Two years ago, you purchase a house of $$100,000.$ You borrow a mortgage with $80\%$ of LTV $($loan to value ratio$).$ The annual interest rate on the mortgage is $6\%.$ Payments are being made monthly, and the loan tem is $30$ years. You have found another lender who will refinance only the current outstanding loan balance at $4\mathrm{.}5\%$ with monthly payments for $30$ years. The new lender will charge three discount points and the refinancing cost is equal to $$3,000.$ Note that the points and refinancing cost will be from your own pocket.

If the new lender will allow you to refinance the current outstanding loan balance plus all the costs associated with the new loan, what is your new loan amount if you choose to refinance?

Option $1$: $$83,478\mathrm{.}96$

Option $2$: $$73,103\mathrm{.}83$