Rachel died in the current year and her executor is finalizing her estate tax return. The executor has determined that Rachel$$s gross estate is $$12,150,000$ and that her estate is entitled to a charitable deduction in the amount of $$500,000.$ In addition the estate has certain expenses including funeral expenses of $$30,000.$ Rachel had a mortgage of $$240,000$ on her residence and unpaid bills at death of $$4,000.$ Finally, the estate expects legal and administrative costs of $$120,000.$ Rachel made a bequests to her sister for $$600,000.$ Calculate the adjusted gross estate for Rachel$$s estate.