consider three bonds with $7\%$ coupon rates, all making annual coupon payments and all selling at face value. the short term bond has a maturity of $4$ years, the intermediate term bond has maturity $8$ years, and the long term bond has maturity $30$ years. a$)$ what will be the price of each bond if their yields increase to $12\%.$ b$)$ what will be the price of each bond if their yields decrease to $5\%.$ c$)$are long term bonds more or less affected than short term bonds by a rise in interest rates? d$)$ would you expect long term bonds to be more or less affected by a fall in interest rates?