A certain sum amounts to Rs 29,282 in 4 years at 10% p.a. when the interest is compounded yearly. What is the simple interest (in Rs ) on the same sum for 5 years at the same rate?

Options

A. 10000
B. 11500
C. 7000
D. 9000

Answer

To solve the problem step by step, we need to find the principal amount first using the compound interest formula, and then calculate the simple interest for 5 years.

### Step 1: Use the Compound Interest Formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \(A\) = Amount after time \(T\)
- \(P\) = Principal amount (initial sum)
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

Given:
- \(A = 29,282\)
- \(R = 10\%\)
- \(T = 4\)

Substituting the values into the formula:
\[ 29,282 = P \left(1 + \frac{10}{100}\right)^4 \]
\[ 29,282 = P \left(1.1\right)^4 \]

### Step 2: Calculate \( (1.1)^4 \)
Calculating \( (1.1)^4 \):
\[ (1.1)^4 = 1.4641 \]

### Step 3: Solve for Principal \(P\)
Now we can rearrange the equation to find \(P\):
\[ P = \frac{29,282}{1.4641} \]
Calculating the value:
\[ P \approx 20,000 \]

### Step 4: Calculate Simple Interest
Now that we have the principal amount, we can calculate the simple interest for 5 years using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P = 20,000\)
- \(R = 10\%\)
- \(T = 5\)

Substituting the values:
\[ SI = \frac{20,000 \times 10 \times 5}{100} \]
\[ SI = \frac{1,000,000}{100} = 10,000 \]

### Final Answer
The simple interest on the same sum for 5 years at the same rate is Rs 10,000.

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