An old article is available for Rs 12,000 at cash payment or is available for Rs 7000 cash payment and a monthly instalment of Rs 630 for 8 months. The rate percent per annum is

Options

A. 2.15 per cent
B. 3 per cent
C. 3.25 per cent
D. 3.3 per cent

Answer

To find the rate percent per annum for the given question, we can follow these steps:

### Step 1: Identify the components
- Cash price of the article (C) = Rs 12,000
- Cash payment option = Rs 7,000
- Monthly installment = Rs 630
- Number of installments (n) = 8 months

### Step 2: Calculate the remaining amount to be financed
The remaining amount after the cash payment is:
\[ \text{Remaining Amount} = \text{Cash Price} - \text{Cash Payment} = 12,000 - 7,000 = 5,000 \]

### Step 3: Calculate the total amount paid through installments
The total amount paid through installments is:
\[ \text{Total Installment Payment} = \text{Monthly Installment} \times \text{Number of Installments} = 630 \times 8 = 5,040 \]

### Step 4: Calculate the total amount paid for the article
The total amount paid for the article (including cash payment and installment payments) is:
\[ \text{Total Amount Paid} = \text{Cash Payment} + \text{Total Installment Payment} = 7,000 + 5,040 = 12,040 \]

### Step 5: Calculate the interest paid
The interest paid can be calculated as:
\[ \text{Interest} = \text{Total Amount Paid} - \text{Remaining Amount} = 12,040 - 7,000 = 5,040 \]

### Step 6: Use the formula for calculating the rate of interest
The formula for calculating the rate of interest (R) based on the principal (P), interest (I), and time (T) is:
\[ R = \frac{I \times 100}{P \times T} \]
Where:
- \( I \) = Interest paid = 5,040
- \( P \) = Principal amount (Remaining Amount) = 5,000
- \( T \) = Time in years = \( \frac{8}{12} = \frac{2}{3} \) years

### Step 7: Substitute the values into the formula
Substituting the values into the formula:
\[ R = \frac{5,040 \times 100}{5,000 \times \frac{2}{3}} \]

### Step 8: Simplify the equation
Calculate the denominator:
\[ 5,000 \times \frac{2}{3} = \frac{10,000}{3} \]
Now, substitute this back into the equation:
\[ R = \frac{5,040 \times 100 \times 3}{10,000} \]

### Step 9: Calculate R
Calculating \( R \):
\[ R = \frac{15,120,000}{10,000} = 1,512 \]

### Step 10: Finalize the rate of interest
Finally, converting this to a percentage:
\[ R = 1,512 \text{ per annum} \]

### Final Answer
The rate percent per annum is approximately **2.15%**.

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