On January $1,2023,$ ABC Corporation issued an $8\%$ annual coupon bond. Each unit of the bonds has $$1,000$ par value and the bond will mature on January $1,2048.$ Suppose you bought $1$ unit of ABC bonds at its issuance. a$)$ On January $1,2034,$ how much did each unit of ABC bonds cost if the YTM is $12\%$ on that date? $(5$ marks$)$ b$)$ Based on your purchase price on January $1,2034,$ what is the current yield of ABC bond? $(2$ marks$)$ c$)$ Today is the end of March $2035.$ Suppose immediately after receiving the coupon on January $1,2035,$ you sold the bond at $10\%$ YTM$.$ What was the capital gains yield of your bond investment from January $1,2034$ to January $1,2035?$