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Suppose that 1-year interest rates over next 5 years are expected to be 5%, 6%, 7%,...

Suppose that 1-year interest rates over next 5 years are expected to be 5%, 6%, 7%, 8% and 9%. Investor's preferences for short-term bonds and liquidity premiums for 1-year to 5-year bonds are 0%, 0.25%, 0.5%, 0.75%, and 1.0%. What is interest rate on 3-year bonds?
(A) 6.0%.
(B) 6.5%.
(C) 6.75%.
(D) 7.0%.
(E) 7.25%.

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Answer #1

One year interest rate=       5.00%
interest rate after 1 year =       6.00%
interest rate after 2 year =       7%


As per pure expectation theory, 3 year interest rate = ((1+1 year interest rate)^1*(1+1 year interest rate after 1 year)^1)*(1+1 year rate after 2 year))^(1/3) -1      
(((1+5%)^1*(1+6%)^1*(1+7%)^1)^(1/3)) -1      
((1.05*1.06*1.07)^(1/3) ) -1      
1.059968553       -1
0.05996855253       or 6%


liquidity premium for 3 year Bonds =   0.50%  
interest rate on 3 year bonds= Interest rate + liquidity premium      
6%+0.5% = 6.5%      
So interest rate on 3 year bonds is 6.5%      
      

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