A security with a periodically adjustable interest rate is typically known as a:

A security with a periodically adjustable interest rate is typically referred to as a floating rate bond. This type of bond has its interest payments reset at regular intervals based on a reference interest rate, such as LIBOR or the U.S. Treasury rate. This feature allows the bond's yield to fluctuate with changes in market interest rates, providing investors with protection against inflation and rising rates, as the interest payments will increase if prevailing rates rise.

In contrast, the other types of securities mentioned do not have this adjustable feature. A sinking fund involves a systematic payment arrangement to gradually repay bonds, rather than an adjustment in interest rates. A zero coupon bond, on the other hand, pays no periodic interest and is sold at a discount to its face value, maturing at par. Lastly, convertible preferred stock offers the option to be converted into a certain number of common shares but does not typically involve fluctuating interest rates like a floating rate bond does.