They plan to use their $40,000 is savings to cover the closing costs the bank will charge them,...

Question:

They plan to use their $40,000 is savings to cover the closing costs the bank will charge them, which are 1% of the amount they borrow from the bank. The rest of the savings will be used as a down payment. For example, if they borrow $330,000 using $20,000 for a down payment, the closing costs will be $3,300, which still leaves them some savings. Determine the largest amount they can use for a down payment and still pay the closing costs.

Down Payment:

The down payment is the upfront payment on a loan, which is to reduce the remaining balance and lower the interest expenses. In some cases, the down payment is required by laws to lower the risk for lenders.

Answer and Explanation:

Assume:

  • X: Amount of closing cost
  • Y: Amount of down payment

The largest amount of down payment happens when they spend all of $40,000 for the down payment and closing costs.

X + Y = $40,000 (1)

Purchase price = $330,000 + $20,000 = $350,000

X = ($350,000 - Y) x 1% (2)

Substitute (2) to (1):

($350,000 - Y) x 1% + Y = $40,000

==> Y = $36,869

==> X = $40,000 - $36,869 = $3,131


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Buying a House: Mortgage Types & Loan Length

from Finance 102: Personal Finance

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