$($a$)$ Suppose that you have purchased a $3-$year zero$-$coupon bond with face value of $$1000$ and a price of $$850.$ If you hold the bond to maturity, what is your annual rate of return?

$($b$)$ Now suppose you have purchased a $3-$year bond with face value of $$1,000,7\%$ annual coupon rate, and a price of $$975.$ Assuming that you hold the bond to maturity, is the IRR greater or less than the return on the bond in part $($a$)?$