The interest earned on an amount after 2 yrs at 10 % per annum compounded yearly is Rs 672. Find the interest earned on same amount after 4 yr at 14 % per annum at simple interest?

Options

A. Rs 1792
B. Rs 1864
C. Rs 1912
D. Rs 1754

Answer

To solve the problem step by step, we will first determine the principal amount using the information provided about the compound interest, and then we will calculate the simple interest for the specified conditions.

### Step 1: Understand the given information
We know that the interest earned after 2 years at a rate of 10% per annum compounded yearly is Rs 672.

### Step 2: Use the formula for Compound Interest
The formula for the amount \( A \) after \( t \) years with compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Where:
- \( A \) is the total amount after \( t \) years,
- \( P \) is the principal amount,
- \( r \) is the rate of interest,
- \( t \) is the time in years.

### Step 3: Set up the equation
From the problem, we know:
\[ A = P + \text{Compound Interest} = P + 672 \]
Substituting this into the compound interest formula, we have:
\[ P + 672 = P \left(1 + \frac{10}{100}\right)^2 \]
This simplifies to:
\[ P + 672 = P \left(1 + 0.1\right)^2 = P \left(1.1\right)^2 = P \cdot 1.21 \]

### Step 4: Rearrange the equation
Rearranging the equation gives:
\[ P + 672 = 1.21P \]
\[ 672 = 1.21P - P \]
\[ 672 = 0.21P \]

### Step 5: Solve for \( P \)
Now, we can solve for \( P \):
\[ P = \frac{672}{0.21} = 3200 \]

### Step 6: Calculate Simple Interest
Now we need to calculate the simple interest for the same principal amount \( P = 3200 \) at a rate of 14% per annum for 4 years.

The formula for Simple Interest \( SI \) is:
\[ SI = \frac{P \cdot R \cdot T}{100} \]
Where:
- \( R \) is the rate of interest (14%),
- \( T \) is the time in years (4).

Substituting the values:
\[ SI = \frac{3200 \cdot 14 \cdot 4}{100} \]

### Step 7: Simplify the calculation
Calculating the above expression:
\[ SI = \frac{3200 \cdot 56}{100} = \frac{179200}{100} = 1792 \]

### Final Answer
The interest earned on the same amount after 4 years at 14% per annum at simple interest is Rs 1792.

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