$2-(10$ points$)$ Morteza took out a loan from a bank at a $12\%$ APR to buy a house. The loan required him to make monthly payments over a $3-$year period. After paying for $24$ months $(2$ years$),$ Morteza sold the house to Negin. Negin then restructured the remaining loan balance into a new monthly repayment plan spread over $2$ years. However, $1$ year after purchasing the house, Negin decided to pay off the entire remaining loan amount, which was $$100,000,$ thereby gaining full ownership of the house. Determine the original price of the house.