A loan of Rs 305 was taken at a certain rate per annum of compound interest, for 3 years. After three years the amount repaid was Rs 670, calculate the rate of compound Interest.
A. 30%
B. 35%
C. 33%
D. 25%

Options

A. C
B. B
C. A
D. D

Answer

To solve the problem of finding the rate of compound interest for a loan of Rs 305 that amounts to Rs 670 after 3 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = Rs 305
- Amount (A) = Rs 670
- Time (T) = 3 years
- Rate (R) = ?

2. **Use the Compound Interest Formula:**
The formula for the amount in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the known values into the formula:
\[ 670 = 305 \left(1 + \frac{R}{100}\right)^3 \]

3. **Rearranging the Equation:**
To isolate the term with R, divide both sides by 305:
\[ \frac{670}{305} = \left(1 + \frac{R}{100}\right)^3 \]

4. **Calculate the Left Side:**
Calculate \( \frac{670}{305} \):
\[ \frac{670}{305} \approx 2.1967 \]

5. **Take the Cube Root:**
Now, take the cube root of both sides to solve for \( 1 + \frac{R}{100} \):
\[ 1 + \frac{R}{100} = \sqrt[3]{2.1967} \]
Using a calculator, we find:
\[ \sqrt[3]{2.1967} \approx 1.3 \]

6. **Isolate R:**
Now, subtract 1 from both sides:
\[ \frac{R}{100} = 1.3 - 1 = 0.3 \]

7. **Calculate R:**
Multiply by 100 to find R:
\[ R = 0.3 \times 100 = 30 \]

8. **Conclusion:**
The rate of compound interest is:
\[ R = 30\% \]

### Final Answer:
The correct answer is **A. 30%**.

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