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**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: **

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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?