The simple interest accrued on an amount of ₹16,500 at the end of three years is ₹5,940. What would be the compound interest accrued on the same amount at the same rate in the same period ? (rounded off to two digits after decimals)

Options

A. `₹6681.31`
B. ₹`6218.27`
C. ₹`6754.82`
D. ₹`6537.47`

Explanation

To find the compound interest accrued on an amount of ₹16,500 at the same rate and for the same period as the simple interest, we can follow these steps:

### Step 1: Calculate the Rate of Interest
We know the formula for Simple Interest (SI):
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (₹16,500)
- \( R \) = Rate of interest (unknown)
- \( T \) = Time period (3 years)
- \( \text{SI} \) = Simple Interest (₹5,940)

Rearranging the formula to find \( R \):
\[ R = \frac{\text{SI} \times 100}{P \times T} \]

Substituting the known values:
\[ R = \frac{5940 \times 100}{16500 \times 3} \]

Calculating:
\[ R = \frac{594000}{49500} = 12\% \]

### Step 2: Calculate Compound Interest
Now, we will use the formula for Compound Interest (CI):
\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \]
Where:
- \( P = 16,500 \)
- \( R = 12\% \)
- \( T = 3 \)

Substituting the values into the formula:
\[ \text{CI} = 16500 \left(1 + \frac{12}{100}\right)^3 - 16500 \]

Calculating:
\[ \text{CI} = 16500 \left(1 + 0.12\right)^3 - 16500 \]
\[ \text{CI} = 16500 \left(1.12\right)^3 - 16500 \]

Calculating \( (1.12)^3 \):
\[ (1.12)^3 = 1.404928 \]

Now substituting back:
\[ \text{CI} = 16500 \times 1.404928 - 16500 \]
\[ \text{CI} = 23208.24 - 16500 \]
\[ \text{CI} = 6708.24 \]

### Step 3: Round Off to Two Decimal Places
The final compound interest rounded off to two decimal places is:
\[ \text{CI} = ₹6708.24 \]

### Summary
The compound interest accrued on the amount of ₹16,500 at the same rate and for the same period is **₹6708.24**.

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