: Y bought a TV costing 13,000 by making a down payment of ₹3000 and agreeing to make equal annual payment for four years. How much would be each payment if the interest on unpaid amount be 14% compounded annually?

To determine the amount of each annual payment, we need to use the concept of a loan amortization with compound interest. Here's the step-by-step process:

### Step 1: Calculate the Principal Amount Financed
The cost of the TV is ₹13,000. After making a down payment of ₹3,000, the remaining amount (which will be financed through the loan) is:
\[
\text{Principal} = ₹13,000 - ₹3,000 = ₹10,000
\]

### Step 2: Use the Loan Amortization Formula
Since the payments are to be made annually over 4 years with an interest rate of 14% compounded annually, the annual payment \( A \) can be calculated using the formula:
\[
A = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]
where:
- \( P \) is the principal amount (₹10,000),
- \( r \) is the annual interest rate (14% or 0.14),
- \( n \) is the number of years (4 years).

### Step 3: Plug in the Values
\[
A = \frac{10,000 \times 0.14 \times (1 + 0.14)^4}{(1 + 0.14)^4 - 1}
\]

Let's compute the values step by step:

1. Compute \( (1 + r)^n \):
   \[
   (1 + 0.14)^4 = 1.14^4 \approx 1.6895
   \]

2. Multiply by the interest rate and principal:
   \[
   10,000 \times 0.14 \times 1.6895 = 2365.3
   \]

3. Compute the denominator:
   \[
   1.6895 - 1 = 0.6895
   \]

4. Calculate the annual payment:
   \[
   A = \frac{2365.3}{0.6895} \approx 3431.66
   \]

### Final Answer
The amount of each annual payment would be approximately ₹3,431.66.

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Do you have any questions or need further details? Here are some related questions that might interest you:

1. How would the annual payment change if the interest rate were 10% instead of 14%?
2. What would be the total amount paid over the four years?
3. How much of the total payment would go toward interest?
4. How does compound interest affect the payment compared to simple interest?
5. What is the formula to calculate the outstanding balance after each payment?

**Tip:** Always double-check the compounding period (annual, semi-annual, etc.) when working with interest rates, as it can significantly affect the total payment.

Learn how to calculate annual payments for a TV purchase costing ₹13,000 with a down payment of ₹3,000. The payments are spread over four years at a 14% annual compound interest rate. Get a detailed step-by-step solution using the loan amortization formula. Suitable for advanced high school students.

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