You are called in as a financial analyst to appraise the bonds of Olsen's Clothing Stores. The $$1,000$ par value bonds have a quoted annual interest rate of $10$ percent, which is paid semiannually. The yield to maturity on the bonds is $10$ percent annual interest. There are $15$ years to maturity.

a$.$ Compute the price of the bonds based on semiannual analysis.

b$.$ With $10$ years to maturity, if yield to maturity goes down substantially to $8$ percent, what will be the new price of the bonds?