$6-20.$ The Dinosaur Adventure Theme Park needs $$200$ million to build a monorail that will run through the park. The park's financial advisors believe that it will be able to borrow the money by issuing a $30-$year bond with an annual coupon rate of $4\mathrm{.}8$ percent that pays interest every $6$ months. However, interest rates have been very volatile over the last year, ranging from $4\mathrm{.}6$ percent to $5\mathrm{.}1$ percent for borrowers with Dinosaur's credit rating. As a result, Dinosaur's manager is concerned. If rates rise while the offering is in registration, Dinosaur will not get the $$200$ million it needs from the sale of its bonds. To make sure they will be able to raise enough money, Dinosaur$$s financial advisors have recommended that Dinosaur register a total of $$250$ million worth of bonds. In the event that rates rise above $4\mathrm{.}8$ percent, Dinosaur will sell enough additional bonds to get the $$200$ million it needs for the monorail system.

If rates rise to $4\mathrm{.}95$ percent on the day the bonds are sold, how much would Dinosaur receive from the sale of $$200$ million worth of bonds?

What is the par value of the additional bonds that Dinosaur must sell to raise the required $$200$ million?