A sonata watch is sold for ₹ 440 cash or for ₹ 200 cash down payment together with ₹ 244 to be paid after one month. Find the rate of interest charged in the instalment scheme :

Options

A. `10%`
B. `15%`
C. `20%`
D. `25%`

Answer

To find the rate of interest charged in the instalment scheme for the Sonata watch, we can follow these steps:

### Step 1: Identify the cash price and the instalment payment details.
- Cash price of the watch = ₹440
- Down payment = ₹200
- Amount to be paid after one month = ₹244

### Step 2: Calculate the remaining amount after the down payment.
- Remaining amount = Total price - Down payment
- Remaining amount = ₹440 - ₹200 = ₹240

### Step 3: Determine the interest charged.
- Amount to be paid after one month = ₹244
- Interest charged = Amount to be paid after one month - Remaining amount
- Interest charged = ₹244 - ₹240 = ₹4

### Step 4: Calculate the rate of interest.
- The formula for calculating the rate of interest is:
\[ \text{Rate of Interest (R)} = \left( \frac{\text{Interest}}{\text{Principal}} \times 100 \right) \]
- Here, the principal is the remaining amount (₹240) and the interest is ₹4.
- Plugging in the values:
\[ R = \left( \frac{4}{240} \times 100 \right) \]

### Step 5: Simplify the calculation.
- Calculate \( \frac{4}{240} \):
\[ \frac{4}{240} = \frac{1}{60} \]
- Now, multiply by 100 to find the percentage:
\[ R = \left( \frac{1}{60} \times 100 \right) = \frac{100}{60} \approx 1.67\% \]

### Step 6: Calculate the monthly interest rate.
Since the payment is made after one month, we can consider this as a monthly interest rate. To find the annual interest rate, we multiply the monthly rate by 12:
- Annual interest rate = \( 1.67\% \times 12 \approx 20\% \)

### Conclusion:
The rate of interest charged in the instalment scheme is approximately **20%**.

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