Answer to Question #80360 in Financial Math for Penny

Question

B1 - A two year bond with a nominal rate of 3.5% per annum

these bonds have six monthly coupons and a face value of $2,000. Calculate their present values, Macauly durations and convexities using a YTM of 6% (YTM = 0.06).

Answer 1

PV = 2,000*0.035/(1 + 0.06/2) + 70/(1 + 0.06/2)^2 + 70/(1 + 0.06/2)^3 + (2,000 + 70)/(1 + 0.06/2)^4 = $2,037.17.
Macaulay duration = PV/P = 2,037.17/2,000 = 1.019.
Convexity = 1/(2,000*1.06^2)*(70*(1^2 + 1)/(1 + 0.06/2) + 70*(2^2 + 2)/(1 + 0.06/2)^2 + 70*(3*2 + 3)/(1 + 0.06/2)^3 + 2,070*(4^2 + 4)/(1 + 0.06/2)^4) = 16.86.