Suppose you borrow $$688,000$ using a $5/7$ ARM. The interest rate on this loan is indexed to the one$-$year T$-$Bill yield with a $4\mathrm{.}22\%$ margin. The loan has an initial teaser rate of $1\mathrm{.}55\%.$ The lender charges the borrower $1\mathrm{.}36$ points and a $$4,750$ fee to originate this loan. The original term on the loan is $26$ years. Suppose you come into some additional money during the early life of the loan. Because of this windfall, you are able to prepay an additional $$670$ per month, starting at the $25\%$ between loan initiation and the first reset date. Assuming the buyer wishes to pay the mortgage off halfway between the first and second reset dates, how much money will she need to accomplish this? Express your answer in dollars and sense and round appropriately.

HINT $1$: If this were an unrestricted ARM $($it$\text{'}$s not...$)$ the prepayment would begin $25\%$ of the way between origination and reset $1,$ which would be $25\%$ of $12,$ or $3$ months.

HINT $2$: If this were an unrestricted ARM $($it$\text{'}$s not...$)$ the loan would be paid off $50\%$ of the way between reset $1,$ and reset $2,$ which would be $50\%$ of $12,$ or $6$ months.

HINT $3$: This is NOT an unrestricted ARM, so the number from Hint $1$ and the number from Hint $2$ will be different from $3$ and $6.$