Questions: Roberto bought a 410,000 house, paying 18% down, and financing the rest at 6.2% interest for 30 years. Her monthly payments are 2059.12. How much will he really pay for her 410,000 house? Roberto will pay a total of for the house.

Roberto bought a 410,000 house, paying 18% down, and financing the rest at 6.2% interest for 30 years. Her monthly payments are 2059.12. How much will he really pay for her 410,000 house?

Roberto will pay a total of for the house.

Transcript text: Roberto bought a $410,000 house, paying 18% down, and financing the rest at 6.2% interest for 30 years. Her monthly payments are $2059.12. How much will he really pay for her $410,000 house? Roberto will pay a total of $ for the house.

Solution

Solution Steps

Step 1: Calculate the Down Payment

The down payment is calculated as the initial price of the house (\$410000) times the down payment percentage (18%). \[\text{Down Payment} = 410000 \times 0.18 = \$73800\]

Step 2: Calculate the Loan Amount

The loan amount is the initial price of the house minus the down payment. \[\text{Loan Amount} = 410000 - \$73800 = \$336200\]

Step 3: Convert the Annual Interest Rate to a Monthly Rate

The monthly interest rate is the annual interest rate divided by 12. \[r_{\text{monthly}} = \frac{0.062}{12} = 0.00517\]

Step 4: Calculate the Total Number of Payments

The total number of payments is the duration of the loan in years times 12. \[N = 30 \times 12 = 360\]

Step 5: Calculate the Total Amount Paid Over the Life of the Loan

The total amount paid is the monthly payment amount times the total number of payments. \[\text{Total Paid} = 2059.12 \times 360 = \$741283.2\]

Step 6: Calculate the Total Amount Really Paid for the House

The total cost of the house is the down payment plus the total amount paid over the life of the loan. \[\text{Total Cost} = \$73800 + \$741283.2 = \$815083.2\]