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 $$ \square $$

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UpStudy AI · Accepted Answer

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.
The Chens paid a total of \$297,109.20 for the townhome, which includes the down payment and all monthly mortgage payments. They paid \$133,109.20 in interest on their mortgage over 15 years.

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