The following are the current prices of 1000 zerocoupon bond

The following are the current prices of $1.000 zero-coupon bonds: If the one-year forward rate for year 2 (i.e. the one-year effective rate during year 2) is 8%. determine X. 865.35 873.52 874.24 876.82 881.68 A $100 par value bond with 7% annual coupons and maturing at par in 4 years sells at a price to yield 6%. Determine the modified duration of the bond. 3.43 3.46 03.63 3.67 3.72 Determine the convexity of a five-year annuity-immediate with level annual payments, evaluated at I =0. 3.0 4.7 8.2 11.0 14.0 An investment will return $1.000 in two yean and $3,000 in five yean. Determine the ratio of the convexity of the payments to their modified duration, evaluated at i = 7.5%. 4.96 3.33 05.73 6.34 7.65

Solution

1. We are given that f[1,2] = 8%=.08

and for the first year we have

943.4(1+S1)=1000

or (1+s1) = 1000/943.4 , ------->(1)

and for the second year we have

X(1+S2)^2 = 1000

X(1+S1)(1+f[1,2]) = 1000 , ------>(2)

From (1) and (2)

X(1000/943.4)*(1+.08)=1000

=> X = 943.4/1.08 = 873.52

Hence option (B) is correct