On June $1,2023,$ Jill Bow and Aisha Adams formed a partnership to open a gluten$-$free commercial bakery, contributing $$293,000$ cash and $$386,000$ of equipment, respectively. The partnership also assumed responsibility for a $$53,000$ note payable associated with the equipment. The partners agreed to share profits as follows: Bow is to receive an annual salary allowance of $$163,000,$ both are to receive an annual interest allowance of $5\%$ of their original capital investments, and any remaining profit or loss is to be shared $40/60($to Bow and Adams, respectively$).$ On November $20,2023,$ Adams withdrew cash of $$113,000.$ At year$-$end, May $31,2024,$ the Income Summary account had a credit balance of $$510,000.$ On June $1,2024,$ Peter Williams invested $$133,000$ and was admitted to the partnership for a $20\%$ interest in equity. Record the closing of profit to capital and Record the admission of Williams for a $20\%$ interest.