Does a bond's yield (principal and coupon rate) always equal the bank interest rate?
Each fixed income instrument has an interest rate implied by a transaction price, and these prices can move in different directions.
The FRED website has a list of some of the more important interest rates in the United States: link to FRED. However, these are mainly “generic” yields, which are based on fitting a curve through traded bond quotes. For example, the “10-year Treasury bond” yield shown on the website is going to be close to the the market yields of Treasury bonds/notes that are near a 10-year maturity, but there are spreads between them.