Emily owns a small house whose current market value is $$800,000,$ with a $$200,000$ mortgage on the current house. Now she has signed a contract to sell the house at the market price and received $$800,000$ from the buyer. She will use the left cash $($$$600,000)$ to purchase a new house valued at $$1104972$; the rest of the amount will be financed via a new home loan. Emily wants to borrow a $27-$year new home loan from the bank at an annual interest rate of $4\mathrm{.}5\%$ with monthly payments. Suppose that the bank's annual required return rate is $6\mathrm{.}1\%$; what is the present value of the new mortgage loan?$($Keep $2$ decimal places in the solution box and do not input $ in the solution box, e$.$g$.,$ if you obtain $$258\mathrm{.}54613$ as the correct outcome, please input $258\mathrm{.}55$ in your solution box. $)$