When a bond is sold between interest payment dates, the buyer pays the seller:

Why B — Accrued interest from the last payment date to the settlement date

When bonds trade between coupon dates, the buyer pays the seller accrued interest — the interest earned from the last coupon payment date to the settlement date. This is fair because the seller owned the bond during that period but will not receive the next full coupon payment. The buyer will receive the full next coupon and effectively gets reimbursed for the accrued interest paid. Most bonds accrue interest on a 30/360 or actual/actual basis.