The simple interest accrued on an amount of Rs. 14,800 at the end of three years is Rs. 6,216. What would be the compound interest accrued on the same amount at the same rate in the same period?

Options

A. Rs. `6,986cdot1142`
B. Rs. `7,042cdot2014`
C. Rs. `7,126cdot8512`
D. Rs.`8,321cdot4166`

Answer

To find the compound interest accrued on an amount of Rs. 14,800 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):
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest (Rs. 6,216)
- \(P\) = Principal amount (Rs. 14,800)
- \(R\) = Rate of interest (unknown)
- \(T\) = Time (3 years)

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

Substituting the known values:
\[ R = \frac{6216 \times 100}{14800 \times 3} \]

Calculating:
\[ R = \frac{621600}{44400} = 14 \]
So, the rate of interest \(R\) is 14%.

### Step 2: Calculate the Compound Interest
The formula for Compound Interest (CI) is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]

Substituting the known values:
\[ CI = 14800 \left(1 + \frac{14}{100}\right)^3 - 14800 \]

Calculating:
\[ CI = 14800 \left(1.14\right)^3 - 14800 \]

Calculating \(1.14^3\):
\[ 1.14^3 = 1.14 \times 1.14 \times 1.14 \approx 1.481544 \]

Now substituting back:
\[ CI = 14800 \times 1.481544 - 14800 \]
\[ CI \approx 21999.9992 - 14800 \]
\[ CI \approx 7199.9992 \approx 7200 \]

Thus, the compound interest accrued on the amount is approximately Rs. 7,200.

### Final Answer:
The compound interest accrued on Rs. 14,800 at the same rate over 3 years is Rs. 7,200.

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