$.$ Consider the following two bonds both having a par value of $$1,000.$

$-30-$year bond that pays a $5\%$ annual coupon

$-2-$year bond that pays a $5\%$ annual coupon

A$)$ What is the price of each bond assuming the market interest rate $=5\%?$

B$)$ What is the price of each bond if the market interest rate decreases to $4\%?$

C$)$ What do you notice about the percent change in each bond$$s price for the

same decline in interest rate? show work for each part