1. **Stating the problem:** We need to find the time period (in years) for which Rs. 30,000 amount at 7% per annum compound interest becomes Rs. 30,000 + Rs. 4347 = Rs. 34,347. 2. **Formula for compound interest:** The amount $A$ after $t$ years at rate $r$ per annum compounded annually on principal $P$ is given by: $$ A = P (1 + \frac{r}{100})^t $$ 3. **Given values:** - Principal $P = 30000$ - Rate $r = 7$% - Amount $A = 30000 + 4347 = 34347$ 4. **Substitute into the formula:** $$ 34347 = 30000 \times \left(1 + \frac{7}{100}\right)^t = 30000 \times (1.07)^t $$ 5. **Solve for $t$:** \[ (1.07)^t = \frac{34347}{30000} = 1.1449 \] 6. **Take natural logarithm on both sides:** $$ t \ln(1.07) = \ln(1.1449) $$ 7. **Calculate:** $$ t = \frac{\ln(1.1449)}{\ln(1.07)} $$ Calculate each logarithm: - $\ln(1.1449) \approx 0.1352$ - $\ln(1.07) \approx 0.0677$ Then, $$ t = \frac{0.1352}{0.0677} \approx 2.0 $$ 8. **Interpretation:** The time period is approximately 2 years. **Final answer:** (a) 2 years