Question

a) What is the price of a 10-year bond paying semi-annual coupons at the rate of 5% compounded semi- annually, if it is priced to yield 4.8% compounded semi-annually?

b) Is the bond trading at a premium or at a discount?

c) What would be the price quote for this bond?

d) What is the Macaulay duration of this bond in years, rounded to 2 decimal places? (Hint: create a table in excel)

e) What is the price of a 10-year zero coupon bond priced to yield 4.8% compounded semi-annually?

Answer 1

Part (a):

Price of the bond = $101.57 calculated using PV function of Excel as follows:

Part (b):

The bond is trading at premium.

Part (c):

Price quote of the bond=101.57

Part (d):

Macaulay Duration of the bond= 8.01 years as follows:

Part (e):

Zero coupon bond for 10 years. Let the face value (F) be $100.

Compounding frequency= Semi annual . Number of compounding period=20

YTM = 4.8%. Rate per period= 4.8%/2 = 2.4%

Price= $100/(1+2.4%)^20 = $100/ 1.60693804 = $62.23