Question

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 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?