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Math  /  Numbers & Operations

QuestionThe Allens bought a $341,000\$ 341,000 house. They made a down payment of $46,000\$ 46,000 and took out a mortgage for the rest. Over the course of 30 years they made monthly payments of $1768.68\$ 1768.68 on their mortgage until it was paid off. (a) What was the total amount they ended up paying for the house (including the down payment and monthly payments)? $⟦\$ \llbracket (b) How much interest did they pay on the mortgage? $□\$ \square

Studdy Solution

STEP 1

1. The total cost of the house includes the down payment and the total of the monthly mortgage payments.
2. The monthly mortgage payment is constant over the entire 30-year period.
3. The mortgage period is 30 years, which translates to 360 months.

STEP 2

1. Calculate the total amount paid in monthly mortgage payments.
2. Calculate the total amount paid for the house by adding the down payment to the total amount paid in mortgage payments.
3. Calculate the total interest paid by subtracting the initial mortgage amount from the total amount paid in mortgage payments.

STEP 3

Calculate the total amount paid in monthly mortgage payments.
Total Monthly Payments=$1768.68×360 \text{Total Monthly Payments} = \$ 1768.68 \times 360

STEP 4

Perform the multiplication to find the total amount paid in monthly payments.
Total Monthly Payments=$1768.68×360=$636,724.80 \text{Total Monthly Payments} = \$ 1768.68 \times 360 = \$ 636,724.80

STEP 5

Calculate the total amount paid for the house by adding the down payment to the total amount paid in monthly payments.
Total Amount Paid=$46,000+$636,724.80 \text{Total Amount Paid} = \$ 46,000 + \$ 636,724.80

STEP 6

Perform the addition to find the total amount paid for the house.
Total Amount Paid=$46,000+$636,724.80=$682,724.80 \text{Total Amount Paid} = \$ 46,000 + \$ 636,724.80 = \$ 682,724.80

STEP 7

Calculate the initial mortgage amount.
Initial Mortgage Amount=$341,000−$46,000=$295,000 \text{Initial Mortgage Amount} = \$ 341,000 - \$ 46,000 = \$ 295,000

STEP 8

Calculate the total interest paid by subtracting the initial mortgage amount from the total amount paid in monthly payments.
Total Interest Paid=$636,724.80−$295,000 \text{Total Interest Paid} = \$ 636,724.80 - \$ 295,000

STEP 9

Perform the subtraction to find the total interest paid.
Total Interest Paid=$636,724.80−$295,000=$341,724.80 \text{Total Interest Paid} = \$ 636,724.80 - \$ 295,000 = \$ 341,724.80
Solution: (a) The total amount they ended up paying for the house is \$682,724.80. (b) The total interest they paid on the mortgage is \$341,724.80.

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