At the rate of 5% annual interest on sum of money, 1261 compound interest is received in 3 years. The amount is:

Options

A. Rs. 9,000
B. Rs. 8,400
C. Rs. 7,500
D. Rs. 8000

Answer

To solve the problem of finding the amount when the compound interest is given, we can follow these steps:

### Step 1: Understand the formula for Compound Interest
The formula for compound interest (CI) is given by:
\[ CI = A - P \]
where:
- \( A \) is the total amount after time \( t \)
- \( P \) is the principal amount (the initial sum of money)

### Step 2: Use the formula for Compound Interest
The amount \( A \) can also be calculated using the formula:
\[ A = P(1 + r)^t \]
where:
- \( r \) is the rate of interest (in decimal)
- \( t \) is the time in years

### Step 3: Substitute the known values
In this problem:
- The compound interest \( CI = 1261 \)
- The rate of interest \( r = 5\% = 0.05 \)
- The time \( t = 3 \) years

We need to express \( A \) in terms of \( P \):
\[ A = P(1 + 0.05)^3 \]

### Step 4: Calculate \( (1 + 0.05)^3 \)
Calculating \( (1 + 0.05)^3 \):
\[ (1 + 0.05)^3 = (1.05)^3 \]
Calculating \( 1.05^3 \):
\[ 1.05^3 = 1.157625 \]

### Step 5: Substitute back into the amount formula
Now we can express \( A \) in terms of \( P \):
\[ A = P \times 1.157625 \]

### Step 6: Relate CI to A and P
From the compound interest formula:
\[ CI = A - P \]
Substituting \( A \):
\[ 1261 = P \times 1.157625 - P \]
\[ 1261 = P(1.157625 - 1) \]
\[ 1261 = P(0.157625) \]

### Step 7: Solve for P
Now, we can solve for \( P \):
\[ P = \frac{1261}{0.157625} \]
Calculating this gives:
\[ P \approx 8000 \]

### Step 8: Calculate the Amount A
Now that we have \( P \), we can find \( A \):
\[ A = 8000 \times 1.157625 \]
Calculating this gives:
\[ A \approx 9261 \]

### Final Answer
The amount is approximately:
\[ \text{Amount } A \approx 9261 \]

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