The compound interest accured on an amount at the end of two years @ 15 p.c.p.a. is Rs. 2915.4. what is the amount ?

Options

A. Rs. 76,020/-
B. Rs. 9,040/-
C. Rs. 8,540/-
D. None of these

Answer

To find the principal amount based on the compound interest accrued, we can follow these steps:

### Step 1: Understand the formula for Compound Interest
The formula for compound interest (CI) is:
\[ CI = P \left(1 + \frac{R}{100}\right)^t - P \]
Where:
- \( CI \) is the compound interest
- \( P \) is the principal amount
- \( R \) is the rate of interest
- \( t \) is the time in years

### Step 2: Rearranging the formula
We can rearrange the formula to find the principal amount \( P \):
\[ CI + P = P \left(1 + \frac{R}{100}\right)^t \]
This can be rewritten as:
\[ P = \frac{CI}{\left(1 + \frac{R}{100}\right)^t - 1} \]

### Step 3: Substitute the known values
Given:
- \( CI = 2915.4 \)
- \( R = 15\% \)
- \( t = 2 \)

Substituting these values into the rearranged formula:
\[ P = \frac{2915.4}{\left(1 + \frac{15}{100}\right)^2 - 1} \]

### Step 4: Calculate \( \left(1 + \frac{15}{100}\right)^2 \)
First, calculate \( 1 + \frac{15}{100} \):
\[ 1 + \frac{15}{100} = 1 + 0.15 = 1.15 \]
Now, calculate \( (1.15)^2 \):
\[ (1.15)^2 = 1.3225 \]

### Step 5: Substitute back into the formula
Now substitute \( (1.15)^2 \) back into the formula:
\[ P = \frac{2915.4}{1.3225 - 1} \]
Calculating \( 1.3225 - 1 \):
\[ 1.3225 - 1 = 0.3225 \]

### Step 6: Calculate \( P \)
Now we can calculate \( P \):
\[ P = \frac{2915.4}{0.3225} \]
Calculating this gives:
\[ P \approx 9040 \]

### Conclusion
The principal amount is approximately Rs. 9040.

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