Interest rates vs. yield

Hi all,

Currently at the end of the School of Pipsology, and I want to make sure I understand what yield is correctly.

Yield is not a separate entity from interest rates, but it is used to describe the amount of interest versus the price of a bond.

Is that correct? It isn’t a separate type of return or anything, it is just used as a number to represent interest rate versus (or over) price.

So if you have an $100 bond, and your interest is $5 a year, but if the bond were to double you would still make the same $5.
But, why is yield important? Who cares if the price of your bond goes up, if it does not affect your interest payment itself? It isn’t like you’ve paid more for the bond or missed out on money, right?

Thanks!