$5-$ Consider you are an investor interested in investing in the bond market. You have a choice of investment in a particular bond. The bond has a face value of $$2500,$ a coupon rate of $6\%$ and a maturity of $10$ years.

a$.$ If its current yield to maturity is $10\%$ what is the current price of the bond?

b$.$ Suppose due to adverse market conditions the yield falls to $8\%.$ What will be the bond price under these circumstances?

c$.$ Discuss the link between yield to maturity and bond prices? Can you state anything of importance pertaining to this link?