Question

1. A four-year bond with a yield of 8% (continuously compounded) pays a 6% coupon at the end of each year (one coupon per year).

1. What is the bond’s price?
2. What is the bond’s duration?
3. Use the duration to calculate the effect on the bond’s price of a 0.1% decrease in its yield.
4. Recalculate the bond’s price on the basis of a 7.9% per annum yield and verify that the result is in agreement with your answer to (c).
   
   NOTE: Use continuously compounded formulas only. show work and explain. DO NOT JUST POST PIC OF EXCEL.

Answer 1

ASSUMING PAR OF 100

1.
=6%*100*(e^(-8%*1)+e^(-8%*2)+e^(-8%*3)+e^(-8%*4))+100*e^(-8%*4)
=$92.3431

2.
=(6%*100*(1*e^(-8%*1)+2*e^(-8%*2)+3*e^(-8%*3)+4*e^(-8%*4))+4*100*e^(-8%*4))/92.3431
=3.65822

3.
% change=-3.65822*(-0.1%)=0.3658%

New price=92.3431*(1+0.3658%)=$92.6809

4.
=6%*100*(e^(-7.9%*1)+e^(-7.9%*2)+e^(-7.9%*3)+e^(-7.9%*4))+100*e^(-7.9%*4)=92.68159