A bond with a face value of $$10,000$ and an annual coupon rate of $5\mathrm{.}5\%$ convertible semi$-$annually is redeemable at par at the end of $19$ years. The bond is priced using a nominal yield rate of $2\mathrm{.}5\%$ convertible semi$-$annually.

Calculate the amount of premium for this bond. $($give a positive answer to the nearest cent$)$

At the time of the $17$th coupon, calculate the amount of write$-$down of the premium.