4WEEK TUTORIAL 4
ECON2102 Macroeconomics 2
August 2008
1. Consider a discount bond, such as U.S. Treasury Bill. This type of asset has no explicit
interest payments (called coupons) but pays a principal of, say, $1000 at a xed date in the
future. A Bill with one-year maturity pays o one year from the issue date, and similarly for
three-month or six-month Bills. Let P B be the price of a discount bond with one-year maturity
and principal of $1000.
a) Is P B greater or less than $1000?
b) What is the one-year interest rate on these discount bonds?
c) If P B rises, what happens to the interest rate on these bonds?
d) Suppose that, instead of paying $1000 in one year, the bond pays $1000 in two years. What
is the interest rate per year in this two-year discount bond?
2. Suppose that an economy has discount bonds with one- and two-year maturities. Let i1 be
t
an interest rate on a one-year bond issued at the start of t; year and i1+1 be an interest rate
t
on a one-year bond issued at the start of year t + 1: Let i2 be the interest rate (per year) on a
t
two-year bond issued at the start of year t. We can think of i1 as the current short-term interest
t
rate and i2 as the current long-term interest rate.
t
a) Assume that at the start of year t everybody knows not only i1 and i2 ; but also the next
t
t
years one year rate, i1+1 : What must be the relationship between i1 ; i2 ; and i1+1 : Explain
tt
t
t
the answer by considering the incentives of lenders and borrowers.
b) If i1+1 > i1 , what is the relation between i2 , the long-term interest rate, and i1 , the shortt
t
t
t
term interest rate? The answer is an important result about the term structure of interest
rates.
c) How would the results change if we assumed, more realistically, that there was uncertainty
in year t about the future one-year interest rate, i1+1 ?
t
1