Problem
You are a portfolio manager and responsible for managing a bond's portfolio. One of your clients (John Smith) purchased a 30-year, 4.75% coupon bond that pays interest annually. The bond has a face value of $1,000. What is the change in the price of this bond if the market yield to maturity declines to 3.20% from the current rate of 3.50%? Show all the calculations by which you came up with the final answer. Why did the 30-year bond price change? Explain your reasoning.