Quantitative Reasoning

              Inflation Calculator: http://www.bls.gov/data/inflation_calculator.htm #1. (From BLS) According to the Census Bureau, the median value of a home was $11,900 in 1960. In today’s dollars, how much purchasing power did $11,900 have in 1960? Round to nearest cent. (5 points) ____________________________________________________________________ ____________________________________________________________________ #2. (Based on Bolker & Mast. CSM. Exercise 4.7.19.) When is a raise not a raise? Your employment contract calls for a 6% raise every three years. If you began your employment in the beginning of 2010, what was your first effective* raise, applied in the beginning of 2013? (10 points) (*effective = taking inflation into account) ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ #3. (10 points) (Based on Bolker & Mast. CSM. Exercise 4.7.8.) Twenty years as two decades: (A) Use the inflation rate calculator to find the inflation rate (as a percent) (i) From 1995 to 2005, (ii) From 2005 to 2015 and (iii) From 1995 to 2015. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ (B) Explain why the inflation rate from 1995 to 2015 is not just the sum of the rate from 1995 to 2005 and the rate from 2005 to 2015. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ (C) Use the proper method to compute the inflation rate from 1995 to 2015 correctly from the two rates for the two previous decades. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ Name_______________________________________________________ #4. National Debt (20 points) Remember to show all work and identify your sources. According to the United States Department of Treasury, the national debt [also known as gross government debt] on January 1st, 2013 was $16,432,730,050,569.12 ˜ $16.5 trillion. (A) Calculate, to the nearest thousand, the average share of the debt for each person in United States in 2013. (B) By some estimates, this debt increases at an average of just $2.5 billion per day. Estimate the total increase in the debt for one year, to the nearest billion. (C) Use the web to find the current national debt of the United States and check if the value supports the claim in (B); then update the average per capita share of the debt. (D) Use the web to find Greece’s current national debt, and the average share of the debt for each person. (E) Find a country whose current national debt per capita is less than $19,000. #5. (10 points) (Based on Bolker & Mast. CSM. Exercise 4.7.17.) A raise tied to the inflation rate. Stella’s current salary is $65,000. Assuming that the current annual inflation rate is 2.5%, consider these two different ways to calculate a raise that's “12% over the rate of inflation": (A) What is Stella’s new salary if you simply add the inflation rate to her 12% raise and use that as her percentage raise? ____________________________________________________________________ ____________________________________________________________________ Name_______________________________________________________ (B) What will she earn if you first compute her salary after the 12% increase and then increase that to take inflation into account? ____________________________________________________________________ ____________________________________________________________________ (C) Which is the best approach (for Stella - since it's her salary)? ____________________________________________________________________ #6. (Based on Bolker & Mast. CSM. Exercise 4.7.20) (15 points) Private colleges vastly outspent public peers. The Fort Wayne, IN Journal Gazette reported on July 10, 2010 that: “Private institutions, on average, laid out $19,520 per student for instruction [in 2007], a 22 percent increase from a decade earlier”, the Delta Project on Postsecondary Education Costs, Productivity, and Accountability, a Washington-based nonprofit research group said Friday. Public universities spent $9,732 for each student, up 10 percent in the decade, according to the report. (A) How much did private colleges spent per student in 1997? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ (B) When adjusted for inflation, what was the actual percent change in the amount spent per student by private colleges from 1997 to 2007? (You may use any method; it may help to treat the increase in expenditures as “a raise” and use the same approach we used in class to find the “real raise,” or “pay cut,” if applicable) ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ (C) How much did public colleges spent per student in 1997? ____________________________________________________________________ ____________________________________________________________________ (D) When adjusted for inflation, what was the actual percent change in the amount spent per student by public colleges from 1997 to 2007? (You may use any method; it may help to treat the increase in expenditures as “a raise” and use the same approach we used in class to find the “real raise,” or “pay cut,” if applicable) ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ Name_______________________________________________________ #7. (Based on Bolder & Mast. CSM. 2013. Exercise 6.14.6.) Cash-strapped MBTA proposes fare increase. (30 points) On March 29, 2012 the Massachusetts Bay Transportation Authority (MBTA) provided the data summarized in the table below. Provide the table/graphical answers to (A) and (B) in a separate MS-Word file. (A) Create a spreadsheet for this data, with eight rows (one for each of the eight categories: Card-Bus, Card-Subway, Senior-Bus, Senior-Subway, Student-Bus, StudentSubway, Ticket-Bus, Ticket-Subway) and three columns, for the Category Name, the Existing Fare and the Proposed Fare. Create a properly labeled bar graph to display the data. (Hint: select all cells and Insert clustered column chart). Copy and paste the table and the bar chart below. (B) Label the next two columns appropriately to hold the Absolute and Relative (%) changes (Recall that absolute is “proposed – existing”, while relative is the absolute change as a percent of the existing). Fill those columns with Excel formulas to compute the correct values. Do not compute the values elsewhere and enter them in the spreadsheet as numbers. (Refer to Chapter 6 of our textbook and the Excel QuickRef for additional reminders on Excel formulas). Copy and paste the new table below. Create a properly labeled bar graph for the Absolute Change, and another one for the Relative Change. Paste below. Which is more relevant and why? (C) Imagine that you are addressing a public meeting about these fare increases. How would you argue that an unfair burden is being placed on people who pay using a Charlie Ticket? How would you argue that senior citizens are most hard hit? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ________________________________