To pay off a debt we must repay a capital of 5000 euros today, a capital of 5000 euros in 3 years and a capital of 5000 euros in 9 years. We agree to pay off the debt in a single installment in 6 years; How much will we have to pay if the annual compound rate is 4.25%?

To find out how much we need to pay after 6 years with an annual compound rate of 4.25%, we need to calculate the future value of each payment and then add them up.

Step 1: Calculate the future value of €5000 paid in 6 years:
Future Value = Present Value * (1 + Rate)^N
Future Value = €5000 * (1 + 0.0425)^6

Step 2: Calculate the future value of €5000 paid in 3 years:
Future Value = €5000 * (1 + 0.0425)^3

Step 3: Calculate the future value of €5000 paid in 9 years:
Future Value = €5000 * (1 + 0.0425)^9

Step 4: Add up all future values to find the total amount to be paid:
Total = Future Value1 + Future Value2 + Future Value3

Now, let's calculate the total amount to be paid:

1. Future Value_1 = €5000 * (1 + 0.0425)^6

Future Value_1 = €5000 * (1.0425)^6 ≈ €5000 * 1.2882 = €6441

2. Future Value_2 = €5000 * (1 + 0.0425)^3

Future Value_2 = €5000 * (1.0425)^3 ≈ €5000 * 1.1301 = €5650.50

3. Future Value_3 = €5000 * (1 + 0.0425)^9

Future Value_3 = €5000 * (1.0425)^9 ≈ €5000 * 1.4350 = €7175

4. Total = Future Value_1 + Future Value_2 + Future Value_3

Total ≈ €6441 + €5650.50 + €7175 = €19266.50

Therefore, you will need to pay approximately €19266.50 after 6 years with an annual compound rate of 4.25%.

\boxed{Answer: €19266.50} - Total amount to be paid.