In how many years will Rs 7,000 amount to Rs 9,317 at 10 per cent per annum compound interest?

Answer

To solve the problem of how many years it will take for Rs 7,000 to amount to Rs 9,317 at a compound interest rate of 10% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the known values**:
- Principal (P) = Rs 7,000
- Amount (A) = Rs 9,317
- Rate (r) = 10%

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

3. **Substitute the known values into the formula**:
\[ 9317 = 7000 \left(1 + \frac{10}{100}\right)^t \]
Simplifying the term inside the parentheses:
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]
So the equation becomes:
\[ 9317 = 7000 \times (1.1)^t \]

4. **Isolate the term with t**:
Divide both sides by 7000:
\[ \frac{9317}{7000} = (1.1)^t \]
Calculating the left side:
\[ \frac{9317}{7000} \approx 1.331 \]
Thus, we have:
\[ 1.331 = (1.1)^t \]

5. **Take logarithm of both sides**:
To solve for t, we can take the logarithm:
\[ \log(1.331) = t \cdot \log(1.1) \]

6. **Calculate the logarithms**:
Using a calculator:
\[ \log(1.331) \approx 0.1249 \]
\[ \log(1.1) \approx 0.0414 \]

7. **Solve for t**:
\[ t = \frac{\log(1.331)}{\log(1.1)} \approx \frac{0.1249}{0.0414} \approx 3.02 \]
Since time in years is typically rounded to the nearest whole number, we can conclude:
\[ t \approx 3 \text{ years} \]

### Final Answer:
The time required for Rs 7,000 to amount to Rs 9,317 at 10% per annum compound interest is **3 years**.