The compound interest accrued on an amount of Rs. 22,000 at the end of two years is Rs. 5,596.8. What would be the sim ple interest accrued on the same amount at the same rate in the same period ?

Options

A. Rs.5,420
B. Rs.5,360
C. Rs.5,280
D. Rs.5,140

Answer

To find the simple interest accrued on an amount of Rs. 22,000 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. 22,000
- Compound Interest (C.I.) = Rs. 5,596.8
- Time (T) = 2 years

**Hint:** Always start by writing down the values provided in the question clearly.

### Step 2: Calculate the rate of interest (R)
We know that the formula for Compound Interest (C.I.) for 2 years is:
\[ C.I. = P \times \left( \frac{R}{100} \right) + P \times \left( \frac{R}{100} \right)^2 \]

Since we have the C.I. for 2 years, we can also use the formula:
\[ C.I. = P \times \left( \frac{R}{100} \right) \times 2 + P \times \left( \frac{R}{100} \right)^2 \]

Rearranging gives us:
\[ C.I. = P \times \left( \frac{R}{100} \right) \times (2 + \frac{R}{100}) \]

Substituting the known values:
\[ 5596.8 = 22000 \times \left( \frac{R}{100} \right) \times (2 + \frac{R}{100}) \]

**Hint:** Use the formula for compound interest to express the interest in terms of the principal and rate.

### Step 3: Solve for R
To simplify, we can assume \( \frac{R}{100} = r \):
\[ 5596.8 = 22000 \times r \times (2 + r) \]

This is a quadratic equation in terms of r. We can solve for r using numerical methods or by estimating values.

After solving, we find:
\[ R = 12\% \]

**Hint:** If you find it difficult to solve the quadratic equation, consider estimating values for R and checking which fits.

### Step 4: Calculate Simple Interest (S.I.)
The formula for Simple Interest is:
\[ S.I. = \frac{P \times R \times T}{100} \]

Substituting the values we have:
\[ S.I. = \frac{22000 \times 12 \times 2}{100} \]

Calculating this gives:
\[ S.I. = \frac{22000 \times 24}{100} = 5280 \]

**Hint:** Remember to convert the percentage into a decimal when calculating the interest.

### Final Answer:
The simple interest accrued on the same amount at the same rate in the same period is Rs. 5,280.

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