Construct the amortization schedule for a ​$17 comma 000.00 debt that is to be amortized in 10 equal semiannual payments at 6​% interest per​ half-year on the unpaid balance.

To construct the amortization schedule for a $17,000.00 debt that is to be amortized in 10 equal semiannual payments at a 6% interest rate per half-year, we follow the steps outlined below.

### Step-by-step Amortization Schedule Construction:

1. **Loan Amount (Principal)**: $ P = 17,000 $
2. **Interest Rate per Semiannual Period**: 6% (or 0.06)
3. **Number of Payments (n)**: 10
4. **Formula for Payment Calculation (PMT)**:
   The formula for calculating the equal semiannual payment is based on the amortization formula:
   \[
   PMT = \frac{P \cdot r}{1 - (1 + r)^{-n}}
   \]
   Where:
   - $ P $ is the principal loan amount
   - $ r $ is the interest rate per period (0.06)
   - $ n $ is the number of periods (10)

### Step 1: Calculate the Semiannual Payment (PMT)

Let's calculate this first. Then we can construct the amortization schedule.The semiannual payment (PMT) is approximately $2,309.76.

### Step 2: Amortization Schedule
Now, let's construct the amortization schedule. The schedule will show the breakdown of each payment into two parts:
- **Interest**: Based on the current balance
- **Principal repayment**: The remaining part of the payment after subtracting the interest

The process is as follows:
1. Start with the initial balance of $17,000.
2. For each period:
   - Calculate the interest: $ \text{Interest} = \text{Balance} \times r $
   - Calculate the principal repayment: $ \text{Principal Repayment} = \text{Payment} - \text{Interest} $
   - Update the balance: $ \text{New Balance} = \text{Old Balance} - \text{Principal Repayment} $
3. Repeat for each of the 10 payments.

Let's generate the amortization schedule.Here is the amortization schedule for the $17,000.00 debt, amortized over 10 equal semiannual payments at a 6% interest rate:

| Payment # | Payment Amount | Interest | Principal Repayment | Balance |
|-----------|----------------|----------|---------------------|---------|
| 1         | $2,309.76      | $1,020.00 | $1,289.76           | $15,710.24 |
| 2         | $2,309.76      | $942.61   | $1,367.14           | $14,343.10 |
| 3         | $2,309.76      | $860.59   | $1,449.17           | $12,893.94 |
| 4         | $2,309.76      | $773.64   | $1,536.12           | $11,357.82 |
| 5         | $2,309.76      | $681.47   | $1,628.29           | $9,729.53 |
| 6         | $2,309.76      | $583.77   | $1,725.98           | $8,003.55 |
| 7         | $2,309.76      | $480.21   | $1,829.54           | $6,174.00 |
| 8         | $2,309.76      | $370.44   | $1,939.32           | $4,234.69 |
| 9         | $2,309.76      | $254.08   | $2,055.67           | $2,179.01 |
| 10        | $2,309.76      | $130.74   | $2,179.01           | $0.00   |

### Explanation:
- **Payment Amount**: Constant semiannual payment of $2,309.76.
- **Interest**: Calculated on the outstanding balance at the beginning of each period.
- **Principal Repayment**: The portion of the payment used to reduce the loan principal.
- **Balance**: The remaining balance after each payment.

Would you like further details or explanations on this process?

### Related Questions:
1. How does changing the interest rate affect the payment amount?
2. What happens if the number of payments is reduced to 5 instead of 10?
3. How do extra payments affect the amortization schedule?
4. What is the total interest paid over the life of the loan?
5. How can amortization schedules be adjusted for monthly payments?

### Tip:
By paying a little extra towards the principal, you can significantly reduce the total interest paid over the life of the loan!

Construct the amortization schedule for a $17,000.00 debt that is to be amortized in 10 equal semiannual payments at 6% interest per half-year on the unpaid balance.

Learn how to construct an amortization schedule for a $17,000 loan with 6% interest over 10 equal semiannual payments. This problem breaks down the amortization process, including interest calculation, principal repayment, and balance updates. Ideal for advanced high school or college students.

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