Question

What is the price of a 6​-year, 7.8 % coupon​ rate, $ 1,000 face value bond that pays interest annually if the yield to maturity on similar bonds is 7.2 %​? The price of the bond is ​$__. ​ (Round to the nearest​ cent.)

Answer 1

Annual coupon=1000*7.8%=78

Hence price of bond=Annual coupon*Present value of annuity factor(7.2%,6)+$1000*Present value of discounting factor(7.2%,6)

=78*4.73725176+1000*0.658917873

=$1028.42(Approx).

NOTE:

1.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=78[1-(1.072)^-6]/0.072

=78*4.73725176

2.Present value of discounting factor=1000/1.072^6

=1000*0.658917873