Homework 2
Math 114Q, Section 10

  1. The government's Consumer Price Index web page at www.bls.gov/cpi/ starts with this description:
    The Consumer Price Indexes (CPI) program produces monthly data on changes in the prices paid by urban consumers for a representative basket of goods and services.
    Find out what you can about what's in the "representative basket of goods and services."

  2. Use the Inflation Calculator link part way down that page to compute the inflation rate (as a percent) from 2000 to 2003. Explain why you don't get an accurate answer if you use just $1 instead of $100.

  3. Use the calculator to find the inflation rate from 2003 to 2007.

  4. Use the answers to the two previous problems to compute the inflation rate from 2000 to 2007. Do this with your calculator, not with the inflation calculator from the web page.. Explain why what you do will work. Then check your result using the web calculator.

  5. Tuition and fees for a full-time undergraduate at UMass Boston in 2006 were $4,133 per semester. For fall 2007, tuition and fees totaled $4,418.50.

    1. What is the percentage increase in the cost per semester for a full-time student?

    2. Between 2006 and 2007 the value of the dollar changed due to inflation. If you take inflation into account, what is the true percentage increase in tuition and fees?

  6. I saw a great shirt on the clearance rack at my local store and it was marked "50% off original price".  I had a special coupon giving me 50% off the sale price of any item in the store.  Should I get the item for free?   Write a convincing argument as part of your answer.

  7. According to a survey conducted in spring 2006 by Northeast Apartment Advisors, an Acton research firm, the average monthly rent in Greater Boston was $1,355, an increase of 3.6 percent from 2005.  What was the average monthly rent in greater Boston in 2005?

  8. An article in The Christian Science Monitor included the following information:  "...the percentage of adults who report reading daily newspapers has fallen from 81 percent in 1964 to just 52 percent in 2004." Why would it be incorrect to say that the newspaper reading has decreased by 29% from 1964 to 2004?  How could you fix this statement?  Bonus:  Figure out the actual percentage change in newspaper readership from 1964 to 2004? 

  9. Some student loan agencies have set up incentives to reward borrowers who make consistent, on-time payments.  Here's one example:  if a borrower authorizes automatic monthly payments from a bank account, the interest rate on the loan is reduced by 0.25 percentage points.  If a student has a loan at a 6.8% interest rate and authorizes the automatic withdrawals, what would the new interest rate be?  (We'll talk more about loans and interest rates later in the semester.)

  10. On Thursday, September 13 the The Boston Globe published the article "Scores rise, but disparity goes on: MCAS results spur calls to aid minority students" Read the article and look at the graph to answer the following questions:

    1. Find two places in the article where the reports talks about percentage points.  Write them out and try to explain the references.

    2. Write a short statement of how the graph relates to the article.  Does it support the statements in the article?  Can you check any of the percentage point statements in the article using the graph?

    3. In September 2006, the Globe published a story summarizing the results from the spring 2006 MCAS. Here is a link to the graphic that accompanied that article. Use that graph and the graph enclosed with today's story to draw two conclusions with percentage points.
Extra Practice: You do not have to turn these problems in, but we will be happy to look them over if you do They are intended to give you extra practice in working with percentages.

  1. According to Enrollment Services, there are 13,200 students enrolled at UMass Boston this fall.  Enrollment Services reported that 837 of these students are in the College of Nursing. Calculate the percentage of students in the College of Nursing.

  2. In fall 2006 there were 2,426 new undergraduate students.  In fall 2007 there are 2,539 new undergraduate students.  Find the percentage change in undergraduate students from fall 2006 to fall 2007.

  3. In fall 2006 the College of Nursing enrolled 690 undergraduates.  The enrollment of undergraduates in the College of Nursing increased by 20.4% in fall 2007.  What is the enrollment in fall 2007?

  4. Enrollment Services reported that there are 4434 undergraduates in the College of Liberal Arts in fall 2007.  They calculated that this is a 5.8% increase from last fall's enrollment in the College of Liberal Arts.  How many undergraduates were enrolled in the College of Liberal Arts in fall 2006?