Why bond prices move the opposite way to interest rates

You are holding a bond that pays a fixed coupon. Rates go up. New bonds now pay more than yours. Nobody wants yours at full price, so the price drops until your coupon plus the discount adds up to the same return as the new bonds.

That is the whole relationship. Price moves against yield, always.

The shortcut: longer maturity and lower coupon both mean a bigger swing. If a question mentions a 30-year zero-coupon bond, expect the largest price move in the answer set.

The trap: people remember "rates up, prices down" and then forget that the size of the move is what gets tested. Two bonds can both fall and one falls ten times harder.