Amortized Cost vs Fair Value of a bond?

[yohji]

I’m sure this is a simple question, but I’m having a hard time understanding the difference between the amortized cost of a bond vs the fair value of a bond.
Also, why does a bond’s amortized cost not vary with changes in market interest rate but the fair value does?

 

[SeeEfAye]

Amortized cost is based on the book value on the balance sheet.
Fair value equals the remaining cash flows discounted at current market interest rates.
The book value recognized for a bond depends on market interest rates at issuance. The amortization of bond premium or discount each period is based on the difference between interest expense and coupon payment during the period.