Caitlin, Chris, and Molly are partners and share income and losses in a $3$:$4$:$3$ ratio $($in ratio form: Caitlin, $3/10$; Chris, $4/10$; Molly, $3/10).$ The

partnership's capital balances are Caitlin, $$120,000$; Chris, $$80,000$; and Molly, $$100,000.$ Paul is admitted to the partnership on July $1$ with

a $20\%$ equity and invests $$160,000.$ The balance in Paul's capital account immediately after his admission is:

Multiple Choice

$$68,000$

$$460,000$

$$92,000$

$$160,000$