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interest rates:

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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interest rates: was first posted on September 18, 2019 at 10:01 am.
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