Principal ₹ 12000 amounts to ₹ 20736 in 3 years at `R%` p.a. of compound interest. Find the value of `R`?

Options

A. `10%`
B. `25%`
C. `12%`
D. `20%`

Answer

To find the value of `R` in the given problem, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = ₹12,000
- Amount (A) = ₹20,736
- Time (t) = 3 years

2. **Use the formula for compound interest:**
The formula for the amount in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^t \]
Plugging in the values we have:
\[ 20736 = 12000 \left(1 + \frac{R}{100}\right)^3 \]

3. **Rearranging the equation:**
Divide both sides by 12000:
\[ \frac{20736}{12000} = \left(1 + \frac{R}{100}\right)^3 \]

4. **Calculate the left side:**
\[ \frac{20736}{12000} = 1.728 \]
So, we have:
\[ 1.728 = \left(1 + \frac{R}{100}\right)^3 \]

5. **Taking the cube root:**
To eliminate the exponent, take the cube root of both sides:
\[ 1 + \frac{R}{100} = \sqrt[3]{1.728} \]

6. **Calculate the cube root:**
The cube root of 1.728 is 1.2:
\[ 1 + \frac{R}{100} = 1.2 \]

7. **Isolate R:**
Subtract 1 from both sides:
\[ \frac{R}{100} = 1.2 - 1 = 0.2 \]

8. **Multiply by 100 to find R:**
\[ R = 0.2 \times 100 = 20 \]

9. **Conclusion:**
The value of `R` is 20%.

### Final Answer:
The value of `R` is **20% per annum**.

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