A $$1,000$ par value bond has $6\%$ semiannual coupons and is callable at the end of the $10$th through the $15$th years. At the end of year $10,$ bond callable at $$1,100$; at the end of year $11,$ bond callable at $$1,080$; at the end of year $12,$ bond callable at $$1,065$; at the end of year $13,$ bond callable at $$1,050$; at the end of year $14,$ bond callable at $$1,025$; at the end of year $15,$ bond callable at par. $(1)$ Find the prices to yield $4\%$ convertible semiannually. $(2)$ Find the prices to yield $8\%$ convertible semiannually.