There are three bonds in the market as follows:

1. A bond with $4 %$ coupon rate (paid annually), 10 years to maturity, and $\$ 1,000$ face value 13.

2. A bond with $4 %$ plus current (short) rate (paid annually), 10 years to maturity, and $\$ 1,000$ face value 14.

3. A bond with $8 %$ minus current (short) rate (paid annually), 10 years to maturity, and $\$ 1,000$ face value

The prices of the bonds are $\$ 950, \$ 1,100$, and $\$ 900$, respectively.

(a) Derive the price of a zero-coupon bond with 10 years to maturity and $\$ 1,000$ face value.

(b) Derive the price of a floating-rate bond (coupon paid annually) with 10 years to maturity and $\$ 1,000$ face value.