1. The present value of a bond is the sum of its discounted semi-annual coupon payments and its discounted C "par" value at maturity P Ek14 Here C is the semi-annual (twice-a-year) coupon payment (1+r)k (1+r)n in dollars, P is the price of the bond in dollars, n is the number of payout periods (twice the number of years) r is the interest rate (one half the required annual yield), M is the bounds maturity value, and k is the payment time period. Prove that the first term (present value of coupon payments) obeys the annuity formula 1 1- (1 +r) . r (Note: A "zero-coupon" bond is one where C 0 and so an investor receives indirect interest as the difference between the bond's maturity value and its purchase price.) Suppose first that you want to find the price of a 20-year 10% coupon bound with a par value of $1,000. Suppose that the required yield is 11% per year. So there will be 40 semi-annual coupon payments of $50 and you will receive $1,000 in 40 6-month periods from now. What is P? Then find P if the required yield is 6.8%. What happens if the required yield is 10%? 1. The present value of a bond is the sum of its discounted semi-annual coupon payments and its discounted C "par" value at maturity P Ek14 Here C is the semi-annual (twice-a-year) coupon payment (1+r)k (1+r)n in dollars, P is the price of the bond in dollars, n is the number of payout periods (twice the number of years) r is the interest rate (one half the required annual yield), M is the bounds maturity value, and k is the payment time period. Prove that the first term (present value of coupon payments) obeys the annuity formula 1 1- (1 +r) . r (Note: A "zero-coupon" bond is one where C 0 and so an investor receives indirect interest as the difference between the bond's maturity value and its purchase price.) Suppose first that you want to find the price of a 20-year 10% coupon bound with a par value of $1,000. Suppose that the required yield is 11% per year. So there will be 40 semi-annual coupon payments of $50 and you will receive $1,000 in 40 6-month periods from now. What is P? Then find P if the required yield is 6.8%. What happens if the required yield is 10%