If a sum of Rs.9,00,000 is lent to be paid back in 10 equal monthly instalments of Rs. 1,00,000 each, then the rate of interest is?

Options

A. 11.33
B. 11
C. 266.67
D. 26.67

Answer

To find the rate of interest for a loan of Rs. 9,00,000 paid back in 10 equal monthly installments of Rs. 1,00,000 each, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 9,00,000
- Monthly installment (A) = Rs. 1,00,000
- Total number of installments (n) = 10 months

### Step 2: Calculate the total amount paid back
The total amount paid back over 10 months is:
\[ \text{Total Amount} = \text{Monthly Installment} \times \text{Number of Installments} \]
\[ \text{Total Amount} = 1,00,000 \times 10 = Rs. 10,00,000 \]

### Step 3: Calculate the total interest paid
The total interest paid can be calculated as:
\[ \text{Total Interest} = \text{Total Amount Paid} - \text{Principal} \]
\[ \text{Total Interest} = 10,00,000 - 9,00,000 = Rs. 1,00,000 \]

### Step 4: Calculate the simple interest for the loan
The formula for simple interest is:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

Since the installments are monthly, we need to convert the time into years. For 10 months:
\[ T = \frac{10}{12} \text{ years} \]

### Step 5: Set up the equation
Using the simple interest formula:
\[ 1,00,000 = \frac{9,00,000 \times R \times \frac{10}{12}}{100} \]

### Step 6: Simplify the equation
Rearranging the equation:
\[ 1,00,000 = \frac{9,00,000 \times R \times 10}{1200} \]
\[ 1,00,000 = \frac{9,00,000 \times R}{120} \]
Multiplying both sides by 120:
\[ 1,00,000 \times 120 = 9,00,000 \times R \]
\[ 12,000,000 = 9,00,000 \times R \]

### Step 7: Solve for R
Dividing both sides by 9,00,000:
\[ R = \frac{12,000,000}{9,00,000} \]
\[ R = \frac{120}{9} \]
\[ R = 13.33\% \]

### Step 8: Final calculation for monthly interest rate
Since we need to find the effective monthly interest rate, we can convert this to a monthly rate:
\[ \text{Monthly Rate} = \frac{R}{12} = \frac{13.33}{12} \approx 1.11\% \]

### Conclusion
Thus, the rate of interest is approximately:
\[ \text{Rate of Interest} \approx 13.33\% \]

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