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$-2]$ Mateo and Klaus have now saved up their down payment to buy a home, but they still need to borrow to cover the rest. For the home they want this will require a mortgage of $$585,000$ to cover the remaining amount and they're not sure whether they could afford the monthly loan payments. The bank has offered them a mortgage interest rate of $5\mathrm{.}15\%,$ compounded semi$-$annually.

How much would they have to be able to afford to pay each month in order to pay off their mortgage in $25$ years? $[$Blank$-1]$

What is the total amount of interest that would be paid to the lender after $25$ years of payments? $[$Blank$-2]$ What if Mateo and Klaus could only afford a monthly payment of $$2,500?$

What would be the maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same? $[$Blank$-1]$

What is the total amount of interest that would be paid to the lender over $25$ years? $[$Blank$-2]$ nabling unlimited submissions requires answers to be formatted. Format answers as follows:

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