A new partner $C$ is invited to join in the $AB$ partnership. Currently, A$\text{'}$s and B$\text{'}$s capital are $$540,000$ and $$100,000,$ respectively. According to their profit and loss sharing contract, partner A and $B$ share income in a $3$:$1$ ratio, respectively. The $AB$ partnership is using the bonus method.

Assuming that A$\text{'}$s capital is surprisingly decreased by $$7500$ after recording a new partner C$\text{'}$s investment, how much money are paid by a new partner C for $10\%$ interest of the capital of the new partnership? $($No Partial Points Allowed$)$

Just write down the amount. Do not use dollar sign or commas.

Numeric Response