On what sum of money will compound interest (payable annually) for 2 years be the same as simple interest on Rs 9,430 for 10 years, both at the rate of 5 percent per annum ?

Answer

To solve the problem step by step, we will first calculate the simple interest on Rs 9,430 for 10 years at a rate of 5% per annum, and then we will find the sum of money (let's call it \( x \)) for which the compound interest for 2 years at the same rate equals the simple interest calculated.

### Step 1: Calculate Simple Interest (SI)

The formula for Simple Interest is:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( P = 9430 \) (Principal)
- \( R = 5 \) (Rate of interest)
- \( T = 10 \) (Time in years)

Substituting the values:

\[ SI = \frac{9430 \times 5 \times 10}{100} \]

Calculating:

\[ SI = \frac{9430 \times 50}{100} = \frac{471500}{100} = 4715 \]

### Step 2: Set up the Compound Interest (CI) Formula

The formula for Compound Interest is:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Where:
- \( A \) is the amount after time \( T \)
- \( P \) is the principal amount (which we will denote as \( x \))
- \( R = 5 \) (Rate of interest)
- \( T = 2 \) (Time in years)

Substituting the values:

\[ A = x \left(1 + \frac{5}{100}\right)^2 \]

This simplifies to:

\[ A = x \left(1 + 0.05\right)^2 = x \left(1.05\right)^2 \]

Calculating \( (1.05)^2 \):

\[ (1.05)^2 = 1.1025 \]

Thus,

\[ A = x \times 1.1025 \]

### Step 3: Calculate Compound Interest (CI)

The Compound Interest is given by:

\[ CI = A - P \]

Substituting \( A \) and \( P \):

\[ CI = (x \times 1.1025) - x = x(1.1025 - 1) = x \times 0.1025 \]

### Step 4: Set up the Equation

We know from the problem statement that the Compound Interest for 2 years should equal the Simple Interest calculated in Step 1. Therefore, we can set up the equation:

\[ x \times 0.1025 = 4715 \]

### Step 5: Solve for \( x \)

To find \( x \), we rearrange the equation:

\[ x = \frac{4715}{0.1025} \]

Calculating \( x \):

\[ x = 46000 \]

### Final Answer

The sum of money on which the compound interest for 2 years will be the same as the simple interest on Rs 9,430 for 10 years at the rate of 5% per annum is:

\[ \boxed{46000} \]