A company called Menthos tyres has issued two bonds: bond $007$ and bond $030.$ Both of these bonds have coupon payments of $15\%$ of par, make semi$-$annual payments, and have nominal values of R$1000.$ Bond $007$ has seven years left until maturity; while Bond $030$ has $30$ years left to maturity. Currently both bonds are trading at par.

Requirements:

a$)$ What would the price change be for both bonds if the yield$-$to$-$maturity decreased by $3$ percentage points?

b$)$ what the change in the price of these bonds affect Menthos Tyre? Explain your answers

c$)$ which Bond has bigger interest rate risk? Why? Your answer should also include a brief explanation of the term interest risk