The Taylors have purchased a $240,000 house. They made an initial down payment of $10,000 and secured a mortgage with interest charged at the rate of 9%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? (Round your answer to the nearest cent.)
$ 
1850.63
 
Correct: Your answer is correct.


What is their equity (disregarding appreciation) after 5 years? After 10 years? After 20 years? (Round your answers to the nearest cent.)
5 years    	$139582.32 
Incorrect: Your answer is incorrect.
10 years    	$ 
83907.97
 
Incorrect: Your answer is incorrect.
20 years 

To determine the Taylors' equity after 5, 10, and 20 years, we need to first understand how equity is calculated and track their mortgage payments over time.

### Steps to Calculate Equity:
1. **Equity** is the difference between the market value of the house (which is fixed at $240,000) and the remaining mortgage balance at any point in time.
   
2. **Monthly Payment** is already provided: $1,850.63.

3. **Initial Loan Amount**: 
   \[
   240,000 - 10,000 = 230,000
   \]
   This means the Taylors borrowed $230,000.

4. **Monthly Interest Rate**: 
   The annual interest rate is 9%, so the monthly rate is:
   \[
   \frac{9\%}{12} = 0.75\% = 0.0075
   \]

5. **Using the Amortization Formula**:  
   The balance of the mortgage can be determined using the amortization formula:
   \[
   B = P \times \frac{(1 + r)^n - (1 + r)^p}{(1 + r)^n - 1}
   \]
   Where:
   - $B$ = remaining loan balance
   - $P$ = loan amount ($230,000)
   - $r$ = monthly interest rate (0.0075)
   - $n$ = total number of payments (30 years $\times$ 12 months = 360 payments)
   - $p$ = number of payments made so far (5, 10, or 20 years $\times$ 12 months)

6. **Equity** after any number of years is:
   \[
   \text{Equity} = \text{House value} - \text{Remaining loan balance}
   \]
   Where the house value is $240,000 (since we are disregarding appreciation).

### Now, let's compute the mortgage balance after 5, 10, and 20 years.

#### 5 Years (60 Payments):
\[
p = 60
\]
#### 10 Years (120 Payments):
\[
p = 120
\]
#### 20 Years (240 Payments):
\[
p = 240
\]

Let me calculate the remaining loan balance at these points using the amortization formula.Here are the calculated equity values for the Taylors after 5, 10, and 20 years:

- **Equity after 5 years**: $19,475.69
- **Equity after 10 years**: $34,311.59
- **Equity after 20 years**: $93,907.98

These values show the portion of the house the Taylors own after paying down the mortgage for these durations.

Would you like more details or have any further questions?

### Relative Questions:
1. How does the mortgage amortization schedule work in detail?
2. What factors affect how quickly equity builds in a mortgage?
3. How does the interest rate impact the total amount paid over the life of a mortgage?
4. What is the difference between fixed-rate and adjustable-rate mortgages?
5. How can early payments on a mortgage increase equity?

### Tip:
Making additional payments toward the principal early on in a mortgage can significantly reduce the loan term and increase equity faster.

The Taylors have purchased a $240,000 house. They made an initial down payment of $10,000 and secured a mortgage with interest charged at the rate of 9%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? What is their equity (disregarding appreciation) after 5 years, 10 years, and 20 years?

Learn how to calculate the monthly payment for a $230,000 mortgage with a 9% interest rate amortized over 30 years, as well as the Taylors' equity after 5, 10, and 20 years using the amortization formula. Understand how mortgage payments impact equity buildup over time.

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