A $$1,600$ bond has coupons at a rate $8\%$ paid semi$-$annually and matures on July $1,2024$ at $$1,630.$ Find the practical clean book value of this bond on August $16,2018$ to yield $4\%$ compounded semi$-$annually. From July $1$ to January $1$ there are $184$ days.

The book value on July$1,2018$ is $$1,962$ 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 August $16,2018$ to the nearest cent.