Homework Answers
Expected future 1-year interest rate for year 1=current yield on bonds of maturity 1 year=4%
Let expected future 1-year interest rate for year 2 be i2
Expectation theory of term structure of interest gives us
(1+4%)*(1+i2)=(1+3%)^2
i2=((1.03)^2/1.04)-1=2.0096%
Expected future 1-year interest rate for year 2=i2=2.0096%
Let expected future 1-year interest rate for year 3 be i3
Expectation theory of term structure of interest gives us
(1+4%)*(1+2.0096%)*(1+i3)=(1+3%)^3
i3=(1.03^3)/(1.04*1.020096)-1=3.0000%
Expected future 1-year interest rate for year 3=i3=3.0000%
Let expected future 1-year interest rate for year 4 be i4
Expectation theory of term structure of interest gives us
(1+4%)*(1+2.0096%)*(1+3.0000%)*(1+i4)=(1+4%)^4
i4=(1.04^4)/(1.04*1.020096*1.030000)-1=7.0586%
Expected future 1-year interest rate for year 4=i4=7.0586%
Let expected future 1-year interest rate for year 5 be i5
Expectation theory of term structure of interest gives us
(1+4%)*(1+2.0096%)*(1+3.0000%)*(1+7.0586%)*(1+i5)=(1+4%)^5
i5=(1.04^5)/(1.04*1.020096*1.030000*1.070586)-1=4%
Expected future 1-year interest rate for year 5=i5=4%
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