There exist two coupon bonds with equal time to maturity (5 years) and face values ($1000). They pay coupons semi-annualy. The coupon rate for Bond A is 8% paid annually and the coupon rate for Bond B is 13% paid annually. Bond A and Bond B are trading at $900 and $1350 per bond, respectively.

Show your work in every step to determine the prices of:

(a) An annuity with time to maturity 5 years and face value of $1000

(b) A zero coupon bond with time to maturity 5 years and face value of $1000