Consider the following amortization schedule:
Payment #
Payment
Interest
Debt Payment
Balance
1
1
,
167.34
540.54
626.80
259
,
873.20
2
1
,
167.34
539.24
628.10
259
,
245.10
3
1
,
167.34
x
y
z
 
With the exception of column one, all amounts are in dollars. Calculate  
z
  to the nearest dollar. Do not include commas or the dollar sign in your answer.

We are provided with the following amortization schedule:

| Payment # | Payment | Interest | Debt Payment | Balance   |
|-----------|---------|----------|--------------|-----------|
| 1         | 1167.34 | 540.54   | 626.80       | 259873.20 |
| 2         | 1167.34 | 539.24   | 628.10       | 259245.10 |
| 3         | 1167.34 | x        | y            | z         |

### Step 1: Understand the pattern

- Total Payment = Interest + Debt Payment
- New Balance = Old Balance - Debt Payment

For the second payment:
- Total Payment = 1167.34
- Interest = 539.24
- Debt Payment = 1167.34 - 539.24 = 628.10
- New Balance after the second payment: 259245.10 = 259873.20 - 628.10

### Step 2: Calculate \( z \) (Balance after the third payment)

To calculate the balance after the third payment:
1. The Debt Payment for the third payment is \( y = 1167.34 - x \), where \( x \) is the interest for the third payment.
2. Assuming the interest is decreasing consistently, we can approximate the interest \( x \) for the third payment.

Since the interest decreased from 540.54 to 539.24 (a difference of 1.30), the interest for the third payment can be approximated as:
\[
x = 539.24 - 1.30 = 537.94
\]

Thus, the Debt Payment \( y \) for the third payment is:
\[
y = 1167.34 - 537.94 = 629.40
\]

3. Now, calculate the new balance \( z \) after the third payment:
\[
z = 259245.10 - 629.40 = 258615.70
\]

Rounding to the nearest dollar, the value of \( z \) is \( 258616 \).

### Final Answer:
\[
z = 258616
\]

Would you like further details or explanations? Here are 5 related questions for deeper exploration:

1. How do amortization schedules work, and why does interest decrease over time?
2. What is the formula for calculating monthly interest in an amortization schedule?
3. How can extra payments affect the overall amortization schedule?
4. What factors influence the rate at which principal is paid down in a loan?
5. How does the length of the loan term affect the amortization process?

**Tip:** Understanding how interest is calculated each period is key in working with amortization schedules—it’s usually based on the remaining balance.

Consider the following amortization schedule:
Payment #
Payment
Interest
Debt Payment
Balance
1
1167.34
540.54
626.80
259873.20
2
1167.34
539.24
628.10
259245.10
3
1167.34
x
y
z

With the exception of column one, all amounts are in dollars. Calculate z to the nearest dollar. Do not include commas or the dollar sign in your answer.

Learn how to calculate the remaining balance after the third payment in an amortization schedule. This problem involves key concepts such as interest calculation, debt payment, and balance determination, with detailed step-by-step guidance. Suitable for students in Grades 10-12.

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