SBI lent Rs. 1331 lakh to the TATA group at compound interest and got Rs. 1728 lakh after 3 yr. What is the rate of interest charged, if compounded annually ?

Options

A. 0.11
B. 0.0909
C. 0.12
D. 0.0833

Answer

To find the rate of interest charged by SBI to the TATA group when compounded annually, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Data:**
- Principal (P) = Rs. 1331 lakhs
- Amount (A) after 3 years = Rs. 1728 lakhs
- Time (T) = 3 years

2. **Use the Compound Interest Formula:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^T \]
where:
- \(A\) = Amount after time \(T\)
- \(P\) = Principal amount
- \(r\) = Rate of interest per annum
- \(T\) = Time in years

3. **Substitute the Known Values:**
Substituting the known values into the formula:
\[ 1728 = 1331 \left(1 + \frac{r}{100}\right)^3 \]

4. **Divide Both Sides by the Principal:**
\[ \frac{1728}{1331} = \left(1 + \frac{r}{100}\right)^3 \]

5. **Calculate the Left Side:**
Calculate the ratio:
\[ \frac{1728}{1331} \approx 1.298 \]

6. **Take the Cube Root of Both Sides:**
\[ 1 + \frac{r}{100} = \sqrt[3]{1.298} \]

7. **Calculate the Cube Root:**
Using a calculator or estimation, we find:
\[ \sqrt[3]{1.298} \approx 1.1 \]

8. **Isolate the Rate of Interest:**
\[ \frac{r}{100} = 1.1 - 1 = 0.1 \]

9. **Convert to Percentage:**
\[ r = 0.1 \times 100 = 10\% \]

### Final Result
The rate of interest charged is approximately **10%**.