The compound interest accrued on an amount of 25500 at the end of 3year is 8440.50. What would be the simple interest accrued on the same amount at the same rate in the same period?

Options

A. 4650
B. 5650
C. 6650
D. 7650

Answer

To find the simple interest accrued on an amount of Rs 25,500 at the same rate and for the same period as the compound interest, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 25,500
- Compound Interest (CI) = Rs 8,440.50
- Time (T) = 3 years

### Step 2: Calculate the total amount after 3 years using compound interest
The total amount (A) after 3 years can be calculated as:
\[ A = P + CI \]
Substituting the values:
\[ A = 25,500 + 8,440.50 = 33,940.50 \]

### Step 3: Use the formula for compound interest to find the rate of interest
The formula for the amount in compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^T \]
Substituting the known values:
\[ 33,940.50 = 25,500 \left(1 + \frac{r}{100}\right)^3 \]

### Step 4: Solve for \( \left(1 + \frac{r}{100}\right)^3 \)
Rearranging the equation:
\[ \left(1 + \frac{r}{100}\right)^3 = \frac{33,940.50}{25,500} \]
Calculating the right side:
\[ \left(1 + \frac{r}{100}\right)^3 = 1.3333 \]

### Step 5: Take the cube root to find \( 1 + \frac{r}{100} \)
Taking the cube root:
\[ 1 + \frac{r}{100} = \sqrt[3]{1.3333} \]
Calculating the cube root:
\[ 1 + \frac{r}{100} \approx 1.100 \]

### Step 6: Solve for \( r \)
Subtract 1 from both sides:
\[ \frac{r}{100} \approx 0.100 \]
Multiplying by 100 gives:
\[ r \approx 10\% \]

### Step 7: Calculate the simple interest
The formula for simple interest (SI) is:
\[ SI = \frac{P \times r \times T}{100} \]
Substituting the values:
\[ SI = \frac{25,500 \times 10 \times 3}{100} \]
Calculating:
\[ SI = \frac{765000}{100} = 7650 \]

### Final Answer
The simple interest accrued on the same amount at the same rate in the same period is Rs 7,650.

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