value of bond
In an example in SS15 - Fixed Income, it says -
the yield on a 6%, 20yr $1000 bond has declined from 6% at issuance to 4% on Jun 22, 2017 (first call option date). If there was no call option, the bond would trade at $1224. The issue date is Jun 22, 2012.
How did they arrive at $1224? Even if a bond is expected to yield 4%, the Present value 15 years of coupons at 4% will be – 40/(1.04) + 40/(1.04^2) + 40/(1.04^3) + … + 40/(1.04^15) = $444.74
So I was expecting the value of bond to be $1444.74. I am new to finance so bear with me if I am getting the concept of “bond value” totally wrong. I know “something” is wrong as the bond should trade at lower value than the PV of all coupons+principal for buyer to make any money but not sure how to determine the value