Six months ago, you purchased a $$100,000,4\%$ coupon bond with $4$ years to maturity. The bond makes semi$-$annual coupon payments, and, at the time of purchase, had a yield$-$to$-$maturity of $4\mathrm{.}44\%.$

a$)$ Calculate price $($per hundred dollars of face value$)$ you paid for the bond.

b$)$ Today, after noticing that the yield has increase to $5\%,$ you sell the bond. What is the current price $($per hundred dollars of face value$)?$

c$)$ Calculate your gains or losses, and the holding period yield from the purchase and subsequent sale of the bond.