/ (1. 05) ^40 = $2,840. 91 First we need to get the present value of the annuity for the 1,500 semiannual PMTs at year 14 Present Value of Annuity = $13,295 $13,295 becomes $3,391 at year 0 We then get the annuity of the 1,200 semiannual PMTs at year 6, and then at Present Value $13,005 at year 6 with a PV of $7,242 at year 0 The sum of the 3 PV’s gives us the value of the bond ,841 + 3,391 + 7,242 = $13,474 Bond N Face value 20,000 Present value of 20,000 = 20,000/ (1. 05) ^40 = $2,840. 91 38. Non-constant growth: Storico Co. just paid a dividend of aud 3. 5 per share. The company will increase its dividend by 20% next year, and will then reduce its dividend growth rate by 5% per year, until it reaches the industry average of 5% industry average growth, after which the company will keep a constant growth rate forever. If the required return on Storico stock is 13%, what will a share of stock s ell for today? Solution  : D0 = $3. 5 D1= 3. 5*1. 2= $4. 2 D2= 4. 2*1. 15= $4. 3 D3=4. 83*1. 1= $5. 31 D4=5. 31*1. 05= $5. 58 Since the first 4 periods are different we get the PV of each one alone, then as of the 4th year we get the perpetuity of the rest, and sum them up to get the final NPV We now get the PV of each Dividend PV D1 = 4. 2/ (1. 13) = $3. 72 PV D2 = 4. 83/ (1. 13) ^2 = $3. 78 PV D3 = 5. 31/ (1. 13) ^3 = $3. 68 So the PVs of D1+D2+D3 = $11. 18 NPV of perpetuity at constant growth = 5. 58(0. 08) / (1. 13) ^3 = 69. 75 / (1. 13) ^3 = $48. 34 NPV perpetuity + NPV dividends = NPV price of stock today 48. 34 + 11. 18 = $59. 52