Term paper due Thursday, December 11.

1. Take this opportunity to review what you've learned this semester, in preparation for the final. Go through all the previous homeworks. Look at some of the problems you got wrong and try to do them now. Then check the answer.

   Turn in

   • a list of the problems you got wrong then and know how to do now,

   • questions for us about problems you got wrong then and still don't know how to do even after trying and looking at the answer. (If you send us some of those questions in email we can try to answer them in class.)

2. Use the spreadsheet PayingOffADebt.xls we studied in class to answer the following questions:

   1. How long would it take to pay off a $200,000 mortgage if the interest rate is 7% and you can afford $17,000 a year in mortgage payments. How much will you have paid in interest by the time you're done.

   2. What would you have to pay each year in order to pay off the mortgage in 15 years? In 30 years? How much will you have paid in interest in each case?

3. Suppose you are buying a new car for $20,000 and want to know what it will be worth as it ages.
   Use the auto depreciation calculator at www.ncbuy.com/auto/calc.html?show=1007 to complete the second column of this table in Excel

        age of car    value     percent change
             0        20,000
             1        15,000         -25
             2        13,200         -12
           ...
            20           741
   

   The third column is the percent change in the previous year. Tell Excel to compute that for you.
   1. Create a chart displaying this information. Find an exponential model (an exponential trend line) that best fits this data.

   2. For the exponential model you found, what is the fixed annual percentage decrease in the value of the car?

   3. Write a few sentences comparing the results from the model with the values calculated at the web site.

4. (Extra credit). Suppose you owe $1000 on a credit card that charges you 2% interest per month. You can pay this off by sending them $100 each month, or by sending them $50 every two weeks. Compare the total interest you pay in each of these cases.

   You can assume there are exactly four weeks in each month, and that the credit card company makes its interest and balance computations each time it receives a payment from you.

5. (Extra credit) Thomas Malthus, an economist and clergyman in England wrote in "An Essay on the Principle of Population" in 1798:

   I think I may fairly make two postulata. First, That food is necessary to the existence of man. Secondly, That the passion between the sexes is necessary and will remain nearly in its present state. These two laws, ever since we have had any knowledge of mankind, appear to have been fixed laws of our nature, and, as we have not hitherto seen any alteration in them, we have no right to conclude that they will ever cease to be what they now are, without an immediate act of power in that Being who first arranged the system of the universe, and for the advantage of his creatures, still executes, according to fixed laws, all its various operations.

   The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction, and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague advance in terrific array, and sweep off their thousands and tens of thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world.

   1. Malthus claimed that the food supply grows in a linear fashion. He constructed a unit for the food supply that measured the amount of food needed for one person for one year. He estimated that the food production in Britain in 1798 was 7,000,000 food units and that food production might increase by a constant amount of 280,000 units each year. Write a linear function that models this situation.

   2. Malthus also believed that the populuation of Britain was growing at a rate of 2.8% each year. In 1798, the population of Britain was about 7,000,000. Write an exponential function that models this situation.

   3. Was there enough food for each individual in Britain in 1798?

   4. Using Malthus' models, determine whether there be enough food for each individual in Britain in 1800.

   5. Malthus claimed that the size of the population in Britain would eventually be larger than the size of the available food supply - a prediction we now call "the Malthusian dilemma." He didn't have Excel to do the arithmetic for him, but we do. Use it to build a table showing the amount of food per person for each year starting in 1798 and estimate when Malthus predicted disaster would occur.

   6. Was Malthus correct?

6. (Extra credit) Most credit cards set the minimum payment as a fixed percentage of your balance, not as a fixed amount. Modify the spreadsheet PayingOffADebt.xls so that it uses the fixed percentage to use each period rather than a fixed amount and adjust the formulas like =MAX(C11*(1+RATE)-PAYMENT,0) accordingly.

   Then compare how long it would take to pay off a $1000 credit card bill accruing interest at 1.65% per month if

   • the fixed monthly payment is $40.
   • the monthly payment is 4% of the outstanding balance.