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Need detailed calculations for the following:

If a half-year 2.7 percent coupon bond (paying twice per year) is trading at 100.62 and a one-year 8.7 percent coupon bond (paying twice per year) is trading at 106.5, find half-year and one-year discount factors. The face value of either bond is $100. Assume semi-annual compounding.

Write your answers for the following:

1. Half-year discount factor.
2. One-year discount factor.
3. Half-year spot interest rate.
4. One-year spot interest rate.
5. Forward rate for 6 to 12 months.

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