A debt of Rs1,00,000, which is due 5 years from now, is instead to be paid off by three payments:  ₹. 20,000 now,  ₹. 30,000 in 3 years and a final payment at the end of 6 years. If the interest rate 10% compounded annually, how much is the final payment?

Select one:
₹. 35,398.87
₹. 34,638.78
₹. 34,653.72
 ₹. 35,325.47

To find the final payment that needs to be made, we need to calculate the future value of each of the payments considering the given interest rate and then determine what the final payment should be so that the total debt is paid off.

### Given:
- Original debt: ₹ 1,00,000 due 5 years from now.
- Payments: ₹ 20,000 now, ₹ 30,000 in 3 years, and a final payment at the end of 6 years.
- Interest rate: 10% compounded annually.

### Steps to Solve:

1. **Future Value of the Debt:**
   Since the debt is due in 5 years, we calculate what the debt will grow to at the end of 6 years (one year after the original due date).

   \[
   FV_{\text{debt}} = 1,00,000 \times (1 + 0.10)^{6-5}
   \]

2. **Future Value of Payments:**
   We calculate the future value of each payment at the end of 6 years.

   - **Payment Now:** ₹ 20,000 (growing for 6 years)
     \[
     FV_1 = 20,000 \times (1 + 0.10)^6
     \]

   - **Payment in 3 Years:** ₹ 30,000 (growing for 3 years)
     \[
     FV_2 = 30,000 \times (1 + 0.10)^{6-3}
     \]

3. **Final Payment Required:**
   The final payment at the end of 6 years is calculated by subtracting the future values of the first two payments from the future value of the debt.

   \[
   \text{Final Payment} = FV_{\text{debt}} - (FV_1 + FV_2)
   \]

Let's calculate the final payment.The final payment required to settle the debt at the end of 6 years is approximately **₹ 34,638.78**.

Therefore, the correct answer is:

**₹ 34,638.78**

Do you have any further questions or would you like additional details?

Here are some related questions you might find useful:

1. What is the difference between simple and compound interest?
2. How does the timing of payments affect the total interest paid?
3. What if the payments were made with a different frequency, like monthly or semi-annually?
4. How does changing the interest rate impact the final payment?
5. What happens if no payments are made until the due date?

**Tip:** When making payments over time, understanding how interest accrues on both the remaining debt and payments already made can help in planning more cost-effective repayment strategies.

Explore how to calculate the final payment required to settle a debt using compound interest. This problem involves a debt of ₹ 1,00,000 due in 5 years, with payments of ₹ 20,000 now, ₹ 30,000 in 3 years, and the final payment at the end of 6 years, compounded annually at 10%. Learn step-by-step with detailed formulas and solutions.

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