Which of the following statement is FALSE?

Group of answer choices

The value of existing bonds usually decreases when there is an increase in interest rates.

Zero$-$coupon bonds are generally more susceptible to changes in interest rates compared to a $10\%$ coupon paying bonds, given all other things being equal.

Zero$-$coupon bonds are priced above their face value before they mature.

Long$-$term bonds are generally more susceptible to changes in interest rates compared to short$-$term bonds, given all other things being equal.