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