Calculate the sum of money on which the compound interest (payable annually) for 2 years be four times the simple interest on Rs 4,715 for 5 years, both at the rate of 5 per cent per annum.

Answer

To solve the problem step by step, we need to calculate the sum of money on which the compound interest (CI) for 2 years is four times the simple interest (SI) on Rs 4,715 for 5 years at the rate of 5% per annum.

### Step 1: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \(P = 4715\) (Principal amount)
- \(R = 5\%\) (Rate of interest)
- \(T = 5\) (Time in years)

Substituting the values into the formula:
\[ SI = \frac{4715 \times 5 \times 5}{100} \]

### Step 2: Simplify the SI Calculation
Calculating the multiplication:
\[ SI = \frac{4715 \times 25}{100} \]
\[ SI = \frac{117875}{100} = 1178.75 \]

### Step 3: Calculate Compound Interest (CI)
According to the problem, the compound interest for 2 years is four times the simple interest calculated above:
\[ CI = 4 \times SI = 4 \times 1178.75 = 4715 \]

### Step 4: Use the Compound Interest Formula
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Rearranging gives:
\[ CI + P = P \left(1 + \frac{R}{100}\right)^T \]

Substituting \(CI = 4715\), \(R = 5\%\), and \(T = 2\):
\[ 4715 + P = P \left(1 + \frac{5}{100}\right)^2 \]
\[ 4715 + P = P \left(1.05\right)^2 \]
\[ 4715 + P = P \times 1.1025 \]

### Step 5: Rearranging the Equation
Rearranging gives:
\[ 4715 = P \times 1.1025 - P \]
\[ 4715 = P(1.1025 - 1) \]
\[ 4715 = P \times 0.1025 \]

### Step 6: Solve for Principal (P)
Now, solving for \(P\):
\[ P = \frac{4715}{0.1025} \]
Calculating this gives:
\[ P = 46000 \]

### Final Answer
The sum of money on which the compound interest for 2 years is four times the simple interest on Rs 4,715 for 5 years at the rate of 5% per annum is **Rs 46,000**.

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