A partnership began its first year of operations with the following capital balances:

South, Capital: $$100,000$

West, Capital: $$150,000$

Door, Capital: $$200,000$

The Articles of Partnership stipulated that profits and losses be assigned in the following manner:

West was to be awarded an annual salary of $$10,000.$

Each partner was to be attributed with interest equal to $10\%$ of the beginning capital balance.

The remainder was to be assigned on a $2$:$4$:$4$ basis to South, West, and Door, respectively.

Assume that the net income for the first year was $$160,000.$ How much net income will be allocated to South for the first year $($i$.$e$.$ what is South's share in net income$)?$