mortgage problem: how many months for payments to be....

[tigerpawz74]

A couple is considering two banks for a morgage. Bank One and Banker's Trust. The monthly mortgage payments with Bank One would be $889 per month plus a one-time application fee of $900. The monthly payment with Banker's Trust would be $826 plus a one-time fee of $1200. How many months would it take for the total payments for both banks to be teh same?

I have set this up several ways, but none of them makes any sense. I know the difference between the totals is $237 and that the difference between the payments is $63 and I tried dividing $237 by $63 and came up with 3.76, but I am really lost as to how this should be set up. Please help!!!!!!!! Thanks, Marilyn

[soroban]

Hello, Marilyn!


A couple is considering two banks for a morgage: Bank One and Banker's Trust.
The monthly payments with Bank One would be $889 per month plus a one-time fee of $900.
The monthly payments with Banker's Trust would be $826 plus a one-time fee of $1200.
How many months would it take for the total payments for both banks to be the same?
Look at the question: When are the total payments equal?

Write expression for the Total Payments and set them equal to each other.

For Bank One, they will pay $900, plus $889 per month for x months.
\;\;Total payment to Bank One: \,900\,+\,889x dollars.

For Banker's Trust, they will pay $12-- plus $826 per month for x months.
\;\;Total payment to Banker's Trust: \,1200\,+\,826x dollars.


When are they equal? \;\;900\,+\,889x\:=\:1200\,+\,826x

\;\; and solve for x . . .

[Denis]

Well tiger, that makes no sense...
$237 is difference between WHAT totals?
Are the 2 banks charging the SAME interest rate?
Where does that problem come from? Are you giving us ALL the information?

Edit: Is that the way you read that, Soroban: fees = payment?
In that case, they will NEVER be the SAME:
4 months: 1200 + 826*4 = 4504; 900 + 889*4 = 4456
5 months: 1200 + 826*5 = 5330; 900 + 889*5 = 5345

[tigerpawz74]

Thanks so much for showing me how to set up that problem! I had tried different ways to do it but never came up with the correct way to solve it. I worked it out and checked it, and using the 4.7619047 as my answer, I checked it and it does work out to be the same. WOW, Thanks again, and have a great day! Marilyn