ALEKS: Serena Jones Done Matico Propertions, and Porcents Computing the total cost and interest for a lonn Gerena The Chens bought a \( \$ 212,000 \) townhome. They made a down payment of \( \$ 48,000 \) and took out a mortgag Over the course of 15 years they made monthly payments of \( \$ 1383.94 \) on their mortgage untii it was paid (a) What was the total amount they ended up paying for the townhome (including the down payment and monthly payments)? 5 \( \square \) (b) How much interest did they pay on the mortgage? 5 \( \square \)

To solve the problem, we will break it down into two parts: ### Part (a): Total Amount Paid for the Townhome 1. **Identify the known values:** - Purchase price of the townhome: \( P = 212,000 \) - Down payment: \( D = 48,000 \) - Monthly payment: \( M = 1383.94 \) - Duration of the mortgage: \( T = 15 \) years 2. **Calculate the total amount paid in monthly payments:** - The total number of monthly payments over 15 years is: \[ N = T \times 12 = 15 \times 12 = 180 \] - The total amount paid in monthly payments is: \[ \text{Total Monthly Payments} = M \times N = 1383.94 \times 180 \] 3. **Calculate the total amount paid for the townhome:** - The total amount paid for the townhome is the sum of the down payment and the total monthly payments: \[ \text{Total Amount Paid} = D + \text{Total Monthly Payments} \] ### Part (b): Total Interest Paid on the Mortgage 1. **Calculate the total amount paid for the townhome (from part a).** 2. **Calculate the total interest paid:** - The total interest paid on the mortgage is the total amount paid minus the amount borrowed (which is the purchase price minus the down payment): \[ \text{Amount Borrowed} = P - D \] - The total interest paid is: \[ \text{Total Interest Paid} = \text{Total Amount Paid} - \text{Amount Borrowed} \] Now, let's perform the calculations for parts (a) and (b). ### Calculations 1. Calculate the total monthly payments: \[ \text{Total Monthly Payments} = 1383.94 \times 180 \] 2. Calculate the total amount paid for the townhome: \[ \text{Total Amount Paid} = 48000 + \text{Total Monthly Payments} \] 3. Calculate the amount borrowed: \[ \text{Amount Borrowed} = 212000 - 48000 \] 4. Calculate the total interest paid: \[ \text{Total Interest Paid} = \text{Total Amount Paid} - \text{Amount Borrowed} \] Let's perform these calculations. Calculate the value by following steps: - step0: Calculate: \(212000-48000\) - step1: Subtract the numbers: \(164000\) Calculate or simplify the expression \( 1383.94 * 180 \). Calculate the value by following steps: - step0: Calculate: \(1383.94\times 180\) - step1: Multiply the numbers: \(249109.2\) Calculate or simplify the expression \( 48000 + 249109.2 \). Calculate the value by following steps: - step0: Calculate: \(48000+249109.2\) - step1: Add the numbers: \(297109.2\) Calculate or simplify the expression \( 297109.2 - 164000 \). Calculate the value by following steps: - step0: Calculate: \(297109.2-164000\) - step1: Subtract the numbers: \(133109.2\) ### Final Results Now that we have completed the calculations, here are the results for both parts of the problem: #### Part (a): Total Amount Paid for the Townhome - The total amount paid for the townhome, including the down payment and monthly payments, is: \[ \text{Total Amount Paid} = 297109.2 \] #### Part (b): Total Interest Paid on the Mortgage - The total interest paid on the mortgage is: \[ \text{Total Interest Paid} = 133109.2 \] ### Summary - **Total Amount Paid for the Townhome:** \( 297109.2 \) - **Total Interest Paid on the Mortgage:** \( 133109.2 \) These calculations provide a clear understanding of the financial commitment made by the Chens for their townhome.