You are working at one of the top investment banks and you are adivising a client on a new bond issue. Suppose the yield curve is as in the table below.

t	0.5	1.0	1.5	2.0	2.5	3.0
Spot rate	0.02	0.025	0.03	0.03	0.035	0.04

All interest rates are annual, but semi-annually compounded.

What is the value of a three-year floating rate bond that pays coupons semi-annually based on the prevailing half-year spot rate at the start of each period? Suppose that the bond has a face value of $100.

What is the value of a three-year zero coupon bond with a face value of $100?

What is the value of a security that has three years to maturity and at each six-month horizon pays 100 x r/2, where r is the half-year spot rate at the start of the six month period? e.g. The first payment is 100 x 0.02/2 = 1.