In how many years will 800 amount to Rs 882 at 5% per annum be compounded annually ?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem of how many years it will take for Rs. 800 to amount to Rs. 882 at 5% per annum compounded annually, we can use the formula for compound interest:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (in percentage).
- \( n \) is the number of years the money is invested or borrowed.

### Step-by-Step Solution:

1. **Identify the values**:
- Principal \( P = 800 \)
- Amount \( A = 882 \)
- Rate \( r = 5\% \)

2. **Set up the equation**:
\[ 882 = 800 \left(1 + \frac{5}{100}\right)^n \]

3. **Simplify the equation**:
\[ 882 = 800 \left(1 + 0.05\right)^n \]
\[ 882 = 800 \left(1.05\right)^n \]

4. **Divide both sides by 800**:
\[ \frac{882}{800} = (1.05)^n \]
\[ 1.1025 = (1.05)^n \]

5. **Take logarithm on both sides**:
\[ \log(1.1025) = n \cdot \log(1.05) \]

6. **Solve for \( n \)**:
\[ n = \frac{\log(1.1025)}{\log(1.05)} \]

7. **Calculate the logarithms**:
- Using a calculator:
- \( \log(1.1025) \approx 0.0414 \)
- \( \log(1.05) \approx 0.0212 \)

\[ n \approx \frac{0.0414}{0.0212} \approx 1.95 \]

8. **Round to the nearest whole number**:
Since \( n \) must be a whole number, we round 1.95 to 2.

### Final Answer:
It will take approximately **2 years** for Rs. 800 to amount to Rs. 882 at 5% per annum compounded annually.

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