A new corporate bond with a coupon rate of $8\%$ was initially sold by a

stockbroker to an investor for $$1000.$ The issuing corporation promised to pay the

bondholder $$40$ interest on the $$1000$ face value of the bond every $6$ months, and

to repay the $$1000$ at the end of $10$ years. After one year, the bond was sold by the

original buyer for $$950.$

$($a$)$ What rate of return did the original buyer receive on his investment?

$($b$)$ What rate of return can the new buyer $($paying $$950)$ expect to receive if he

keeps the bond for its remaining $9-$year life?