Mateo and Klaus would like to buy a house and their dream starter home costs $$650,000.$ Their goal is then to save $$65,000$ for a down payment and then would take out a mortgage loan for the rest. They plan to put their monthly saved amount in a conservative mutual fund that has a track record of a $4\mathrm{.}25\%$ rate of return, compounded quarterly. To be sure they don't go spending this money on other things, they are going to move it into their investment account at the beginning of each month. Their hope is to be able to buy this home in $7$ years.

What would their monthly savings amount have to be to reach this goal? $[$Blank$-1]$

What will be the total interest earned? $[$Blank$-2]$