You have a choice between a $30-$year fixed rate loan at $3\mathrm{.}5\%$ and an adjustable rate mortgage $($ARM$)$ with a first year rate of $2\%.$ Neglecting compounding and changes in principal, estimate your monthly savings with the ARM during the first year on a $$225,000$ loan. Suppose that the ARM rate rises to $10\mathrm{.}5\%$ at the start of the third year. Approximately how much extra will you then be paying over what you would have paid if you had taken the fixed rate loan?

What is the approximate monthly savings with the ARM during the first year?

$ $($Round to the nearest dollar as needed.$)$