A) Coupon bonds with maturity T = 10 years, face value $1,000, and coupon rate c = 0.05 p.a. are currently trading at $945 per bond.

B) Coupon bonds with maturity T = 10 years, face value $1,000, and coupon rate c = 0.10 p.a. are currently trading at $1,250 per bond.

Assuming that there is no arbitrage, determine the prices of each of the following fixed income securities. Note that both bonds pay coupons semi-annually.

1. A zero coupon bond with face value $1,000 and maturity 10 years.

2. An annuity that will make payments of $250 every six months for the next 10 years.