Question

Aubrey would like to buy 2 bonds. She has enough money to buy both bonds. The following are 2 bonds that she considers purchasing: (Hint: Calculate both prices. Total price = Bond 1 price + Bond 2 price) Bond 1: It is a zero-coupon bond. The YTM is 8.0%. It will mature in 35 years. Annual compounding. Bond 2: It is a bond with a market rate of 5.5%. Its coupon rate is 8.0%, compounded semiannually. This bond will mature in 17 years. Both bonds have a face value of $1,000. How much money does Aubrey need today, to buy both of the above bonds?

Answer 1

bond 1

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =35

Bond Price =∑ [(0*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^35

k=1

Bond Price = 67.63

bond 2

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =17x2

Bond Price =∑ [(8*1000/200)/(1 + 5.5/200)^k]     +   1000/(1 + 5.5/200)^17x2

k=1

Bond Price = 1273.83

total amount required = bond price 1 + bond price 2 = 1273.83+67.63 = 1341.46