The amount (in Rs) received at 10% per annum compound interest after 3 yrs is Rs 1,19,790. What was the principal?

Options

A. 90000
B. 1,00,000
C. 80000
D. 75000

Answer

To find the principal amount (P) when the amount received after 3 years at a compound interest rate of 10% per annum is Rs 1,19,790, we can use the formula for compound interest:

### Step 1: Write down the formula for the amount in compound interest
The formula for the amount (A) in compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]
Where:
- \( A \) = Amount after N years
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( N \) = Number of years

### Step 2: Substitute the known values into the formula
From the question, we have:
- \( A = 1,19,790 \)
- \( R = 10\% \)
- \( N = 3 \)

Substituting these values into the formula, we get:
\[ 1,19,790 = P \left(1 + \frac{10}{100}\right)^3 \]

### Step 3: Simplify the expression
Now, simplify the term inside the parentheses:
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]

Thus, the equation becomes:
\[ 1,19,790 = P \cdot (1.1)^3 \]

### Step 4: Calculate \( (1.1)^3 \)
Now we need to calculate \( (1.1)^3 \):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]

### Step 5: Substitute back into the equation
Now substituting this back into the equation:
\[ 1,19,790 = P \cdot 1.331 \]

### Step 6: Solve for P
To find the principal \( P \), rearrange the equation:
\[ P = \frac{1,19,790}{1.331} \]

### Step 7: Calculate the value of P
Now, perform the division:
\[ P \approx \frac{1,19,790}{1.331} \approx 90,000 \]

### Conclusion
Thus, the principal amount is Rs 90,000.

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