Question

(c) (20 marks) We consider a n-year bond (where n > 10) issued today. You are given that The bond pays coupon semi-annually (The first coupon is paid 6 months after today). The annual effective yield rate of the bond is 4.8576% and remains unchanged throughout the life of the bond. • The book value at the end of 25th month is $3437.6085 The book value at the end of 50th month is $3361.802 Find the book value at the end of 100th month.

Answer 1

annual effective yield is 4.8576%

Coupon Rate?

Annual effective yield=[{(1+Coupon Rate/number of compounds per year)}^number of compounds per year]-1

Number of compounds is 2 as the coupon is paid once in 6 months

Coupon=C

0.048576=[(1+C/2)^2]-1

1.048576=((2+C)/2)^2

(1.048576)^0.5=(2+C)/2

2.048=2+C

C=0.048 I.E.,4.8%

Difference of book value=3437.6085-3361.802=75.8065 is nothing but interest amortized in books of accounts in 25 months

Let face value be X

75.8065=X*4.8%*5/12+X*4.8%*6/12+X*4.8%*6/12+X*4.8%*6/12+X*4.8%*2/12

75.8065=X*0.1

X=758.065

Book value at the end of 100th Month=Book value at the end of 50th Month- Interest amortized between the period

=3361.802-758.065*4.8%*50/12

=3361.802-151.613

=3210.189