Question

Question: Consider a bond with a settlement date of February 22, 2012, and a maturity date of March 15, 2020. The coupon rate is 5.5%. If the yield to maturity of the bond is 5.34% (bond equivalent yield, semi-annual compounding), what is the list price of the bond on the settlement date? What is the accrued interest on the bond? What is the invoice price of the bond?

Short answer

Answer

List price = 101.71

Accrued interest = 0.6391

Invoice price = 101.349

Step-by-step solution

Given information

Semi annual coupon rate = 5.5%

Semi-annual yield to maturity rate = 5.34 %

Calculation of the list price of the bond

The semi-annual coupon = 5.34 % x face value = 5.5% x 100 = 5.5

Here:

C = 5.5

YTM / 2 = 0.534

t = 8

F = 100

The list price is thesale price divided by the difference of 1 minus the result of discount divided by 100.

L = S / (1 – D/100)

List price of Bond = 101.71

Calculation of the accrued interest/income on the bond 

The formulae for accrued income = (accrued interest rate / 2 ) x ( days between ask price date and last interest payment / coupon period ) x ask price

= 5.5% x (21/ 182 ) x 100.71

Hence accrued interest = 0.6391

Calculation of the invoice price of the bond 

Invoice price = Ask price + Accrued income

= 100.71 + 0.6391 = 101.349