The Scotts bought a \( \$ 241,000 \) house. They made a down payment of \( \$ 49,000 \) and took out a mortgage for the rest. Over the course of 15 years they made monthly payments of \( \$ 1620.22 \) 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)? (b) How much interest did they pay on the mortgage?

1. The total purchase price of the house is \[ \$241{,}000. \] They made a down payment of \[ \$49{,}000. \] The amount financed by the mortgage is then \[ 241{,}000 - 49{,}000 = \$192{,}000. \] 2. They made monthly payments of \[ \$1{,}620.22 \] for 15 years. Since there are 12 months in a year, the total number of monthly payments is \[ 15 \times 12 = 180. \] The total amount paid in monthly payments is \[ 1{,}620.22 \times 180 = \$291{,}639.60. \] 3. (a) The total amount paid for the house, including the down payment, is \[ 49{,}000 + 291{,}639.60 = \$340{,}639.60. \] 4. (b) The total interest paid on the mortgage is the total of the monthly payments minus the mortgage principal: \[ 291{,}639.60 - 192{,}000 = \$99{,}639.60. \] Thus, the final answers are: (a) The Scotts paid a total of \( \$340{,}639.60 \). (b) They paid approximately \( \$99{,}639.60 \) in interest on the mortgage.