$1.$ Naomi and Winnie established a partnership on January $1,2022.$ Naomi invested cash of $$95,000$ and Winnie invested $$30,000$ in cash and equipment with a book value of $$15,000$ and a fair value of $$50,000.$ For both partners, the beginning capital balance was to equal the initial investment. Naomi and Winnie agreed to the following procedures for sharing profits and losses:

$-5\%$ interest on the yearly beginning capital balance

$-$ $$25$ per hour of work that can be billed to the partnership$$s clients

$-$ The remainder divided $70\%$ and $30\%$ for Naomi and Winnie, respectively.

Additionally, the Articles of Partnership specified that each partner should withdraw no more than $$1,000$ per month.

For $2022,$ the partnership$$s income was $$135,000.$ Naomi had $1,700$ billable hours and Winnie had $1,100$ billable hours. Each partner withdrew the maximum amount they could during $2022.$

Required:

a$.$ Determine the amount of net income allocated to each partner for $2022.$

b$.$ Calculate the capital account balances at December $31,2022.$