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

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 (A) after 3 years using the compound interest formula
The formula for compound interest is:
\[ A = P + CI \]
Substituting the known values:
\[ A = 25,500 + 8,440.50 \]
\[ A = 33,940.50 \]

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

### Step 4: Solve for \( \left(1 + \frac{R}{100}\right)^3 \)
First, divide both sides by 25,500:
\[ \frac{33,940.50}{25,500} = \left(1 + \frac{R}{100}\right)^3 \]
Calculating the left side:
\[ 1.333333 \approx \left(1 + \frac{R}{100}\right)^3 \]

### Step 5: Take the cube root of both sides
To find \( 1 + \frac{R}{100} \):
\[ 1 + \frac{R}{100} = \sqrt[3]{1.333333} \]
Calculating the cube root:
\[ 1 + \frac{R}{100} \approx 1.1 \]

### Step 6: Isolate R
Subtract 1 from both sides:
\[ \frac{R}{100} \approx 0.1 \]
Multiply by 100 to find R:
\[ R \approx 10\% \]

### Step 7: Calculate the simple interest (SI)
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{25,500 \times 10 \times 3}{100} \]
Calculating:
\[ SI = \frac{765,000}{100} = 7,650 \]

### 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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