A $$1,400$ bond has coupons at a rate $10\%$ paid semi$-$annually and matures on July $1,2023$ at $$1,410.$ Find the practical clean book value of this bond on September $8,2018$ to yield $7\%$ compounded semi$-$annually. From July $1$ to January $1$ there are $184$ days.

The book value on July$1,2018$ is $$1,582$ to the nearest dollar. Find the book value to the nearest cent.

Find the book value on January $1,2019$ to the nearest cent.

Find the practical clean book value of September $8,2018$ to the nearest cent.