Which one of the following statements concerning bond yields or bond prices is TRUE?

Select one:

a$.$ A credit rating upgrade is likely to lead to a fall in the price of the upgraded bond.

b$.$ A bond with $5$ years to maturity will tend to fluctuate more in price than a bond with $10$ years to maturity as bond yields fluctuate, other things being equal.

c$.$ The bond yield is likely to decrease if the expected rate of inflation rises.

d$.$ A $10-$year Treasury bond issued with a face value of $$1000$ and a coupon of $$40$ will rise in price if the next day a new $10-$year Treasury bond with an identical face value is sold with a coupon of $$30.$