The amount received at 10% per annum com pound interest after 3 yrs is₹ 10,648. What was the principal (in Rs)?

Options

A. 8000
B. 9000
C. 8500
D. 7500

Answer

To find the principal amount when the amount received after 3 years at a compound interest rate of 10% per annum is ₹10,648, we can follow these steps:

### Step 1: Understand the formula for compound interest
The formula for the amount \( A \) in compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount (initial investment)
- \( r \) = Rate of interest per annum
- \( t \) = Time in years

### Step 2: Substitute the known values into the formula
In this case, we know:
- \( A = 10,648 \)
- \( r = 10\% \)
- \( t = 3 \)

Substituting these values into the formula gives:
\[ 10,648 = P \left(1 + \frac{10}{100}\right)^3 \]

### Step 3: Simplify the equation
Calculate \( 1 + \frac{10}{100} \):
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]
Now raise \( 1.1 \) to the power of 3:
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]
Now the equation becomes:
\[ 10,648 = P \times 1.331 \]

### Step 4: Solve for the principal \( P \)
To find \( P \), rearrange the equation:
\[ P = \frac{10,648}{1.331} \]

### Step 5: Calculate the value of \( P \)
Now, perform the division:
\[ P = \frac{10,648}{1.331} \approx 8000 \]

### Conclusion
The principal amount \( P \) is ₹8000.

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