Five years ago, Aladdin bought $100$ newly issued "Magic Lamp" bonds with fifteen years left to maturity, a charming $12\%$ coupon rate, and semi$-$annual coupon payments. At the time of issue, the TM on these bonds was $12\%.$ Until now, he was able to reinvest any coupons received at an interest rate of $12\%,$ compounded semi$-$annually. Today, the YTM of these bonds sit at $11\mathrm{.}75\%,$ and Aladdin wishes to sell his bonds and embark on a new adventure.

$($a$)$ What magical price did Aladdin pay for these bonds?

$($b$)$ What enchanting price can Aladdin sell the bonds for in the market today?

$($c$)$ How much interest $($in $$\text{'}$s$)$ has Aladdin earned by reinvesting the received coupons?

$($d$)$ What is the rate of return he realized in this investment.