Kidwell_ Peterson_ Blackwell _ Whidbee_ 9th Edition

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					                                              CHAPTER 6

                        THE STRUCTURE OF INTEREST RATES


           This chapter discusses the relationship between security-specific factors and the interest rates
            on their debt securities. It builds on the material of Chapter 4 which discusses how market-
            based factors such as real rates and the inflation rates affect the level of interest rates in the
           The chapter explains the relationship between term to maturity and interest rates and extends
            the discussion into the role of the yield curve in the business cycle. Three theories that seek to
            explain the shape of the yield cure are identified.

           Additionally, other security-specific factors such as 1) default risk, 2) tax treatment, 3)
            marketability, and 4) options on debt securities – call, put, or conversion – also affect the yield
            of a given security. The impact of these factors is analyzed here.

           While there are many other variables, these factors affect the yield of a security more
            significantly than others. It is important to not only know what these factors are but also how
            changes in these factors influence the yield of a security.


The last three chapters and the many to come are discussing and describing what happens each working
day in financial markets and institutions. Your text and this Study Guide give you a good understanding of
what goes on in the financial markets. Many finance and economics graduates take the first step of their
working career in a financial institution. All business firms need to understand what the economy is like
and how their firm may be affected by changes in interest rates.

Finance is alive, dynamic, and happening each moment of the day and night! Fortunes are made and lost;
and the employment opportunities in the field are unlimited. How can you keep in touch? Pick up and
read the daily Wall Street Journal (WSJ) or business periodicals like Business Week, Forbes, Fortune, or
Smart Money. You are also not restricted these days to printed material. Get on the web. Visit finance
related sites like CNNMoney, Yahoo Finance or Bloomberg. As many of you spend time on the computer,
a few minutes of scanning these websites for articles and news of interest will soon prepare you for your
classes and the future as well.

If you are interested in a particular area of finance, such as banking, or any other industry, such as housing
or chemicals, be aware of the several monthly or daily periodicals that you should be reading. Anticipate
the economic conditions of "your" industry in the next two or three years, when you will be looking for a
job and beginning your career. If you think you are studying now, wait until then! Meanwhile, get ready!


There are many "look it up" assignments in this Study Guide. Your time on the assignment should be
spent on the assigned material and not thumbing page by page through the paper. The WSJ has three
tables of contents to assist you. The first is found at the bottom of the front page. The left-hand section on
the front page titled “What’s News” makes references to major feature articles appearing that day in all
sections of the paper. The second table of contents, titled "Index To Businesses," is located on the first
inside page of Section B. All firms with significant references in that day's WSJ are listed, along with the
page of the article. If you are following a firm for an investment project or employment opportunities, a
brief review of this listing can save considerable time and keep you "tuned in" at the same time. The third
table of contents is located at the bottom-left of front page of Section C, titled "Money & Investing
Index." All the regular and frequently appearing columns and tables are listed. Use these tables of
contents for more effective use of your precious time. If you are subscribing to Journal, the Interactive
Edition is also available to you. The Interactive Edition includes an opportunity to create a "Personal
Journal" set up so that specific industry and company information will be compiled in your Personal
Journal for your review.

One table of information in the third section that is of relevance to this chapter is the table titled “Bonds”.
This table contains the daily prices and yields of U.S. and foreign government bonds as well as U.S.
corporate bonds.You can use this information to plot the yield curve on any day.


 I.     Interest rate changes and differences between interest rates can be explained by several variables.

        A.       Term to Maturity
        B.       Default Risk
        C.       Tax Treatment
        D.       Marketability
        E.       Callability

II.     Term Structure of Interest Rates

        A.       Relationship between interest rates and term-to-maturity. Term structure may be studied
                 visually by plotting a yield curve at a point in time.

                 1.       A graphical plot of yield vs. maturity for securities that are similar in all other
                          aspects is called the yield curve.
                 2.       A yield curve is a smooth line which shows the relationship between maturity and a
                          security's yield at a point in time.
                 3.       The yield curve may be ascending, flat, descending, or twisted.
                 4.       Several theories explain the shape of the yield curve. The three main theories that
                          are discussed in this chapter are the expectations theory, the liquidity premium
                          theory, and the market segmentation theory.

B.   The Expectations Theory

     1.       The expectations theory argues that the shape of the yield curve is determined solely
              by expectations of future interest rate movements and changes in these expectations
              lead to changes in the shape of the yield curve.

     2.       Investors are assumed to trade in a very efficient market with excellent
              information and minimal trading costs. Other theories discussed later presume
              less efficient markets.

     3.       The slope of the yield curve reflects investors' expectations about future interest
              a.      An ascending yield curve is formed when interest rates increase with
                      maturity. Such yield curves are also called Normal Yield Curves.
                      According to the expectations theory, an ascending yield curve reflects
                      expectations of increasing interest rates in the future.
              b.      Descending yield curves imply that short-term rates are higher than long-
                      term rates. These curves are inverted yield curves and reflect expectations
                      of lower interest rates in the future.
              c.      A flat yield curve implies that interest rates are expected to be stable in the
                      near future.

     4.       Long-term interest rates represent the geometric average of current and expected
              future (implied, forward) interest rates. Forward rates (which are expected future
              rates) may be calculated by observing two spot interest rates of differing maturity.

C.   Liquidity Premium Theory

     1.       Long-term securities have (a) greater price variability and (b) less marketability
              than short-term securities. Consequently, investors require a premium for
              investing in less liquid securities.

     2.       Liquidity may be a more critical factor to investors at one point in time relative to
              another. As a result, liquidity premiums change over time!

     4.       Since the liquidity premium increases with maturity, it causes the observed market
              yield curve to be more upward sloping than that predicted by the expectations theory.

     5.       The liquidity premium suggests a more upward sloping yield curve than that
              predicted by the expectations theory. It means that the liquidity premium theory
              can explain why the yield curve slopes upward most of the time.

D.   Market Segmentation and Preferred Habitat Theories of the Term Structure

     Maturity preferences may affect security prices, explaining variations in yields by time.

     1.        Investors (lenders) and borrowers (issuers) choose securities with maturities that
          satisfy their forecasted cash needs. As a result, the yield curve is determined by the
                    supply of and the demand for securities at or near a particular maturity.

               2.       The choice of short-term vs. long-term maturities is pre-determined according to
                        need rather than expectations of future interest rates.
                        a       Pension funds and life insurance companies generally prefer long-term
                                investments that match their long-term liabilities. Commercial banks may
                                prefer short-term investments to coincide with their short-term liabilities.
                        b       Borrowers will also issue securities with maturities that match their needs.

               3.       Under this theory, investors will not shift out of their preferred maturities even if
                        offered higher yields.

               4.       A variation of the market segmentation theory is the preferred habitat theory.
                        Under this theory, investors may be willing to move out of their preferred maturity
                        in return for a premium if expectations of yields dictate they do so.

               5.       The segmentation theory can explain twists, spikes, and discontinuities in the
                        yield curve, while the preferred habitat theory explains why the yield curve is
                        usually a smooth line without discontinuities.

       E.      Which theory is right?

               1.       The expectations and liquidity premium theories are important long-term
                        influences on term structure and find support among economists.
               2.       Short-term analysis of yield curves supports the preferred habitat theory and is
                        favored by market participants.

       F.      Yield Curves and the Business Cycle

               1.       Interest rates are directly related to the level of economic activity.
                        a.       An ascending yield curve notes the market expectations of economic
                                 expansion and/or inflation.
                        b.       A descending yield curve forecasts lower rates possibly related to slower
                                 economic growth or lower inflation rates.
               2.       Security markets respond to updated new information and expectations and reflect
                        their reactions in security prices and yields.

       G.      Yield Curves and Financial Intermediaries (FI)

               1.       The current and expected slope of the yield curve is important to FIs that bear
                        maturity intermediation risk.
               2.       Depository institutions traditionally did well in periods with positively sloped
                        yield curves - borrow short (deposits) and lend long (mortgages) at a higher rate.

III.   Default risk: Differences in interest rates may be explained by relative levels of default risk.

       A.      Default risk is the probability of the borrower not honoring the security contract.
             1.      Losses may range from "interest a few days late" to a complete loss of principal.

             2.      Risk-averse investors want adequate compensation for expected default losses.

      B.     Investors require a default risk premium (above risk-free or less risky securities) for added
             risk assumed.

             1.      DRP = i - irf
             2.      The default risk premium (DRP) is the difference between the promised or
                     nominal rate and the yield on a comparable (same term) risk-free security
                     (Treasury security).
             3.      Investors are satisfied if the default risk premium is equal to the expected default

      C.     Default risk premiums increase (widen) in periods of recession and decrease in economic

             1.      In good times, risky security prices are bid up; yields move nearer those of risk-
                     free securities.
             2.      With increased economic pessimism, investors sell risky securities and buy
                     "quality," widening the DRP.

      D.     Credit rating agencies measure and grade relative default risk among DSUs and their

             1.      Cash flow, level of debt, profitability, and variability of earnings are indicators of
                     default riskiness.
             2.      As conditions change, rating agencies alter ratings of businesses and
                     governmental debtors.
             3.      Bonds in the top four rating categories – Aaa to Baa (Moody’s) or AAA to BBB
                     (S&Ps) – are called investment grade bonds. Bonds rated below Baa or BBB are
                     called speculative grade ( or junk) bonds.

IV.   Tax Treatment: The taxation of security gains and income affects the yield differences among
      securities. Investors are interested in their after-tax return on investments.

      A.     The after-tax return, iat, is found by multiplying the pre-tax return by one minus the
             investor’s marginal tax rate.
             iat = ibt (1-t)

      B.     Municipal bonds issued by state and local governments are usually exempt from federal
             income taxes.

      C.     Treasury securities are exempt from state income taxes.

V.    Differences in marketability affect interest yields.

      A.      Marketability - The costs and speed with which investors can resell a security.

              1.      Cost of trade
              2.      Physical transfer cost
              3.      Search costs
              4.      Information costs

      B.      Securities with good marketability have higher prices (and demand) and lower yields. This
              is because higher marketability lowers the risk to investors.

VI.   Varied option provisions may explain yield differences between securities.

      A.      An option is a contract provision which gives the holder the right, but not the obligation,
              to buy, sell, or convert an asset at some specified price within a defined future time period.

      B.      A call option permits the issuer (borrower) to call (redeem) the obligation before maturity.

              1.      Borrowers will "call" if interest rates decline.
              2.      Investors in callable securities bear the risk of losing their high-yielding security.
              3.      With increased call risk, investors demand a call interest premium (CIP).

                      a.       CIP = ic - inc
                      b.       A callable bond, ic, will be priced to yield a higher return (by the CIP)
                               than a similar non-callable, inc bond.

      C.      A put option permits the investor (lender) to sell the bond or terminate the contract at a
              designated price before maturity.

              1.      Investors are likely to "put" their security or loan back to the borrower during
                      periods of increasing interest rates. The difference in interest rates between
                      putable and non-putable contracts is called the put interest discount (PID).
                      a.      PID = ip - inp
                      b.      The yield on a putable bond, ip, will be lower than the yield on a similar
                              non-putable bond, inp, by the PIP.

      D.      A conversion option permits the investor to convert a security contract into another
              security, usually common stock.

              1.      Convertible bonds generally have lower yields, icon, than non-convertibles, incon.
              2.      The conversion yield discount (CYD) is the difference between the yields on
                      convertibles relative to non convertibles.
              3.      CYD = icon - incon. Investors accept the lower yield on convertible bonds because
                      they have an opportunity for increased rates of return through conversion.

VII.   Co-movement of Interest Rates - Interest rates tend to move up and down together.

       A.      Securities of varying maturity, default risk, and contract provisions tend to have some
               substitutability among investors.

       B.      Yield differences will be generally maintained by investors.

       C.      Co-movement increases if investors are willing and able to invest and trade a variety of


1.     Expectations of future interest rates may explain why interest rates vary by _______________.

2.     An ascending yield curve reflects investors' expectations that future short-term interest rates will
       be _______________.

3.     Long-term rates represent a geometric average of current___________-term interest rates and
       expected ____________-term interest rates.

4.     A ____________ premium may be added by investors in order for them to purchase long-term

5.     When securities of varied terms are not acceptable substitutes for investors and institutions in the
       short run, the _________ __________ theory may explain the shape of the yield curve.

6.     The default risk premium on a corporate bond may be computed by subtracting the yield on a
       ____________ bond from that of the ____________ bond.

7.     An increase in the required default risk premium of a security will lead to a(n) _______________
       in the price of the security.

8.     Default risk premiums narrow/widen in recession periods and narrow/widen in periods of
       economic prosperity.

9.     The relevant interest rate to investors is the ____________-tax return.

10.    A      option is an option of the lender to sell the security back to the issuer; a   _ option is an
       option of the borrower to pay off the debt.


T    F        1.      A yield curve plots coupon yields by maturity.

T    F        2.      Treasury and corporate security yields may be plotted together when generating a
                      yield curve.

T    F        3.      One area of expectations affecting yields by maturities is anticipated inflation.

T    F        4.      The expectations theory states that long-term rates represent the market estimate
                      of the average of current and future short-term rates.

T    F        5.      If interest rates are expected to increase in the future, one would expect to see an
                      upward sloping yield curve

T    F        6.      According to the preferred habitat theory, investors may move out of their
                      preferred maturities in response to expected yield premiums.

T    F        7.      The default risk premium compensates the holder of the risky security for the risk

T    F        8.      Liquidity premiums cause an observed yield curve to be less upward sloping than
                      that predicted by the expectations theory

T    F        9.      The higher the marginal tax bracket of the investor, the less the attraction of
                      municipal bonds.

T    F       10.      Bonds with call options are likely to have lower yields than non-callable bonds.


1.   The term structure of interest rates
     a.     describes the relationship between maturity and yield for similar securities.
     b.     ranks security yield according to the default risk structure.
     c.     describes how interest rates vary over time.
     d.     describes the pattern of interest rates over the business cycle.

2.   The yield curve is a plot of
     a.      maturity changes as risk changes.
     b.      yields by varied risk-taking of varied bond issuers.
     c.      yields by maturity of securities with similar default risk.
     d.      interest rates over time past.

3.   Applying the expectations theory, a bank depositor has the option of purchasing a one-year CD at
     7 percent and a 9 percent two-year CD. If indifferent between the two, the depositor must expect
     one-year CDs one year from now to have a rate of
     a.       8 percent.
     b.      11 percent.
     c.      slightly over 11 percent.
     d.      12 percent.

4.   The yield differentials between a AAA corporate bond and a BAA corporate bond of the same
     maturity may be explained by
     a.      marketability.
     b.      tax treatment.
     c.      default risk.
     d.      term to maturity.

5.   A call option on a bond
     a.      increases the price an investor may pay.
     b.      decreases the price an investor may pay.
     c.      decreases the yield required by investors.
     d.      has no effect on price or yield.

     Use the data below to answer questions 6 through 9.
     Treasury Bill (6 month)                                               6.41%
     Treasury Bill (1 year)                                                6.57%
     Treasury Bill (2 year)                                                7.02%
     Treasury Note (10 year)                                               7.58%
     Treasury Bond (30 year)                                               7.43%
     Corporate Bond (10 year AA)                                           9.25%
     Municipal Bond (10 year AA)                                           7.12%
     Expected Annual Inflation Rate                                        3.50%

6.   The slope of the yield curve for U.S. Treasury securities indicates
     a.      declining interest rates in the future.
     b.      increasing interest rates in the future.
     c.      increasing prices on U.S. Treasuries in the future.
     d.      constant interest rates in the future.

7.   The default risk premium on the ten-year corporate bond is
     a.     1.67%
     b.     2.13%
     c.     2.84%
     d.     1.82%

8.    The expected real return on a one-year Treasury bill is
      a.     3.50%
      b.     10.07%
      c.     3.76%
      d.     3.07%

9.    The yield difference between the corporate and municipal bond may be best explained by the fact
      a.      the muni has lower default risk.
      b.      the capital gain income on a municipal bond is tax-free.
      c.      the interest income on each is federal tax exempt.
      d.      the interest income on the municipal bond is federal tax exempt.

10.   Which of the following bonds probably has the highest call premium included in its yield?
      a.     a low coupon, short-term corporate note in an increasing rate market
      b.     a high coupon rate bond in a falling interest rate market
      c.     a high coupon rate bond in a rising interest rate market
      d.     a low coupon rate bond in an increasing interest rate market.

11.   A downward sloping yield curve indicates that future short-term rates are expected to ______ and
      outstanding security prices will _______.
      a.      fall; rise.
      b.      fall; fall.
      c.      rise; rise.
      d.      rise; fall.

12.   Suppose we consider a yield curve that has taken into consideration both the expectations theory
      and the liquidity premium theory. Assume the yield curve is initially downward sloping. If
      liquidity premium theory is no longer important, the yield curve you would expect to see would be:
      a.       more steeply downward sloping
      b.       more upward sloping
      c.       less steeply downward sloping
      d.       none of the above.

13.   According to expectations theory, an investor who believes that interest rates are likely to decrease
      in the near future would
      a.       would invest in short-term securities immediately.
      b.       would invest in long-term securities immediately.
      c.       would sell long-term securities from her portfolio.
      d.       would sell short-term securities from her portfolio.

14.   According to expectations theory, if the market believes that interest rates are expected to increase
      in the near future,
      a.       borrowers would immediately increase their supply of short-term securities.
      b.       investors would immediately increase their demand for long-term securities.
      c.       borrowers would immediately increase their supply of long-term securities.
      d.       neither borrowers nor investors would do anything until the interest rates actually
15.     According to expectations theory, if the market believes that interest rates are likely to decrease in
        the near future, it would lead to:

        a.        An increase in the demand for short-term securities.
        b.        An increase in the demand for long-term securities.
        c.        A decrease in the supply of short-term securities.
        d.        An increase in the supply of long-term securities.


A)      Plotting a Yield Curve

        Open the web page You will see a table that contains the yields of
        U. S. government securities.
        a)      Plot the yield to maturity (Y-axis) by maturity (X-axis) and fit a yield curve to the plot of
                points. (Hint: Plot a scatter diagram and fit a line to the points.)
        b)      Interpret the yield curve using the expectations theory. What is the market's forecast of
                future short-term interest rates?

B)      Computing Forward Rates

        You will be asked "What's going to happen to interest rates?" many times in the future. If any one
        of us could predict future interest rates consistently over time, we would easily become rich and
        famous! Few persons have been able to forecast future interest rates consistently even though
        many business economists are paid well to do so.

        If interest rate expectations are a significant factor in the trading of short- and long-term treasuries,
        then we can calculate expected future interest rates as implied by two actual market interest rates.
        The text has given us an excellent background, but below is a formula for calculating forward
        (expected) interest rates, f, given any two observed (actual) interest rates, R, of different maturities.

                                                      1 t rn n 
                                                                           1/ k

                                                fk                             1
                                       t nk
                                                      1 t rnk nk 
where t+n-kfk =   the k-year forward rate beginning (n - k ) years from today.

          k =     time period between two actual observed rates and also the maturity of the forward
                  security in years.

        tRn   =   actual observed interest rate at time t for an n period security (years to maturity)

Example: An investor is interested in purchasing one of the following government bonds, each of which
yields (annual compounding):

                                          Term           Market Yield
                                          2 year            6.50%
                                          5 year            7.25%

Should the investor buy the two- or five-year bond? Of course it depends on what interest rates will be two
years from now. A $100 investment in the five-year bond will yield (1.0725)5 = $141.90 in five years.
Purchase of the two-year bond would give the investor (1.065)2 = $113.42 at the end of the two years and
the need to reinvest the proceeds for three more years. At what rate does he need to reinvest to accumulate
a sum of $141.90 by the end of the fifth year? We need to solve for the three-year forward rate, two years
from now, that allows a $113.42 investment to grow to $141.90. Or, what are expected three-year rates
two years from now as revealed by the current yield structure of interest rates?

Using our formula above where k = 3,

                  1 t r5 5 
                                   1/ 3                      1/ 3
                                               1.0725 5 
                                                                                     1/ 3
                                                                         1.4190 
            f3             2
                                          1        2 
                                                                    1                     1  7.75 %
                  1 t r2                                            1.1342 
     t 2
                                                1.065                          
The expected one-year interest rate two years from now is 7.75 percent. Investing $113.42 at 7.75 percent
for three years equals $141.90 at the end of five years. This is the same as the total return from the five-
year bond (1.0725)5 = $141.90. The three-year forward rate of 7.75 percent is the forecasted or expected
three-year rate two years from now as indicated by today's actual market rates.


1)          In July 2002 the yield curve for U.S. Treasury securities was the following:

                            Treasury                                Yield
                            3 month                                 1.71%
                            6 month                                 1.73%
                            9 month                                 1.73%
                            1 year                                  1.83%
                            2 year                                  2.60%
                            3 year                                  3.18%
                            4 year                                  3.59%
                            5 year                                  3.90%
                            6 year                                  4.09%
                            7 year                                  4.36%

Calculate the implied one-year forward (expected) rates over the next six years. What are the expectations
of future one-year rates one, two, three, four, five, and six years from July, 2002? How accurate was the
market in predicting interest rates for the next few years?

2)   Calculate the expected 90-day (3-month) rates 3 months, 6 months, and 9 months from now using
     the rates above. (Hint: Use the same formula, but with fractions of the year: 1/4 for 3 months, 2/4
     for 6 months, etc.; then annualize when finished.) Prove your answers.

3)   Bond Rating Changes. From a recent issue of Standard and Poor's Credit Week or Moody's The
     Bond Record, what corporate security ratings have been changed recently and why? These two
     sources are excellent sources for keeping in touch with changes in default risk as assessed by two
     important rating services.


1.    term or maturity

2.    higher

3.    short; short

4.    liquidity

5.    market segmentation

6.    Treasury; corporate

7.    decline

8.    widen; narrow

9.    after

10.   put; call


1.    F           A yield curve plots market yields by maturity.

2.    F           Default risk is held constant to study yields by time.

3.    T           Inflation expectations affect both the level and slope of the yield curve.

4.    T           Current long-term rates reflect expectations of future short-term rates.

5.    T           Investors expecting rates to go up will invest in short-term securities and shun long-term
                  securities. This drives up the price of short-term securities and its yield down. At the same
                  time long-term securities’ prices decrease driving up its yield.

6.    F           If yields increase sharply, security prices must be falling, indicating a movement away
                  from a maturity range - market segmentation.

7.    T           Default risk premiums reflect the market's expected default losses from a large portfolio of
                  securities of similar risk.

8.    F           Liquidity premiums actually cause the slope of the yield curve to be more upward sloping
                  because liquidity premiums increase with maturity.

9.    F           The higher the marginal tax bracket, the greater the after-tax return compared to other
                  taxable bonds.
10.   F    Investors demand a yield premium if the borrower has an option to terminate their
           investment, usually when rates are low.


1.    a.   Term structure of interest rates describes the relationship between maturity and yield for
           similar securities.

 2.   c.   A graphical plot of yield vs. maturity for securities that are similar in all other aspects is
            called the yield curve.

3.    c    The two-year CD available at 9 percent represents the geometric average of current one-
           year CDs at 7 percent and an estimated one-year rate one year from now of slightly more
           than 11 percent.

           Llet X equal the t+1f1, or one-year forward rate one year from today.

                                         1.09= (1.07)(X)

                                             X = 11.04%

           The geometric mean is a more accurate average with compound interest rates or growth
           rates than an arithmetic mean.

4.    c    The ratings on the bond refer to relative default risk between the securities.

5.    b    Investors will pay less, requiring a higher yield on a bond with a call option.

6.    b    The upward sloping yield curve reflects the market expectation of higher short-term rates
           in the future.

7.    a    The difference between a risk-free ten-year (holding maturity constant) and a risky
           corporate bond.

8.    d    A yield of 6.57 percent on the one-year bill less the expected loss in purchasing power of
           3.5 percent.

9.    d    The market requires a lower yield on tax-free municipals.

10.   b    The high coupon bond in a falling rate market has the best chance of being called, thus
           investors want added returns for added call risk.

11.   a.   A descending yield curve forecasts lower rates possibly related to slower economic growth
           or lower inflation rates. Investors demand for short-term securities will decline driving
           down their prices.

12.   a.   The removal of liquidity premiums will decrease the yield at every maturity making the
           yield curve to be more steeply downward sloping

13.   b.   Investors wanting to lock in on the current higher rates would invest in long-term
           securities immediately.

14.   c.   To avoid higher rates, borrowers would immediately increase their supply of long-term

15.   b.   Investors wanting to lock in on the current higher rates would invest in long-term
           securities immediately leading to an increase in the demand for long-term securities.


1.   The expected one-year rate three years from July, 2002, using the forward rate calculator:

                                    (1.0359 )4
                     t  3 f1   =                    - 1 = 1.0483 - 1 = 0.0483 = 4.83%
                                    (1.0318 )3

                            Proof : (1.0359 )4 = (1.0318 )3 (1.0483 )1

2.   The expected 90-day (three months) rate three months (one quarter) from today is

                                                              (1.0173 )0.5
                                        t  0.25   f 0.25 =                 -1
                                                              (1.0171 )0.25

                                        =           = (1.00435 )4 - 1

                                            = 1.75%( annualized)

     Proof: (1.0171).25 (1.0175).25 = (1.0173).5. Investing for six months (0.5 exponent) at 1.73%
     annualized is equivalent to investing in a three-month or one-quarter (0.25 exponent) rate of
     1.71% followed by another quarter at 1.75%.