Question

What is the purchase price of a $15,000, 5.5% bond with monthly coupons redeemable in eight years if the bond is bought to yield 4.5% compounded semi-annually?

Answer 1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

Effective Annual Rate = ((1+4.5/2*100)^2-1)*100

Effective Annual Rate% = 4.55

K = Nx12

Bond Price =∑ [(Monthly Coupon)/(1 + YTM/12)^k]     +   Par value/(1 + YTM/12)^Nx12

k=1

K =8x12

Bond Price =∑ [(5.5*15000/1200)/(1 + 4.5506/1200)^k]     +   15000/(1 + 4.5506/1200)^8x12

k=1

Bond Price = 15953.44