We can solve for $X$, the amount that will pay off the loan at the end of year 5, by considering the loan with compound interest. Since the company borrowed $10,000 at 12% interest, the interest accumulates each year.

The loan repayment schedule involves annual payments of $2,000 for the first four years, and the final payment $X$ at the end of year 5. We assume the interest is compounded annually.

Step-by-Step Process:

1. Initial Loan and Interest Rate: $P = 10,000 \quad \text{(principal)}$ $r = 12\% = 0.12 \quad \text{(annual interest rate)}$

2. Effective debt at the end of each year:

   • At the end of Year 1, the debt becomes: $10,000 \times (1 + 0.12) - 2,000 = 11,200 - 2,000 = 9,200$
   • At the end of Year 2: $9,200 \times (1 + 0.12) - 2,000 = 10,304 - 2,000 = 8,304$
   • At the end of Year 3: $8,304 \times (1 + 0.12) - 2,000 = 9,300.48 - 2,000 = 7,300.48$
   • At the end of Year 4: $7,300.48 \times (1 + 0.12) - 2,000 = 8,176.54 - 2,000 = 6,176.54$

3. Final payment at the end of Year 5: At the end of Year 5, the remaining balance with interest is: $6,176.54 \times (1 + 0.12) = 6,917.72$

Thus, the final payment $X$ at the end of Year 5 must be: $X = 6,917.72$

So, the amount $X$ that will pay off the loan at the end of year 5 is $6,917.72.

Would you like more details or have any questions?

Here are five related questions:

1. How does compound interest affect loan repayments over time?
2. What if the interest rate was compounded monthly instead of annually?
3. How would the total interest paid differ if the payments were larger?
4. Can the loan be paid off earlier if extra payments are made?
5. How does the final repayment $X$ change with different interest rates?

Tip: For loans with interest, earlier payments reduce the overall interest accrued significantly.