2 Bond Pricing Basics 6 points Consider a bond that matures in n years, pays a coupon of 0 each yer, and has a face value FV. The nominal interest rate (bond yield) is i. 1. The general formula to calculate the price of the bond is C' C C' FV P:(1+i)+(1+i)2+"'+(1+i)\"+(l+i)\" (1) C' 1 FV P=?(1_(1+i)\")+(1+i)" (2) Show how to derive equation (2) from equation (1). *Hint: how do you calculate the sum of a geometric sequence. 2. Suppose that the bond trades right at its face value,show mathematically that the coupon rate must be equal to the interest rate. Coupon rate is c = %. 3. Assume thyat the coupon rate is now higher than the interest rate. Assume n = 1 (the bond matures in one year), show mathematically that the price of the bond must be higher than its face value. 4. Consider a bond with the following characteristics: n = 10, C = 80, FV = $1000. If the market interest rate is i = 3%, what is the price of the bond when issued? 5. Imagine that two years later, the nominal interest rate suddenly drops from 3% to 1% due to Fed's policy. What is the price of this bond right at the beginning of third year? 6. Suppose there is a capital gain tax of a- = 40%, calculate the rate of return from holding this bond over the last year (between year 2 and year 3)