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., 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 given r_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:

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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