The amount (in Rs) received at 10% per an num 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-by-Step Solution:

1. **Identify the given values:**
- Amount (A) = Rs. 1,19,790
- Rate of interest (r) = 10% per annum
- Time (t) = 3 years

2. **Recall the formula for the amount in compound interest:**
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- A = Amount
- P = Principal
- r = Rate of interest
- t = Time in years

3. **Substitute the known values into the formula:**
\[ 1,19,790 = P \left(1 + \frac{10}{100}\right)^3 \]
Simplifying the expression inside the parentheses:
\[ 1 + \frac{10}{100} = 1 + 0.10 = 1.10 \]
Therefore, we have:
\[ 1,19,790 = P (1.10)^3 \]

4. **Calculate \( (1.10)^3 \):**
\[ (1.10)^3 = 1.10 \times 1.10 \times 1.10 = 1.331 \]
So, we rewrite the equation:
\[ 1,19,790 = P \times 1.331 \]

5. **Solve for P (Principal):**
\[ P = \frac{1,19,790}{1.331} \]
Now, perform the division:
\[ P \approx 90,000 \]

6. **Conclusion:**
The principal amount is Rs. 90,000.