Right now, 1 year maturity T-bonds sell for 2% yield, 2-year maturity bonds sell for 2.5% yeild and 3-year maturity bonds sell for 3% yield.
a. Compute the expected 1-year interest rate in the second year, i.e., one year from now?
b. What is the exoected 1-year interest rate two years from now, i.e., in the third year?
According to the expectation theory,
the one year interest rate, compounded over the next year , will give us the same return as the return compounded over 2 years by a 2 year bond.
a. 1 year maturity T bonds for 2% yield ,
( 1.02) (1 + x ) = (1.025)^2
( 1.02) (1+x) = 1.0506,
(1+x ) = 1.03
x = 3%
the 1 year interest rate 1 year from now is 3%'
b. (1.025)^2 (1 +x ) = ( 1.03)^3
or, (1+x ) = 1.0927/1.0506
(1+x) = 1.0401
x = 4%
therefore, the one year treasury bond expected interest rate two years from now is 4%
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