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The problem in the image describes a situation where Subesh purchases a refrigerator on terms that involve paying Rs. 1,500 as a cash down payment, followed by Rs. 1,020 at the end of the first year, Rs. 1,013 at the end of the second year, and Rs. 980 at the end of the third year. The interest is charged at the rate of 10% per annum, and we are tasked with calculating the cost price of the refrigerator.

Let's solve the problem step-by-step.

### Step 1: Identify the key details
- **Down payment**: Rs. 1,500
- **Payments** after each year:
  - Year 1: Rs. 1,020
  - Year 2: Rs. 1,013
  - Year 3: Rs. 980
- **Interest rate**: 10% per annum

### Step 2: Present value calculation
The total cost of the refrigerator is the sum of the present value (PV) of all the payments, discounted at the interest rate of 10% per annum.

The formula to calculate the present value is:
\[
PV = \frac{C}{(1 + r)^t}
\]
Where:
- \( C \) is the payment amount,
- \( r \) is the interest rate (10% = 0.10),
- \( t \) is the time period in years.

Now we will compute the present value of each of the three payments, discounted back to the time of purchase.

### Step 3: Calculate the present value of payments
1. **Down payment (no discount needed)**: Rs. 1,500.
2. **First payment after one year**:
   \[
   PV = \frac{1020}{(1 + 0.10)^1} = \frac{1020}{1.10} = 927.27
   \]
3. **Second payment after two years**:
   \[
   PV = \frac{1013}{(1 + 0.10)^2} = \frac{1013}{1.21} = 837.19
   \]
4. **Third payment after three years**:
   \[
   PV = \frac{980}{(1 + 0.10)^3} = \frac{980}{1.331} = 736.42
   \]

### Step 4: Add up the present values
The total cost price of the refrigerator is:
\[
\text{Cost Price} = 1,500 + 927.27 + 837.19 + 736.42 = 4,000.88
\]

Rounding off, the cost price of the refrigerator is approximately **Rs. 4,000**, which corresponds to option **(a) Rs. 4,000**.

Would you like further details or have any questions about the steps? 

### Related Questions:
1. How would the cost price change if the interest rate was 12% instead of 10%?
2. What if the payments were made semi-annually instead of annually?
3. How would the cost price be affected if there were no down payment?
4. What would the present value of the third payment be if it were made in the fourth year?
5. How would inflation impact the value of these payments over time?

### Tip:
When solving problems with payments over time, always discount future payments to the present value using the appropriate interest rate!

Subesh purchased a refrigerator on the terms that he is required to pay Rs. 1,500 as cash down payment followed by Rs. 1,020 at the end of first year, Rs. 1,013 at the end of second year, and Rs. 980 at the end of third year. Interest is charged at the rate of 10% per annum. Calculate the cost price of the refrigerator.

Learn how to calculate the cost price of a refrigerator based on future payments with a 10% interest rate. The problem includes calculating the present value of each payment and summing them to determine the total cost. Suitable for students in Grades 10-12.

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