Question A1 Answer the questions for bonds A and B and show all your calculations. Coupons are paid semi-annually Bond A Bond B Coupon rate 8% 9% Yield to maturity 8% 8% Maturity (years) 2 5 Par $100 $100 a) Calculate the price of bonds A and B. (4 marks) b) Calculate the new price of the bonds for a 100 basis point increase in interest rates. (4 marks) c) Calculate the annualized modified duration for each bond. (4 marks) d) Using the calculated modified duration in part c), estimate the price of the bonds for a 100 basis point interest rate increase. (4 marks) e) Comment on the accuracy of your results in parts b) and d), and state why one approximation is closer to the actual price than the other. 

1. Price of Bond A = $100

when coupon rate and yield to maturity is same, bond price always be equal to face value .

2.Value of bond = I(PVIFA r,k)+FV(PVIF r.,k)

=4.5(PVIFA 4%,10 ) +100(PVIF 4%,10)

=4.5*8.1109+100*0.6756

=36.499 + 67.56 =$104.059

b)

Price of Bond A after increase in 100 points in interest rate:

New interest rate = 9%

Value of bond = 4 (PVIFA 4.5,4)+100(PVIF 4.5 ,4)

=4*3.5875 +100 * 0.8386

= 14.35 +83.86 = 98.21

2.Price of Bond B after increase in 100 points in interest rate:

New interest rate = 9%

Now coupon rate and yield rate both are same so Bond price will be equal to face value .

Value of bond = $100

c.Modified Duration of bond A =Duration /(1 +Yield )= -1.814948

percentage change in Price = Modified duration *Change in Yield

= -1.814948 *1%

= - 0.0181495

New Price of bond A = Old Price *(1 + Percentage change in price)

=100 *( 1 +(-0.0181495))

=$98.19

C.2.

Modified DUration of bond B ==Duration /(1 +Yield) = 3.994417

percentage change in Price = -Modified duration *Change in Yield

= -3.994417 *1%

= -0.039944

New Price of bond A = Old Price *(1 + Percentage change in price)

=100 *( 1 +( -0.039944))

=$99.9