Problem 1:  Fill in the table below for each of the following interest rates:

 

 

 

                                                                Compounding                                                                                   PV of $1000

 

Case     Stated Annual Rate        Periods Per Year               Effective Annual Rate                         at t = 2

 

   1                    .12                                      1

 

   2                    .12                                      2

 

   3                    .12                                      4

 

   4                    .12                                    12

 

   5                    .12                                    24

 

   6                    .12                                infinity

 

 

 

Problem 2:    

 

 

 

The effective annual rate is 3% (i.e., re = .03).  What is the stated rate for compounding semi-annually that is associated with this effective rate?   That is, solve for rs such that 1+re = (1+(rs/2))2 given re = .03.

 

 

 

Problem 3:

 

 

 

Consider the following information on a yield curve (where t = 0 is now)

 

 

 

                Time (in years) to Maturity (TTM)             Effective Annual Rate                   

 

  1. .01                                              

  2. .015

  3. .02

  4. .0225

  5. .0235

 

 

 

Part 1:  Using this yield curve, calculate the present value of the following payment streams:

 

 

 

  1. $100 at t = 1,

  2. $100 at t = 2,

  3. $100 at t = 3,

  4. $100 at t = 4,

  5. $100 at t = 5,

  6. $100 at t = 1 and $100 at t = 4

  7. $200 at t = 2 and $200 at t = 5

 

 

 

Part 2:  Also using the above yield curve, calculate the forward rate for the one-year yield next year at    t = 1.    If you take your answer to b above divided by your answer to a above and then subtract 1, do you get the same answer? 

 

 

 

Part 3:  Consider the following two strategies for getting a return over three years: 

 

 

 

Strategy 1:  Invest for three years at the three year rate;

 

Strategy 2:  invest at the two-year rate for two years and then roll over into the one-year rate in two years. 

 

You can calculate a forward rate for the one-year rate in two years (at t = 2) by considering the one-year rate in two years that would make you indifferent between Strategy 1 and Strategy 2.  What is that forward rate? 

 

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    FIN 7000 Problem Set 2 Solution
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