The market price of refrigerator is Rs 10,000. It is available on a cash down payment of 2000 and 9 monthly installment of 1000 each. Find the rate of installment.

Options

A. a)`30(1)/(3)%`
B. b)`32(1)/(3)%`
C. c)`30(2)/(3)%`
D. d)`33(1)/(3)%`

Answer

To solve the problem step by step, we need to find the rate of interest for the refrigerator installment plan.

### Step 1: Identify the total cost and down payment
The market price of the refrigerator is Rs 10,000. The cash down payment is Rs 2,000.

**Hint:** Start by determining how much money is left to be paid after the down payment.

### Step 2: Calculate the remaining amount to be financed
Remaining amount after down payment = Total price - Down payment
= 10,000 - 2,000 = Rs 8,000.

**Hint:** This remaining amount is what you will pay through installments.

### Step 3: Calculate the total amount paid through installments
You will pay 9 monthly installments of Rs 1,000 each.
Total installments = 9 * 1,000 = Rs 9,000.

**Hint:** This total amount includes both the principal and the interest.

### Step 4: Calculate the total interest paid
Total interest paid = Total installments - Remaining amount
= 9,000 - 8,000 = Rs 1,000.

**Hint:** This interest is what you need to analyze to find the rate.

### Step 5: Calculate the equivalent principal for each month
The principal amount decreases each month as you pay the installments. The principal for each month is:
- Month 1: 8,000
- Month 2: 7,000
- Month 3: 6,000
- Month 4: 5,000
- Month 5: 4,000
- Month 6: 3,000
- Month 7: 2,000
- Month 8: 1,000
- Month 9: 0

**Hint:** You can find the average principal over the months to simplify calculations.

### Step 6: Calculate the total equivalent principal over 9 months
Total equivalent principal = 8,000 + 7,000 + 6,000 + 5,000 + 4,000 + 3,000 + 2,000 + 1,000 + 0 = Rs 36,000.

**Hint:** This total is used to determine the interest rate.

### Step 7: Set up the equation for interest
Using the formula for simple interest:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

Here, the total interest is Rs 1,000, the total principal is Rs 36,000, and the time is 9 months (which is 9/12 years).

**Hint:** Rearranging the formula will help you isolate the rate.

### Step 8: Solve for the rate
Using the formula:
\[ 1,000 = 36,000 \times \text{Rate} \times \frac{9}{12} \]

Rearranging gives:
\[ \text{Rate} = \frac{1,000 \times 12}{36,000 \times 9} \]

Calculating this:
\[ \text{Rate} = \frac{12,000}{324,000} = \frac{1}{27} \]

To convert this into a percentage:
\[ \text{Rate} = \frac{1}{27} \times 100 \approx 3.70\% \]

**Hint:** Remember to convert your final answer into a percentage for clarity.

### Final Answer
The rate of installment is approximately **3.70% per month**.