$2.$ The Longview Manufacturing Company just issued a $$1,000$ par zero$-$coupon bond with a $10\mathrm{.}5\%$ yield to maturity, due to mature $12$ years from today $($assume semiannual compounding$).$

a$.$ What is the market price of the bond?

b$.$ If interest rates remain constant, what will the bond's price be in four years?

c$.$ If interest rates fall to $8\%,$ what will the bond's price be in four years?

d$.$ If interest rates rise to $12\%,$ what will the bond's price be in four years? Please do it on excel.