Current 3 year discount factor for risk free cash flows is 0.58.

The face value is $100 and all securities are risk free.

1. what is the price of a zero coupon bond maturing in exactly 3 years?
2. Addition to the bond in (1), you observe: a 2 year coupon bond paying 10% annual coupons with a market price of $95, and two annuities that are trading at the same market price as each other. The first annuity matures in 3 years and pays annual cash flows of $20, while the second annuity pays annual cash flows of $28 and matures in 2 years.

i) complete the term structure of interest rates, what are the one and two year discount factors ?

ii) determine the price of the annuities.