Assuming each has the same length of time to maturity, which of the following would have the largest change in price $($in percentage terms$)$ for a given change in interest rates:

A$.$ a variable coupon bond.

b$.$ a zero coupon bond.

c$.$a fixed coupon bond.

d$.$ all bonds with the same length of time to maturity would have the same percentage change in price.

e$.$ It depends on whether rates move up or down.