Winooski Lamp Co$.$ has borrowed $$90,000$ for capital expansion. The company must pay the interest on the loan at the end of every $6$ months and make equal payments at the time of the interest

payments into a sinking fund until the loan is retired in twenty years. Interest on the loan is $7\mathrm{.}5\%$ compounded semi$-$annually, and interest on the sinking fund is $5\mathrm{.}5\%$ compounded semi$-$annually.

$($a$)$ Determine the size of the periodic interest expense of the debt.

$($b$)$ Determine the size of the periodic payment into the sinking fund.

$($c$)$ What is the periodic cost of the debt?

$($d$)$ What is the book value of the debt after $13$ years?