When will the carrying value of bonds equal the market price?

On the date that the bonds are issued, that is the only time a bond will be traded at book value or at par.

Explanation:

The carrying value of bonds is equal to the book value of the bonds. It is very rare that a bond will be traded at its book value. Generally bonds are traded at a lower value, discount bonds, or are traded at a higher value, premium bonds. Interest rates are not fixed, usually the FED sets a reference interest rate for US securities that changes over time and the market rate also changes over time depending on how the economy is doing. The bond prices are affected by the market interest rates, so if the market rates vary, the price of the bonds will vary also.