What periodic payment would be required to amortize a $1000 debt in eight semiannual payments of
interest is 6 percent, compounded semiannually?

To find the periodic payment required to amortize a $1,000 debt over 8 semiannual payments with 6% interest compounded semiannually, we use the **amortization formula**:

\[
PMT = \frac{P \cdot r}{1 - (1 + r)^{-n}}
\]

Where:
- $ P $ = Principal amount ($1,000)
- $ r $ = Interest rate per period (6% annually, compounded semiannually, so $ r = 0.06 / 2 = 0.03 $)
- $ n $ = Total number of payments (8 semiannual payments)
- $ PMT $ = Periodic payment

### Step 1: Plug in the values

\[
PMT = \frac{1000 \cdot 0.03}{1 - (1 + 0.03)^{-8}}
\]

### Step 2: Calculate the periodic payment
Let me calculate that for you.

The periodic payment required to amortize the $1,000 debt over 8 semiannual payments at a 6% annual interest rate (compounded semiannually) is approximately **$142.46**.

Would you like further details or have any questions?

Here are 5 related questions to expand this topic:
1. How does the amortization formula change for monthly payments?
2. What happens if the interest rate changes mid-term?
3. How would the amortization change if compounded annually instead?
4. What is the total interest paid over the loan term?
5. How can the amortization period affect the total cost of the loan?

**Tip:** Longer amortization periods reduce your periodic payments but increase the total interest paid over the life of the loan.

What periodic payment would be required to amortize a $1000 debt in eight semiannual payments of interest is 6 percent, compounded semiannually?

Discover how to calculate the periodic payment required to amortize a $1000 debt over 8 semiannual payments at a 6% interest rate compounded semiannually. Learn key concepts of amortization and compound interest with detailed formulas and step-by-step solutions. Suitable for high school students (Grades 10-12).

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