Mountain Ski Resort had the following transactions for the month of January $2020$:

$1.$ Owner invested $$5,000.$

$2.$ Purchased a snow$-$grooming machine for $$28,000(50\%$ on account$).$

$3.$ Paid $$62,700$ in salaries and wages.

$4.$ Sold $$19,250$ in their restaurant.

$5.$ Sold $$34,100$ in their gift shop.

$6.$ Sold $$47,800$ in hotel room rentals.

If the company's assets increased by $$12,000$ in January, what is the net change in the company's liabilities for January?

Select answer from the options below

decrease by $$31,450$

increase by $$27,450$

increase by $$5,450$

decrease by $$17,450$