A man gets a simple interest of Rs. 2500 on a certain principal at the rate of 10% per annum in 5 years . What compound interest will the man get on twice the principal in two years at the same rate?

Options

A. Rs. 1500
B. Rs. 2100
C. Rs. 1750
D. Rs. 1350

Answer

To solve the problem step by step, we will first find the principal amount using the given simple interest, and then we will calculate the compound interest on twice that principal amount.

### Step 1: Find the Principal Amount

We know the formula for Simple Interest (SI):

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

Where:
- \( SI \) = Simple Interest (Rs. 2500)
- \( P \) = Principal amount (unknown)
- \( R \) = Rate of interest (10%)
- \( T \) = Time (5 years)

Substituting the known values into the formula:

\[ 2500 = \frac{P \times 10 \times 5}{100} \]

### Step 2: Simplify the Equation

First, simplify the right side:

\[ 2500 = \frac{50P}{100} \]

This simplifies to:

\[ 2500 = \frac{P}{2} \]

### Step 3: Solve for Principal (P)

To find \( P \), multiply both sides by 2:

\[ P = 2500 \times 2 = 5000 \]

So, the principal amount is Rs. 5000.

### Step 4: Calculate Compound Interest on Twice the Principal

Now, we need to find the compound interest on twice the principal amount, which is:

\[ 2P = 2 \times 5000 = 10000 \]

Using the compound interest formula:

\[ CI = P \left(1 + \frac{R}{100}\right)^n - P \]

Where:
- \( P = 10000 \)
- \( R = 10\% \)
- \( n = 2 \) years

### Step 5: Substitute Values into the Compound Interest Formula

Substituting the values into the formula:

\[ CI = 10000 \left(1 + \frac{10}{100}\right)^2 - 10000 \]

This simplifies to:

\[ CI = 10000 \left(1 + 0.1\right)^2 - 10000 \]

\[ CI = 10000 \left(1.1\right)^2 - 10000 \]

### Step 6: Calculate \( (1.1)^2 \)

Calculating \( (1.1)^2 \):

\[ (1.1)^2 = 1.21 \]

### Step 7: Substitute Back to Find CI

Now substitute back into the equation:

\[ CI = 10000 \times 1.21 - 10000 \]

\[ CI = 12100 - 10000 \]

\[ CI = 2100 \]

### Final Answer

The compound interest on twice the principal in two years at the same rate is Rs. 2100.

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