The time required for Rs 1,000 to amount to 1,331 at interest of 10% per annum, compounded annually, is

Options

A. 2 years
B. 2 years, 6 months
C. 3 years
D. 3 years, 6 months

Answer

To solve the problem of finding the time required for Rs. 1,000 to amount to Rs. 1,331 at an interest rate of 10% per annum, compounded annually, we can use the formula for compound interest.

### Step-by-Step Solution:

1. **Understand the Compound Interest Formula**:
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- \( A \) = final amount
- \( P \) = principal amount (initial investment)
- \( r \) = rate of interest per annum
- \( t \) = time in years

2. **Identify the Given Values**:
From the problem, we have:
- \( A = 1331 \)
- \( P = 1000 \)
- \( r = 10\% \)

3. **Substitute the Values into the Formula**:
Plugging the values into the compound interest formula:
\[ 1331 = 1000 \left(1 + \frac{10}{100}\right)^t \]
Simplifying the expression inside the parentheses:
\[ 1331 = 1000 \left(1 + 0.1\right)^t \]
\[ 1331 = 1000 \left(1.1\right)^t \]

4. **Isolate the Exponential Term**:
To isolate \( (1.1)^t \), divide both sides by 1000:
\[ \frac{1331}{1000} = (1.1)^t \]
\[ 1.331 = (1.1)^t \]

5. **Recognize the Exponential Relationship**:
Notice that \( 1.331 \) can be expressed as \( (1.1)^3 \):
\[ 1.331 = (1.1)^3 \]
Therefore, we can equate the exponents since the bases are the same:
\[ t = 3 \]

6. **Conclusion**:
The time required for Rs. 1,000 to amount to Rs. 1,331 at an interest rate of 10% per annum, compounded annually, is **3 years**.