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To solve this problem, we need to calculate the equivalent value of all payments at the final payment date (six years from now) using the given interest rate of 1.7%, compounded annually.

Here's a step-by-step approach:

1. **Convert each debt and payment to their equivalent value at six years:**

   The formula for future value $ F $ given a present value $ P $ is:
   \[
   F = P \times (1 + r)^n
   \]
   where:
   - $ r = 0.017 $ (interest rate of 1.7%)
   - $ n $ is the number of years until the payment is due or past the payment.

### Step 1: Calculate Future Values of Debts
1. **$5000 due in five years**: We need its value at six years, so $ n = 6 - 5 = 1 $.
   \[
   5000 \times (1 + 0.017)^1
   \]

2. **$5000 due in ten years**: We need its value at six years, so $ n = 6 - 10 = -4 $.
   \[
   5000 \div (1 + 0.017)^4
   \]

### Step 2: Calculate Future Values of Payments
1. **$2100 in two years**: We need its value at six years, so $ n = 6 - 2 = 4 $.
   \[
   2100 \times (1 + 0.017)^4
   \]

2. **$4200 in four years**: We need its value at six years, so $ n = 6 - 4 = 2 $.
   \[
   4200 \times (1 + 0.017)^2
   \]

### Step 3: Set Up Equation for Final Payment
Let the final payment be $ X $.

Combine all values at the six-year mark:
\[
5000 \times (1.017)^1 + \frac{5000}{(1.017)^4} = 2100 \times (1.017)^4 + 4200 \times (1.017)^2 + X
\]

After calculating these values, solve for $ X $.

I'll proceed with these calculations.The final payment should be approximately **$3168.48** when rounded to the nearest cent.

Would you like a detailed breakdown of the calculations? 

Here are some related questions to explore further:
1. How would the final payment change if the interest rate was different?
2. What would happen if payments were made on different dates?
3. How does compounding frequency affect the final payment amount?
4. Can you solve similar problems with continuous compounding?
5. How can this approach be applied to other types of loans?

**Tip:** When dealing with compound interest problems, remember that timing and compounding frequency are key factors in determining the future value of payments.

A debt of $5000 due five years from now and $5000 due ten years from now is to be repaid by a payment of $2100 in two years, a payment of $4200 in four years, and a final payment at the end of six years. If the interest rate is 1.7% compounded annually, how much is the final payment?

Learn how to calculate the final payment required to repay a debt with two initial amounts due in five and ten years, with partial payments made at two and four years. The solution involves calculating future values with a 1.7% annual compound interest rate, suitable for Grades 11-12.

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