The test will be 60 minutes long, given during class on
Friday, Feburary 28. You may not use any notes or books.
A calculator is recommended, but not strictly required.
Please bring a photo ID.
Information concerning Midterm #1
Make up tests will be allowed only if pre-arranged. If you are sick,
or call me in my office (632-7306) before the test.
The exam will cover Chapters 1 and 3 of the text.
The following is a partial list of concepts and skills you may need during
- Understand and be able to explain how each of the following voting
systems works: Plurality, Runoff, Borda's Method, and Approval Voting. Be
able to explain the advantages and disadvantages of each system.
- Be able to explain what a Condorcet winner is. Understand that not
every election has a Condorcet winner!
- Given a table of preference rankings, be able to figure out which
candidate would win each type of election, and which candidate (if any) is a
- Be able to explain what Pareto optimality and independence from
irrelevant alternatives mean. Know which of the voting systems we've
studied (plurality, runoff, Borda) satisfies each of these properties. Give
an example of a voting system that does not satisfy the Pareto optimality
- Know Arrow's Impossibility Theorem: Other than a dictatorship, no voting
system based on preference rankings satisfies both the Pareto optimality and
the independence from irrelevant alternatives properties.
- Know basic properties of logarithms. Be able to use logarithms to solve
equations involving exponents.
- Understand that simple interest means that interest is paid only on the
amount originally deposited, which is called the principal, or present
value. With simple interest, the future value is calculated by the formula
- Understand that in a compound interest account, interest is compounded at
regular intervals, and is paid on the principal as well as on all previous
interests payments credited to the account. If the annual interest rate is
r and interest is compounded n times per year, then the periodic interest
rate is r/n, and the future value of the account is given by the formula
F=P(1+r/n)T where T is the number of periods the money is in the
account (That is, T=nt, where t is years).
- Know that the APY (Annual Percentage Yield) of an account is the actual
percentage by which your balance increases each year, which depends on the
annual interest rate and on the frequency of compounding. You may compare two
investments by comparing their APYs. Understand the formula
APY =(1+r/n)n-1. You don't need to memorize it.
- You should understand how systematic savings work. Given the formula
F= R( (1+r/n)T - 1)/ (r/n)
on the exam, you should know what each of the letters stands for,
and you should be able to use the formula to solve problems similar to your
homework problems. Also, understand that the formula tells you what answer
you would get if you added up the first deposit plus the interest it earns
plus the second deposit plus the interest it earns, etc.
- Know that an amortized loan is a loan that is paid back with equal
payments at regular intervals. The lender uses the Loan Formula (pg 164) to
calculate the dollar amount of each payment. If you are given the formula
on the exam, you should know what each of the letters stands for
(F,R,r,n,t), and you should be able to use the formula to solve problems
similar to the homework problems.
- Understand that the loan formula sets the amount of each payment so
that, if the lender were to deposit the payment checks as he received them,
the amount in this account when the loan is finally paid off (as calculated
by the systematic savings plan formula) equals the amount he could have made
by investing the entire amount of the loan in the first place.
- Know that the loan balance of an amortized loan is the amount that one
would need in order to pay off the entire loan today. Said differently, the
loan balance is the principal that one would have to borrow today in order
to yield the series of payments remaining to be paid.