4. (15 points) Bonds are a type of loan made by an investor, typically to a company or govern- ment agency. In return, the investor receives fixed-rate interest income, usually semiannu- ally, which remains the same regardless of how market interest rates may change. Suppose you purchase a bond with a par value (or loan principal) of $1,000 that has 10 years until the loan principal is repaid. On the date the bond matures, you'll get the original $1,000 back. The bond has a 3% coupon (or interest payment) rate, which means the bond pays you $30 a year. If you're paid semiannually, you'll receive $15 in coupon payments. (1) Suppose the market interest rate remained at 3% after an year. Compute the remaining value of your bond after an year (9 years to maturity). Call this value as x. (ii) Suppose the market interest rate increased to 4% after an year. Let y denote the re- maining value of your bond after an year. Which one of the following is true: x y? (iii) Briefly argue why bond price should change with when interest rate changes in gen- eral. Do they have positive or negative correlation? (iv) is the futures price of a fixed rate bond likely to be higher, lower or the same as its forward price? Explain your reasoning