Say a bond was originally worth say $100 and generated $10 of income in time T (10%). If interest rates rise so that $100 will now generate $20 (20%), then the original bond is worth less to a buyer. If we ignore the time delta, that bond would only really be worth $50 ($50 to generate $10 is the same 20%), so it's half as valuable. (The time change would bring it somewhere in between, depending on how long has elapsed).
But basically:
Say a bond was originally worth say $100 and generated $10 of income in time T (10%). If interest rates rise so that $100 will now generate $20 (20%), then the original bond is worth less to a buyer. If we ignore the time delta, that bond would only really be worth $50 ($50 to generate $10 is the same 20%), so it's half as valuable. (The time change would bring it somewhere in between, depending on how long has elapsed).