Accrued interest is designed to:

Compensate the buyer of an interest-bearing bond for interest earned, (but not paid) since the previous coupon payment date

Compensate the seller of an interest-bearing bond for interest earner, (but not paid) relating to the next coupon payment date

Compensate the buyer of an interest-bearing bond for interest earned, (but not paid) relating to the next coupon payment date

Compensate the seller of an interest-bearing bond for interest earned, (but not paid) since the previous coupon payment date