A fixed interest security pays coupons of $5\%$ per annum convertible half$-$yearly in arrears. The security is redeemable at $110\%$ at the option of the borrower on any anniversary date between $15$ and $25$ years after the date of issue.

An investor, who is liable to tax on income at a rate of $25\%$ and on capital gains at a rate of $30\%,$ intends to buy the product exactly two months after issue for a price that gives a net effective yield of at least $6\%$ per annum.

$($i$)$ Determine whether the investor would make a capital gain if the bond is held until redemption.