Financial Maths

FINANCIAL MATHEMATICS 1. RATE OF RETURN 2. SIMPLE INTEREST 3. COMPOUND INTEREST 4. MULTIPLE CASH FLOWS 5. ANNUITIES 6. LOAN REPAYMENT SCHEDULES Financial Math Support Materials Page 1 of 85 (1) RATE OF RETURN FINANCIAL MATHEMATICS CONCERNS THE ANALYSIS OF CASH FLOWS BETWEEN PARTIES TO A CONTRACT. IF MONEY IS BORROWED THERE IS AN INTIAL CASH INFLOW TO THE BORROWER BUT AFTERWARDS THERE WILL BE A CASH OUTFLOW IN THE FORM OF REPAYMENTS. A person borrows $100 and promises to repay the lender $60 after 1 year and $60 after 2 years. Show the resulting cash flows for the borrower and lender. Financial Math Support MaterialsPage 2 of 85 Time Now 1 End of 2 years Borrower 0 End of 1 year Lender 2 $100 is loaned out $120 is received back The extra $20 is the lenders compensation for foregoing current consumption to obtain future consumption. The lender requires compensation for: Financial Math Support Materials Page 3 of 85 THE â€Å"TIME VALUE† OF MONEY CONSIDER A CHOICE OF ? $100 NOW, OR ? $100 LATER ANY RATIONAL PERSON WOULD CHOOSE $100 NOW! BUT WHY? â€Å"MONEY HAS A TIME VALUE† Financial Math Support Materials Page 4 of 85 Time Value of Money (TVM) ? Refers to the difference between ? The concept enables ? Provides the means for valuing multiple cash lows that occur at different times The level of interest rates is the index used to determine prevailing TVM. Interest rates are determined by the level of †¦ For every type of financing transaction there is potentially a different interest rate. Interest rates are distinguished by the nature of the underlying transaction and focus on three characteristics: ? ? ? Financial Math Support Materials Page 5 of 85 An important aspect of valuation is applying the appropriate interest rate. For example, valuing a fixed-rate loan to a highly speculative company using a government bond rate is inappropriate; an adjustment must be made reflecting he relative creditworthiness of the borrower. While different TVMs may exist for every borrower and lender, it is the Most financial math formulae are a form of present value calculation; that is, these formulae identify the future cash flows of a financial instrument and then calculate the value at which these instruments could be exchanged for cash today. Financial Math Support Materials Page 6 of 85 RATE OF RETURN Suppose I purchase a watch for $200 and sell it a year later for $250. What is the dollar return and rate of return of this transaction? Financial Math Support Materials Page 7 of 85 Interest Interest a fee for borrowing money – about as old as civilisation itself Prime rate – the interest charged to the largest and most secure corporations. Interest is a cost to business, hence it is very important to understand how it is calculated and how it impacts on the business. There are two basic types of interest Simple Interest and Compound Interest Simple Interest Compound Interest Financial Math Support Materials Page 8 of 85 (2) SIMPLE INTEREST When a financial institution quotes an interest rate for a loan it can do so in different ways. For example, a quote 10% p. a. simple interest has different cash flows than a quote of 10% p. . compound interest payable quarterly. If the quote is offered as a SIMPLE INTEREST RATE, then the rate is taken as a proportion of the initial loan amount. eg 12% p. a. (SIMPLE), is equivalent to 1% per month, or 3% per quarter, or 6% semi-annually. * NOTE – The quoted rate is often referred to as the nominal rate. Financial Math Support Materials Page 9 of 85 SIMPLE INTEREST Suppose we lend $300 and quote a simple interest rate of 8% p. a. What will be the interest and repayment if the loan is made over: (a) six months, (b) one year, (c) three years. (a) 8% p. a. = Interest = Repayment = (b) Interest = Repayment = (c) 8% p. a. =Interest = Repayment = Financial Math Support Materials Page 10 of 85 Symbolically: Interest amount = I = P i t P ~ principal (or amount bor rowed = PV) i ~ rate of interest as a percentage t ~ time is the number of years, or fraction of a year, for which the loan is made The simple interest (I) charged on a loan of $800 for 2. 5 years at 8. 5% is: I = Pit = Simple interest is usually associated with short-term loans, that is, less than 12 months. In the formula time (t) is expressed in years, or fraction of a year. Example: $800 for 9 months at 8. 5% is: I= Financial Math Support Materials Page 11 of 85 Example: $800 for 88 days at 8. % is: I = Pit At the end of the period the amount repaid is: FV = PV(1 + t i) Where t represents the fraction of a year during which the money is borrowed. Financial Math Support Materials Page 12 of 85 SIMPLE INTEREST In general, the amount repayable, or Future Value (FV) of a loan quoted as simple interest is given by: ? ? ? ? f ? i? FV ? PV 1 ? 365 ? ? ? ? ? ? Where: FV – is the future value (amount repayable) PV – is the present value (Principle) f – is the numbe r of days i – is the annual simple interest rate PV = EQUIVALENTLY, Financial Math Support Materials FV ?f? 1+ ? ?i ? 365 ? Page 13 of 85 SIMPLE INTEREST Question 4(a) from 2001, 2nd semester final exam) Leanne buys a watch for $80 and sells it a month later for $85. What nominal annual interest rate of return does she earn? Rate of return in one month = Annual nominal rate = Financial Math Support Materials Page 14 of 85 Principal unknown A borrower can pay an interest amount of $120 at the end of 6 months. If the current interest rate for personal loans is 9% what is the maximum that can be borrowed, that is, what is PV? ? f ? i I ? PV ? ? ? 365 ? I PV ? ?f? ? ?i ? 365 ? Note: Financial Math Support Materials Page 15 of 85 Interest rate unknown A loan of $18,000 for 8 months had an nterest charge of $888. What was the annual rate of interest rate? ? f ? i I ? PV ? ? ? 365 ? I i? ?f? ? ? PV ? 365 ? Financial Math Support Materials Page 16 of 85 Rayleen’s birthday was on the 14th August last year. On this date she received a gift of $4,800 from her family which she placed in an interest earning account at a nominal rate of 5. 75% per annum. If she withdraws all funds in the account on the 8th April this year, how much will she receive? How much interest is earned? August September October November December January February March April 17 30 31 30 31 31 29 31 8 Total number of days = 237 ? ? f FV ?PV ? 1 ? ? ?i ? ? ? 365 ? ? FV = I= Financial Math Support Materials Page 17 of 85 Barns & Co Ltd. currently has a non tradable bank note with a face value of $500,000 that will mature in 85 days. Barns & Co has negotiated with its lender to obtain a loan using the note as security. The lender requires an establishment fee of $440 and charges simple interest of 9% pa. How much will Barns & Co receive, and what is the total cost of the funds? ? ? f FV ? PV ? 1 ? ? ?i ? ? ? 365 ? ? ent ? Establishm ? FV PV ? ? f? ? fee ? ? 1? ? ?i ? 365 ? Cost of funds Cost in simple interest terms Financial Math Support Materials $500,000 – $489,295. 68 = $10,704. 32 = Page 18 of 85 A bill with a face value of $500,000 and term to maturity of 180 days is sold at a yield of 8% p. a. What are the proceeds of the sale? Proceeds = PV ? PV ? FV ?f? 1? ? ?i ? 365 ? $500,000 ? 180 ? 1? ? ? 0. 08 ? 365 ? PV ? $481, 022. 67 Calculate the effective annualised return for a $100,000 investment which earned: ? 6. 5% p. a. for 90 days, then ? 7. 5% p. a. for 60 days, then ? 6. 2% p. a. for 45 days Value of investment after 90 days: 90 ? $100,000 ? 1+ ? 0. 065 = $101,602. 70 ? ? 365 ? Financial Math Support Materials Page 19 of 85 Value of investment after 90 + 60 days:Value of investment after 90 + 60 + 45 days: Value after 195 days = $103,641. 60 Annualised return = Financial Math Support Materials Page 20 of 85 APPLICATIONS OF SIMPLE INTEREST ? TREASURY NOTES ? BILLS OF EXCHANGE ? PROMISSORY NOTES – WHEN CREATED (ISSUED) – WHEN TRADED LA TER We cover these applications in greater detail in a later topic. Financial Math Support Materials Page 21 of 85 (3) COMPOUND INTEREST THE BASIC IDEA: ? PRINCIPAL GENERATES INTEREST ? RE-INVEST INTEREST TO GENERATE STILL MORE INTEREST ? RE-INVEST AGAIN TO GENERATE EVEN MORE INTEREST . . .etc Financial Math Support Materials Page 22 of 85 COMPOUND INTERESTSuppose we invest $100 000 at 10% p. a. with interest payable annually. What annual cash flows result from this investment? $100,000 Invested at 10% Compound Interest $800,000 Amount $700,000 $600,000 $500,000 $400,000 $300,000 $200,000 $100,000 $0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time in years Financial Math Support Materials Page 23 of 85 A LGEBRAICALLY ? ? ? ? ? ? Balance at end of year ? ? ? ? ? ? ? Balance after ? ? ? ? ? n FV = Financial Math Support Materials Balance at start of year ? ? ? ? ? ? (1? i) years is: PV(1 + i) n Page 24 of 85 G ENERALISING Suppose we invest $100 000 at 10% p. a. with nterest payable annually. What is the future value of this investment after 4 years? FV = $ Financial Math Support Materials Page 25 of 85 T HE POWER OF COMPOUNDING WITH COMPOUND INTEREST, â€Å"SMALL† SUMS NOW BECOME â€Å"LARGE† SUMS LATER (a) $1000 AT 13% pa FOR 50 YEARS : FV = $ (b) $1000 AT 14% pa FOR 50 YEARS : FV = $ Financial Math Support Materials Page 26 of 85 PRESENT VALUE : REARRANGING THE COMPOUND INTEREST FORMULA: PV ? FV n (1 ? i) COMPOUNDING NOW SHOWS THAT â€Å"LARGE† SUMS TO BE PAID LATER ARE WORTH ONLY â€Å"SMALL† SUMS NOW What is the present value of $1 million to be paid in 100 years’ time if the interest rate is 15% pa?Financial Math Support Materials Page 27 of 85 PRESENT VALUE : (Question 5 from 2001 2nd semester final exam) Tran Van Ng is to receive from his parents $1,000, $1,500 and $2,500 in 1 year, 2 years and 3 years respectively if he passes all subjects in his university degree each year. (a) What is the present value of th ese cash flows assuming a discount rate of 9% over the three years? (b) What is the present value of this these cash flows assuming a discount rate of 9% in the first year, 8% in the second year and 6% in the third year? Financial Math Support Materials Page 28 of 85 Present Value (a) PV ? $1, 000 ?1. 09 ? 1 ? $1,500 ?1. 9 ? 2 ? $2,500 ?1. 09 ? 3 ? $4,110. 41 (b) The value today of $2,500 received in 3 years time? 0 1 2 3 $2,500 Financial Math Support Materials Page 29 of 85 Measuring Average Growth Rates COMPOUND INTEREST IS A SPECIAL CASE OF COMPOUND GROWTH WHERE THE GROWTH RATE IS THE SAME EACH PERIOD IN COMPOUND GROWTH GENERALLY, THE GROWTH RATE MAY CHANGE EACH PERIOD IN PRACTICE, GROWTH RATES CHANGE FROM YEAR TO YEAR. WE NEED TO BE ABLE TO CALCULATE THE FUTURE VALUE AND PRESENT WHERE VALUE RATES THROUGHOUT OF OF THE AN INVESTMENT RETURN LIFE CHANGE OF THE INVESTMENT. Financial Math Support Materials Page 30 of 85 Measuring Average Growth RatesSUPPOSE YOU INITIALLY INVEST $1,000 IN AN ASSET WHOSE VALUE CHANGED YEAR BY YEAR, AS FOLLOWS: YEAR GROWTH RATE %pa 1 2 3 4 5 35 15 9 What is the future value of this investment? What is the average annual growth rate of this investment? After 4 years, the value of the asset is : Financial Math Support Materials Page 31 of 85 Measuring Average Growth Rates AVERAGE ANNUAL GROWTH RATE (g) NOTE THAT THE ANSWER IS NOT: Financial Math Support Materials Page 32 of 85 Average Growth Rate Suppose we invest $1million in an asset whose value changes as follows, year 1 growth rate 20% 2 -8% 3 -15% 4 3% What is the future value of this nvestment? What is the average annual growth rate of this investment? Financial Math Support Materials Page 33 of 85 Average Growth Rate The average annual growth rate is : Financial Math Support Materials Page 34 of 85 Average Growth Rate (Question 6(a),(b) from 2001 2nd semester final exam) House prices in Melbourne have soared in the past four years. The median price of a house in Clayton at the end of each year is as follows: 1997 – $122,000 1998 – $135,000 1999 – $147,000 2000 – $185,000 (a) What is the annual compounding growth rate for housing prices calculated at the end of each year, that is 1998, 1999 and 2000? b) What is the average annual compound growth rate for housing prices over this period? Financial Math Support Materials Page 35 of 85 Average Growth Rate (a) 1998 – 1999 – 2000 – (b) ?1 ? r ? ? 3 Financial Math Support Materials Page 36 of 85 Calculating Average Growth rate – continued g = average growth rate The average rate of growth per period over n time periods is: n ? ? ? Value at end – Value at beginning ? 1 + g ? = ? 1 + ? ? Value at beginning ? ? ? ? Solving for g, 1 ? Value at end – Value at beginning ? n g = ? 1 + ? -1 Value at beginning ? ? 1 $185,000 – $122,000 ? 3 ? g = ? 1 + ? -1 $122,000 ? ? 1 ?3 ? g = ? 1. 16793 ? ? ? – 1 = 0. 148869 g = 14. 89% Financial Mat h Support Materials Page 37 of 85 Real (after Inflation) Interest Inflation reduces the purchasing power of money. We require a methodology to adjust rates of return for the impact of inflation. TODAY 1 box of biscuits costs $2. 00 I have $200 I can consume 100 boxes of biscuits IN ONE YEAR Inflation rate (10%) 1 box costs $2. 20 To consume the same quantity of biscuits I will require To have a real return of, say, 4% pa, I need to be able to purchase 104 boxes. Financial Math Support Materials Page 38 of 85 Real (after Inflation) Interest Real increase in consumption of 4%Financial Math Support Materials Page 39 of 85 Real (after Inflation) Interest FORMULA : (1 + q) = (1 + r)(1 + p) where : q is the quoted interest rate r is the real interest rate p is the inflation rate A lender quotes an interest rate of 18% pa for an investment. If the inflation rate is currently at 4% pa, what is the real interest rate earned by the investor ? Rearranging: Financial Math Support Materials (1 + q) = (1 + r)(1 + p) Page 40 of 85 EFFECTIVE and NOMINAL (QUOTED) Interest Rates A BANK LENDS $1,000 AND QUOTES AN INTEREST RATE OF: (a) 12% pa, payable quarterly (that is, 3% each quarter) (b) 12% pa, payable semi-annually that is, 6% each half year) (c) 12% pa, payable annually (that is, 12% at the end of the year) How much interest does the bank earn at the end of one year under each of these three scenarios? Financial Math Support Materials Page 41 of 85 EFFECTIVE and NOMINAL (QUOTED) Interest Rates ? interest rate of 12% pa, payable quarterly REPAYMENTS $30 $30 1 2 $30 3 $30 4 Quarter The value at the end of the year of the interest payment in the The bank has effectively earned : Financial Math Support Materials Page 42 of 85 EFFECTIVE and NOMINAL (QUOTED) Interest Rates ? INTEREST RATE OF 12% pa, PAYABLE SEMI ANNUALLY REPAYMENTS $60 1 $60 2 Half YearThe value at the end of the year of the interest payment in the The bank has effectively earned : Financial Math Support Materia ls Page 43 of 85 EFFECTIVE and NOMINAL (QUOTED) Interest Rates ? INTEREST RATE OF 12% pa, PAYABLE ANNUALLY REPAYMENTS $120 1 YEAR The value at the end of the year of the interest payment is $120 The bank has effectively earned : Financial Math Support Materials Page 44 of 85 EFFECTIVE and NOMINAL (QUOTED) Interest Rates So a quoted (Nominal) interest rate of, 12% pa payable = 12. 55% payable annually. quarterly 12% pa payable = 12. 36% payable annually semi annually 12% pa payable = 12. 00% payable annually nnually To compare interest rate quotations (the nominal interest rate) we refer to an effective interest rate, that is, the interest rate that we would receive if interest were paid once at the end of the year. In the above example: Nominal (Quoted Rate) 12% pa payable quarterly 12% pa payable semi annually 12% pa payable annually Financial Math Support Materials Effective Rate 12. 55% pa 12. 36% pa 12. 00% pa Page 45 of 85 Formula Development If the nominal rate is j percent pa , compounding m times pa, Then after one year the principal, P, becomes: m j? ? S = P ? 1 + ? m? ? (C1) The effective annual interest rate, i, is therefore: = S-P S = -1 P P (C2) Replacing S in (C2) with equation (C1) produces: j? ? P ? 1 + ? m? ? i= P m -1 m j? ? i = ? 1 + ? m? ? Financial Math Support Materials ?1 (C3) Page 46 of 85 Effective and Nominal Interest Rates (a) NOMINAL TO EFFECTIVE If the nominal rate is 15% p. a. payable monthly, then the effective rate is : (b) EFFECTIVE TO NOMINAL If the effective rate is 15% pa then the nominal pa, with monthly payments, is : Financial Math Support Materials Page 47 of 85 Effective and Nominal Interest Rates (Question from 2002 mid semester exam) Abdul Hafahed purchases a car for $5,000 and sells it four months later for $6,000. a) What nominal annual rate of return did Abdul receive? (b) What effective annual rate of return did Abdul receive? (c) If inflation is at 2% pa, what real annual effective rate of return did Abdul receive ? Show your calculations. Financial Math Support Materials Page 48 of 85 Effective and Nominal Interest Rates (a) Four month return Annual nominal return = (b) Effective rate (c) Real annual effective rate : (1 + q) = (1 + r)(1 + p) Financial Math Support Materials Page 49 of 85 Compound Interest Formula j? ? FV = PV ? 1 + ? m? ? n Where: FV = future value PV = principal (present value) j = interest rate per annum as a percentage = mT = total number of periods over which investment is held m = number of interest payments per annum Solving for other terms by rearranging variables: PV = FV j? ? 1+ ? ? m? ? n 1 ? ? ? FV ? n ? j = ? – 1? m PV ? ? ? Microsoft Excel functions: Future value: FV(rate, nper, pmt, pv, type) Present value: PV(rate, nper, pmt, pv, type) Financial Math Support Materials Page 50 of 85 CONTINUOUS COMPOUNDING Nominal interest rate We know j? ? FV ? PV ? 1 ? ? ? m? mT Number of years Number of compounding periods per year What if compounding takes place at every moment, that is ? m ? ? ? . It can be shown that as ? m ? ? then: m j? ? j ?1 ? ? ? e lim ? m ? m where e is the base of natural logarithms (e ? 2. 71828) The Future value formula then reduces to: FV ? PVe jT or, FV ? jT PV ? jT ? FVe e Financial Math Support Materials Page 51 of 85 COMPOUNDING FREQUENCY $1,000 invested for 1 year at 12%: Compounding frequency Payment at end of year Annual Semi-Annual Quarterly Monthly Daily Continuously ? As the compounding frequency increases for a given nominal interest rate, the higher the interest repayments. However the interest repayment reaches a maximum with continuous compounding. Financial Math Support Materials Page 52 of 85Continuously Compounded Returns Nominal interest rate Recall FV ? PVe Using the notation and r where r ? jT . pt ? 1 ? PV pt ? FV pt ? pt ? 1e then Number of years rt pt e? pt ? 1 rt and rearranging we have; ? pt ? ln? e ? ? ln? ?p ? ? ? t ? 1 ? rt and ? pt ? ? rt ? ln ? ?p ? ? ? t ? 1 ? rt is the continuously c ompounding return from time period t-1 to t. Financial Math Support Materials Page 53 of 85 Continuously Compounded Returns pt Note: the term pt ? 1 is referred as the Price Relative. It is the proportional price change from time t-1 to t. The logarithm of the price relative is the continuously compounding return.Continuously compounding returns are often easier to work with. Two important properties: (1) Continuously compounding returns over a period can be added up to give a total continuously compounding return. (2) The average continuously compounding return over a period is the arithmetic average of each individual continuously compounding return. Financial Math Support Materials Page 54 of 85 Continuously Compounded Returns A stock price has a closing price of $3. 00, $3. 25 and $2. 90 over 3 days. What is the continuously compounding return on each day? What is the total and average continuously compounding return? Time 0 1 Price 3. 00 . 25 2 Return 2. 90 Total return from ti me 0 to 2 = Financial Math Support Materials Page 55 of 85 Continuously Compounded Returns An investor is given a choice of: (a) investing at 16. 5% p. a. , (b) investing at 4% per quarter, for 1 year (c) investing at 16. 3% p. a. and compounded daily. (d) 16. 3% p. a. continuously compounding. Which investment is chosen? Financial Math Support Materials Page 56 of 85 Calculate the effective rate in each case. (a) 16. 5% pa (b) (c) (d) Financial Math Support Materials Page 57 of 85 (4) MUTIPLE CASH FLOWS Cash Flow Stream : Future Value 0 1 2 3 $200 3. 5 $450 4 5 6 $800 1 2 3 If interest rate 9%pa = $1,712. 50 1 :$ 2 :$ 3 :$ Stream Future Value Financial Math Support Materials Page 58 of 85 Cash Flow Stream : Present Value 0 1 2 3 $200 3. 5 $450 4 5 6 $800 1 2 3 If interest rate = 9%pa 1 2 3 Stream Present Value = $ Financial Math Support Materials Page 59 of 85 Net Present Value – NPV The present value of the following stream of cash flows, using a discount rate of 7. 5%, is: 0 Cash flows: 1 2 3 $880 $560 $420 4 $980 PV’s =$ Suppose it cost the investor $2,000 to purchase this stream of cash flows, the net present value of this stream is: NPV = -$2,000 + $ =$ outflow Investment projects where NPV ? 0 are viable.Financial Math Support Materials Page 60 of 85 Internal Rate of Return – IRR One period: YEAR $ 0 -1000 1 +1120 Dollar return = $ Equivalently, solve for r : What value of r will produce an NPV = 0 ? PV of $1,120 Using discount Rate of r for 1 period Financial Math Support Materials No discounting required since $1,000 occurs â€Å"now† Page 61 of 85 Internal Rate of Return – IRR Two periods YEAR $ 0 -1000 1 +1120 2 + 25 Clearly, IRR > 12% pa but IRR < 14. 5% pa Why? Because this would be the rate of return if the additional $25 was received in year 1. That is, Thus 12% < IRR < 14. 5% But where in this range is the IRR ?

Preoccupation with Death in Hamlet Essay

â€Å"Hamlet† is a play permeated with death. Right from the opening scene of the play death is introduced, where the ghost of Hamlet’s father introduces the idea of death and its consequences. Preoccupation with death is a major theme in this play as shown in the numerous deaths of the main characters of Hamlet, Polonius, Gertrude, Ophelia, Claudius and Laertes. Taken off the web accurate definitions of â€Å"preoccupation† are the following: 1)a state in which you think about something so much that you do not think about other things; 2)something that you think about and want to do because it is important. This is exactly what the main characters are preoccupied by-death. An example would be that Hamlet is preoccupied by death throughout the story. It is apparent that Hamlet is haunted by his father’s death. When Hamlet encounters the ghost of his father, their conversation raises all kinds of unthinkable questions, for example murder by a brother, an unfaithful mother, that triggers Hamlet’s obsession. He feels compelled to determine the reliability of the ghost’s statements so that he can determine how he must act. Ultimately, it is his obsession with death that leads to Hamlet avenging the death of his father by killing Claudius. Although Hamlet’s preoccupation is deeply rooted in his character’s fascination with death, it could be a product of his grief. Hamlet’s most potent consideration of death comes in Act 4, Scene 3. His almost gruesome fixation with the idea of death is revealed by his mockery and such when asked by Claudius where he has hidden Polonius’ body. Hamlet’s answers seem to reveal an extremely morbid state of mind. Hamlet exclaimed how once the body dies, it goes through a cycle where it is eaten by worms, these worms are used to get food for another person therefore, that person digests the dead body. Finally, the graveyard scene shows how Hamlet views death and that he fears how no matter who you were or what you did that someday you too, will be at one with the earth and dirt only to become decayed, fed upon and then nothing. â€Å"No, faith, not a jot; but to follow him thither with modesty enough and likelihood to lead it; as thus: Alexander died, Alexander was uried, Alexander returned into dust; the dust is earth; of earth we make loam: and why of that loam, whereto he was converted, might they not stop at a beer-barrel? † (Act 5, Scene 1 Lines 201-206) As Hamlet continuously postponed the death of Claudius he became more preoccupied with the various ways he could have his revenge. Hamlet has completed his transformation from an unhappy young man to a hardened killer. He has no hope and despite Horatio’s praise, by this time he would not have made a good king.

Curriculum Development Paper

This curriculum paper discusses the normal development that occurs during the Toddlers’ stage of growth. It also discusses some of common respiratory and gastrointestinal diseases and disorders that are present throughout toddlerhood. It emphasizes important information related to the Nursing field. It thoroughly discusses the nursing management involved in the care of normal growth as well as the health deviations seen in toddlers. The target audience is a class of 3rd year nursing students. Pediatric nursing is important branch of nursing that should be tackled by junior level in a Nursing course.Goals/ Learner outcomes of the Lesson The goals of the lesson are for the students to understand the normal growth and development seen in toddlers. They should identify the different health abnormalities affecting toddlers. They should have thorough knowledge about the nature of the disorders discussed. Students should be able to identify the signs and symptoms related in every dis ease/disorder presented. They should enumerate the nursing management and its rationale given to sick toddlers. Learning ObjectivesAt the end of the lesson, the students will be able to understand the nature of Seizures, Cerebral Palsy, Meningitis, Primary Complex, Intestinal Parasitism and Croup. They should be able to describe methods to promote preventive measures against Seizures, Cerebral Palsy, Meningitis, Primary Complex, Intestinal Parasitism and Croup. They should be able to identify different laboratory and diagnostic examinations done for each condition. Students are expected to identify the common presenting clinical manifestation for each condition.And lastly, they should be able to enumerate nursing management done for clients with Seizures, Cerebral Palsy, Meningitis, Primary Complex, Intestinal Parasitism and Croup. Instructional design model, Learner characteristics, Learning theory and other applicable characteristics Instructional design model Dick and Carey Desig n Model. Dick and Carey Model involves all the phases described previously in the ADDIE model, commencing with identification of instructional goals and finishes with summative evaluation. This model is suitable for a variety of context areas including primary and secondary schools as well as business and government.It is also adaptable for a variety of users ranging from movie to expert, as the step by step descriptions aid with progress through the model (Taylor, 2004). Learner Characteristics There are many factors that influence a client’s ability, motivation and desire to learn. Addressing these factors when planning educational interventions is essential, because the effectiveness of the intervention can be at stake. Learner characteristics include, among others, culture/ethnicity, literacy, age, health status, education level, and socioeconomic status (De Young, 2003, p. 59). Learning TheoryCognitive Learning Theory. The key to learning and changing is the individualâ €™s cognition (perception, thought, memory, and ways of processing and structuring information). According to this perspective, to learn, individuals must change their cognitions. A highly active process largely directed by individual, learning involves perceiving the information, interpreting it based on what is already known, and then reorganizing the information into new insights or understanding (Bastable, 2004, p. 50) Content Outline Seizures I. Seizure II. Types of Seizures II. Signs and symptoms of Child with SeizuresIII. Medical management / Pharmacologic management (Nursing considerations) IV. Nursing Management V. Preventive Measures Cerebral Palsy I. Cerebral Palsy II. Signs and symptoms of Child with Cerebral Palsy III. Medical management / Pharmacologic management (Nursing considerations) IV. Nursing Management V. Preventive Measures Meningitis I. Meningitis a. ) Bacterial b. ) Viral II. Signs and symptoms of Child with Meningitis III. Medical management / Pharmacol ogic management (Nursing considerations) IV. Nursing Management V. Preventive Measures Primary Complex I. Primary Complex II.Signs and symptoms of Child with Primary Complex III. Medical management / Pharmacologic management (Nursing considerations) IV. Nursing Management V. Preventive Measures Intestinal Parasitism: I. Nature of Intestinal Parasitism II. Life Cycle of Intestinal Parasites III. Intestinal Parasites: a. ) reservoir b. ) portal of exit from reservoir c. ) method of transmission d. ) Portal of entry e. ) susceptible host IV. Signs and symptoms of Child with Intestinal parasites V. Medical management /Pharmacologic management (Nursing considerations) VI. Nursing Management VII. Preventive Measures CROUPI. Nature of Croup II. Signs and symptoms of Child with Croup III. Medical management / Pharmacologic management (Nursing considerations) IV. Nursing management Instructional Methods Lecture. Lecture can be defined as a highly structured method by which the teacher verbal ly transmits information directly to groups of learners for the purpose of instruction. In its purest form, the lecture format allows for only minimal exchange between the teacher and learner, but it can be an effective method of teaching in the lower-level cognitive domain to impart content knowledge (Bastable, 2004, p. 357)In this type of teaching strategy, the teacher will provide the necessary information about the normal growth and development of toddlers as well as the health deviations common to toddlers. The micro teachers will emphasize the important nursing management involved in caring of sick toddlers Group Discussion. It is a method of teaching whereby learners get together to exchange information, feelings, and opinions with one another and with the teacher. It is one of the most commonly employed instructional techniques. The activity is learner-centered and subject-centered (Bastable, 2004, p. 358).This strategy is incorporated in the lecture. Once in a while, the te acher would be asking questions for the class to discuss. After each video clip of certain illnesses, the class would be asked to give their opinions about what they have watched. They will be asked about certain information that should be remembered in the video clip. Questioning. The use of questioning places learners in an active role. They are asked to recall, to form links between previously isolated information, to analyze statements or beliefs, to evaluate the worth of ideas, and to speculate about what would happen â€Å"if† (De Young, 2003, p.126) This type of strategy will be used as to serve as a recitation for students. This will also serve as a pointing system for them to get rewards and additional credit in their evaluation quiz. Using of audiovisuals (handouts, power point presentation, video clips). If used appropriately, audiovisuals can greatly enhance teaching and can add interest and stimulation to the classroom (De Young, 2003, p. 131). Instructional Mate rials Handouts. The teacher would provide handouts containing important information students can review upon after the class. Power point presentation.Power point presentation is the type of visual aids that will be used; this is for the convenience of both the teachers and students. Students with portable storage devices can acquire the software copy of the report. Video clips. Video clips related to the topics being presented by the micro teachers would be shown to students and they would be asked to give opinions about what they have watched. Evaluation Methods Before the class ends, a 30 item quiz will be given consisting of true-false questions and situational types of questions for analysis and critical thinking using multiple choice.Multiple-Choice Questions. Nursing examinations are often written in the multiple format. There are several reasons for this fact. One is that although they are challenging to create, they are easy to score and can be scored by computer. Another r eason is that licensure and certification examinations are multiple-choice tests, and therefore educators want learners to be familiar with questions like the ones that they will be taking on these exams (De Young, 2003, p. 265). True-False Questions.True-false questions are designed to test a learner’s ability to identify the correctness of statements of fact or principle (De Young, 2003, p. 268). References Bastable, S. B. (2003). Nurse as Educator: Principles of Teaching and Learning for Nursing Practice. Massachusetts: Jones and Bartlett Publishers. De Young, S. (2003). Teaching Strategies for Nurse Educators. New Jersey: Pearson Education, Inc. Taylor,L. Educational Theories and Instructional Design Models. Their Place in Simulation. [PDF document]. Retrieved from Lecture Notes Online Web Site:

Ragging in Colleges Essay

The accurate meaning of the word ‘ragging’ is to ‘tease’, but even the dictionary says it is an archaic meaning. The main objective of ragging is to ‘break the ice’ between the senior students and the new entrants. Ragging is any disorderly conduct whether spoken or written or by an act which causes annoyance, hardship or psychological harm or raises fear or shame in a student. It is generally committed by ‘senior’ students, upon the first year students. Ragging generally takes place in colleges and hostels. The new students feel that they are in for a series of practical jokes at the hands of the senior students. Once they fall into the clutches of the latter, they don’t find a way to escape. There are a few senior students in every hostel who don’t take enough interest in studies. They indulge in ragging, bullying etc. They create an image of themselves as rowdies. No one dares to interfere with their ways. Ragging o riginated in the west. But today, it has reached the Indian society too. Some people feel that it is a socio-cultural problem. The truth is that in some cases, ragging has occasionally, ended in fighting, serious injuries, and even deaths, leading to the ruin of some brilliant careers. Senior students tease the new students about their looks and manners. Students wearing glasses, have their glasses snatched away and are made to read without them. Sometimes the eatables brought by the new students are eaten by the seniors in the formers’ presence. A new student who resists becomes a target for harassment.During the trail, he might be forced to admit his guilt, he is pressurised by physical threats and humiliation. After the trail, the accused asked to polish the shoes of his senior students. Ragging has some positive effect too on the new students. It influences the new students to behave in a socially acceptable way. It makes one change one’ eccentric behavior. It creates self- awareness. Those who endure it get emboldened. They become courageous. They get used to facing hardships in life. They learn to face unpleasant situation boldly. Many a time, it is seen that the juniors and the seniors become very good friends after the ragging period. In the beginning, ‘ragging’ was an amusing practice. it has degen erated into an evil. It has become a synonym for ‘torture’. It should be banned. The supreme court of India has defined it as. â€Å"Any disorderly conduct whether by words spoken, or written or by act which adversely affect the physique or psyche of fresher or a junior student is an act of ragging.† But if through  ragging the decency and morals are violated, one’s body gets injured, if any wrongful restraint and criminals intimidation is involved in it, then ragging becomes a legal offence. More effective steps need to be taken to deal with the evil. Institutes should arrange counseling session for fresher so that they can speak their mind. Anti ragging cells should also be established. A fresher party should be organized by the institutes itself within town weeks of the academic session so that junior and senior can easily interact with one another.

The Homeless Assignment Example | Topics and Well Written Essays - 1500 words

The Homeless - Assignment Example In addition, homelessness can be caused by mental disorders, drug abuse and discrimination by the society due to certain reasons like sexual orientation. Some other people find themselves homeless owing to domestic violence, mortgage foreclosures, eviction by tenants and forced expulsion by government in order to set the land aside for other developments. The problem of homelessness was not existent in pre-historic times. Initially, human beings lived in traditional shelters such as caves, huts, and tents. Building these structures was easy and everyone could afford a dwelling because natural building materials were readily available and almost everyone knew how to build. However, during the modern times, the art of building became professional and expensive. Many individuals migrated to urban areas during the industrial revolution. Increased homelessness occurred because of higher land and house prices and strict housing codes. People who were unable to pay the exorbitant rental fees were evicted and, therefore, became homeless. Around 1500s, the homeless in England were punished because they were seen as unauthorized beggars. However, in the 16th, 17th and 18th centuries, they provided them with housing and training for jobs, instead of punishment in order to prevent them from over-relying on the state. The homeless people on the s treets in the United States increased after the American civil war (Bloom, 2005). More people were left homeless in the 1930s because of the Great Depression, which also resulted in increased poverty. In the 1970s, the homeless population increased due to de-institutionalization of people with mental illnesses. The psychiatric, outpatient, and social services that were promised to these people were not provided and, consequently, most of them ended up being homeless. In the 1980s, the number of homeless people increased

Merits of raising capital through the issuance of Bonds or through Essay

Merits of raising capital through the issuance of Bonds or through issuance of Stocks - Essay Example Merits of raising capital through the issuance of Bonds or through issuance of Stocks Marvin Appel emphasized that â€Å"corporate bonds are debt instruments issued by organizations. And, unlike government which is very least likely to default, there is always risk that a corporate business may not be able to pay its obligations to the bondholders† (10). Matt Evans discussed few advantages of issuing bonds to raise capital for a company’s operations. Some of these advantages are: 1. Interest payments made to bond holders are tax deductible as reflected on the issuing corporation’s income statement; 2. Bond issuances do not dilute earnings per share or decrease control within the company; 3. Usually, cost of bonds issued is fixed; interest and principal do not change within the life of the bond; and 4. Expected return of investment to investors is usually lower than ROI on stocks. For tax purposes, legitimate interest expense payments to banks, financial institutions, and other investors are deductible from income before tax. This will include interest or coupon payments to bondholders of the corporation which issued bonds. This is part of the benefits of using funds from debt financing to augment business performance and the same time paying less tax with respect to the company’s income for a covered period. By issuing bonds, it does not change the control structure of a corporation. Equity holdings of stockholders will remain the same; also the same base for earnings-per-share consideration. On the other hand, Evans also pointed out advantages for a company raising capital through the issuance of stocks. These include: a. Stocks have no fixed payments required to investors; investors will receive return of investment based on profits; b. There is no maturity date on the stocks certificate and invested capital does not have to be repaid within a fixed period; and c. Issuing stocks will improve the credit worthiness of the company. At the company’s standpoint, issuance of stocks to raise capital is the cheapest way to finance business operations contrary to bonds. Unlike bonds, there are no scheduled payments for coupon and bulk of funds upon maturity. Shareholders will get income from their investments through dividends if they opt to hold their stocks for a longer period. By issuing stocks, the generated funds will improve ratios like current ratio, acid-test ratio, and debt equity ratio that are of significant considerations for financial statement users. Moreover, if a company continues to have negative results of operations, the invested capital by the stockholders may be absorbed by the loss. That is why it is regarded as the cheapest way to finance business operations. By its nature, stock holdings are not guaranteed in terms of return of investments. B. Risks of raising capital through the issuance of Bonds or through issuance of Stocks Bonds are debt instruments and usually they are huge fund obligations to pay in the future. Ian Giddy had stated that when a corporation borrows up to its capacity, it loses its flexibility of financing some more future projects through debt financing. â€Å"The corporation that is issuing bonds should continue to perform well in business to make profit enough to pay back its obligations on bonds† (Appel 29). If an issuing corporation will default in paying obligations on bonds, it has a negative impact to the organization in different aspects in the bond market and in the industry. It can be regarded that in the company’s perspective, debt financing through bonds is an expensive way of raising capital

Why Less Homework Should be Assigned to Students Essay

Why Less Homework Should be Assigned to Students - Essay Example Such an increase in the workload of the students has created extra stress for the students besides allowing schools to compete with each other. It is argued that the schools have deliberately increased the level of difficulty of the curriculum therefore naturally the volume and extent of homework given to students has increased too. (HU) It is also critical to note that teachers claim that more homework actually increases the capability of the students to face the world and its challenges. However, studies do suggest that doing extensive homework in the school has little or no effect on the study skills of the students during their college. During college days, students actually have a lot of time to study as they only have few study sessions during the week. More amount of homework therefore not only make the students physical exhausted but it can also create mental fatigue. Carrying heavier books increases the weight which students have to carry thus making them physically fatigued. The above arguments, therefore, suggest that there should be less homework assigned and the students must be allowed to relax and have a lower amount of homework. There is a greater need to re-design and re-develop the way students are taught at schools. This can help the students to have less homework and more chances to engage themselves in creative and innovative activities.