There are three bonds in the market as follows:

$1.$ A bond with $4\%$ coupon rate $($paid annually$),10$ years to maturity, and $$1000$ face value

$2.$ A bond with $4\%$ plus current$($short$)$ rate $($paid annually$),10$ years to maturity, and $$1000$ face value

$3.$ A bond with $8\%$ minus current$($short$)$ rate $($paid annually$),10$ years to maturity, and $$1000$ face value The prices of the bonds are $$950,$ $$1,100,$ and $$900$ respecitvely

a$.$Derive the price of a zero coupon bond with $10$ years to maturiy and $$1000$ face value

b$.$ Dervie the price of a floating rate bond $($coupon paid annually$)$ with $10$ years to maturity and $$1000$ face value