Answer:
What are the rates with continuous compounding?
With continuous compounding the 6-month rate is
= 2Ln1.02 = 0.039605
= 3.961%.
The 12-month rate is
= 2Ln1.0225 = 0.044501
= 4.4501%.
The 18-month rate is
= 2Ln1.02375 = 0.046945
= 4.6945%.
The 24-month rate is
= 2Ln1.025 = 0.049385
= 4.9385%.
What is the forward rate for the six-month period beginning in 18 months?
The forward rate (with continuous compounding) will be calculated as,
[tex]\frac{4.9385*2 - 4.6945*1.5 }{0.5}[/tex]
= 5.6707%.
With semiannual compounding this is:
= [tex]2(e^{0.056707 * 0.5} -1 = 0.057518[/tex]
= 5.75%
What is two-year par yield?
The value of an annuity paying off $1 every six months is
= [tex]e^{-0.039605*0.5} +e^{-0.044501*1} +e^{-0.046945*1.5} +e^{-0.049385*2} = 3.7748[/tex]
The two-year par yield would be 3.7748.
