ATC reports an average asset duration of 4 years and an average liabil.pdf

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ATC reports an average asset duration of 4 years and an average liability duration of 5 years. In its latest financial report, the association recorded total assets of $3 billion and total liabilities of $1 bilion. a) If interest rates began at 4 percent and then suddenly fell to 3.5 percent, what change will occur in the value of ATC's net worth? (5 marks) b) By how much would ATC's net worth change if, instead of falling, interest rates rose from 4 percent to 4.3 percent? Show final answer to 4 significant figures. e.g. 0.01234 billion. ( 5 marks).

ATC reports an average asset duration of 4 years and an average liability duration of 5 years. In
its latest financial report, the association recorded total assets of $3 billion and total liabilities of
$1 bilion. a) If interest rates began at 4 percent and then suddenly fell to 3.5 percent, what
change will occur in the value of ATC's net worth? (5 marks) b) By how much would ATC's net
worth change if, instead of falling, interest rates rose from 4 percent to 4.3 percent? Show final
answer to 4 significant figures. e.g. 0.01234 billion. ( 5 marks)

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Background: Suppose we want to model the spread of an infectious disease through a population. In the previous assignment, we did this with a discrete model. Here, we'll formulate things as a continuous model. We'll keep track of the numbers of individuals susceptible to the disease S ( t ) , infected by the disease I ( t ) , and recovered from the disease R ( t ) at time t (measured in days). Infected individuals have a chance to transmit the disease upon contact with a susceptible individual at a rate > 0 . Infected individuals also recover from the infection at a rate > 0 . We assume that all N individuals in the population produce offspring at a rate b > 0 and these newborns add to the pool of susceptible individuals. Finally, individuals in all disease states can die due to natural causes at a rate equal to the birth rate b . This description can be captured by the following system of equations: d t d S = b N S I b S d t d I = S I I b I d t d R = I b R Problems Problem 1 [3 points]: Given that S , I , and R are measured in number of people and t is measured in days, what must be the units of b , , and ? Justify your answer. Problem 2 [3 points]: Let N ( t ) = S ( t ) + I ( t ) + R ( t ) be the total population size at any point in time t . If the total population size remains constant for all time (i.e., N ( t ) = N for all t , where N is a constant) we say we have a "closed population". Show that the population in our model is closed. (Hint: Think about the rate of change d t d N of the population size and what must be true for the population to be constant.).

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BACKGROUND Jim Norbuck was born in rural central Pennsylvania and graduated from high school in the same town. He subsequently attended Bucknell University for two years and then transferred to the University of Illinois. He graduated from Illinois with a B.A. degree with an English major and a philosophy minor. Norbuck then attended the University of Wisconsin, where he received a master of arts degree. Norbuck started working on a Ph.D. but decided that he was tired of school and wanted to work. Consequently, he moved back to Pennsylvania, where he was a substitute high school teacher and taught as an instructor at a local college. Much to his dismay, the pay was quite poor and he needed a higher-paying job. On August 7, Norbuck applied for a job at the nearby Leech Industries plant. From some friends Norbuck had learned that Leech Industries' policy was not to hire people with a college education for blue-collar jobs (because management believed that college-educated individuals became bored faster in blue- collar jobs, which increased the cost of production). As part of the job application process, Norbuck filled out a written job application. In the education section Norbuck circled the number 12 next to the heading "Highest Grade Completed" and left the block pertaining to college blank. In the experience section of the application, Norbuck did not mention his prior teaching experience. The company did not verify any of his answers. On October 22, Norbuck was hired by Leech Industries and commenced work as a utility person in the tube plating department working the third shift from 11:00 P.M. to 7:00 A.M. After 30 days his wage was increased because he had successfully completed the probationary period for new employees. The steel industry experienced a business slowdown, however, and Norbuck was laid off in December. On January 3 , he was recalled to work as a labor pool person in the foundry department. On January 9 , he was recalled to his original position as a third shift utility person in the plating department. All these positions were part of a bargaining unit represented by the United Steelworkers. Meanwhile, the collective bargaining agreement between the United Steelworkers of America Local 55 and Leech Industries expired on January 18. The negotiators were unable to reach an agreement, and the union went out on strike. During the strike Norbuck was actively involved in supporting the union and wrote several pamphlets. These pamphlets, distributed to striking workers, urged them to maintain solidarity so that the union would be successful in winning new contract gains for the bargaining unit. Susan Napoli, assistant director of human resources at the plant, noticed these pamphlets and heard rumors that Norbuck was college-educated. Thus, Napoli initiated an investigation into Norbuck's background-both his previous employment and his education. Norbuck was the only employee for whom Napoli conducted such an investigation. The .

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