Consider two bonds, a $3-$year bond paying an annual coupon of $5\mathrm{.}80\%$ and a $10-$year bond also with an annual coupon of $5\mathrm{.}80\%.$ Both currently sell at a face value of $$1,000.$ Now suppose interest rates rise to $10\%.$

a$.$ What is the new price of the $3-$year bonds?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Bond price

b$.$ What is the new price of the $10-$year bonds?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Bond price

c$.$ Which bonds are more sensitive to a change in interest rates?