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
.01
.015
.02
.0225
.0235
Part 1: Using this yield curve, calculate the present value of the following payment streams:
$100 at t = 1,
$100 at t = 2,
$100 at t = 3,
$100 at t = 4,
$100 at t = 5,
$100 at t = 1 and $100 at t = 4
$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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