Problem Set 2 FIN 7000

Problem Set 2 FIN 7000

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., r_e = .03).  What is the stated rate for compounding semi-annually that is associated with this effective rate?   That is, solve for r_s such that 1+r_e = (1+(r_s/2))² givenr_e = .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:

a.       $100 at t = 1,

b.      $100 at t = 2,

c.       $100 at t = 3,

d.      $100 at t = 4,

e.      $100 at t = 5,

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

g.       $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?