# Computing the expected interest rates

1. Yearly rates are 4%, 5%, 6%, 7%, and 8% for the next five years. Please compute and explain the expected interest rate for both the three and four-year bonds if we show the liquidity premiums to be 1.25%, 1%, .75%, .5%, and 0%.

2. Yearly rates are 4%, 5%, 6%, 7%, and 8% for the next five years. Please compute and explain the expected interest rate for both the three and four-year bonds during the period.

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1.

Yearly rate for year 1=is1=4%

Yearly rate for year 2=is2=5%

Yearly rate for year 3=is3=6%

Yearly rate for year 4=is4=7%

Yearly rate for year 5=is5=8%

Expected interest rate for 3-year bond=ie3=?

Pure expectation theory suggests that

(1+ie3)^3=(1+is1)*(1+is2)*(1+is3)

(1+ie3)^3=(1+4%)*(1+5%)*(1+6%) =1.15752

ie3=(1.15752)^(1/3)-1=5.00%

Liquidity premium for three year=ilp3=0.75%

Market expectation theory in combination ...

#### Solution Summary

Solution describes the methodology to calculate the expected interest rate for the given three and four year bonds.