Charlie and Lucy share profits and losses in a ratio of $2$:$3,$ respectively, after guaranteed payments $($salary allowances$),$ interest allowances and bonus allocations. Charlie and Lucy receive guaranteed payments $($salary allowances$)$ of $$40,000$ and $$60,00,$ respectively, and both partners receive $10\%$ interest based upon the balance in their capital accounts on January $1.$ Total net income for $2023$ is $$550,000.$ What amount of net income is allocated for $2023$ to each of the partners, Charlie and Lucy's?" January $1$ capital balances Charlie$-$$$900,000$ and Lucy$-$$$700,000$