To raise $$4,500,000$ to expand into new markets, a very successful laptop manufacturing company issued bonds in the market with a coupon rate of $8\mathrm{.}00\%,$ paying interest every $6$ months, and redeemable in $15$ years. They established a sinking fund to retire this debt on maturity and made equal deposits into the fund at the end of every half$-$year. a$.$ If the fund was earning $4\mathrm{.}80\%$ compounded semi$-$annually, calculate the periodic cost of the debt. b$.$ Calculate the book value of the debt after $12$ years.