1. **Problem (a):** Midhil invests 1500 at 4.2% per year compound interest. Calculate the value after 5 years. 2. The compound interest formula is: $$ A = P \left(1 + \frac{r}{100}\right)^t $$ where $A$ is the amount, $P$ is the principal, $r$ is the rate, and $t$ is time in years. 3. Substitute values: $P=1500$, $r=4.2$, $t=5$. $$ A = 1500 \left(1 + \frac{4.2}{100}\right)^5 = 1500 \left(1 + 0.042\right)^5 = 1500 \times 1.042^5 $$ 4. Calculate $1.042^5$: $$ 1.042^5 \approx 1.228 $$ 5. Calculate final amount: $$ A = 1500 \times 1.228 = 1842 $$ --- 6. **Problem (b):** Hitanshi invests money at $x\%$ compound interest. After 11 years, the investment doubles. 7. Using the formula: $$ 2P = P \left(1 + \frac{x}{100}\right)^{11} $$ Divide both sides by $P$: $$ 2 = \left(1 + \frac{x}{100}\right)^{11} $$ 8. Take the 11th root: $$ \sqrt[11]{2} = 1 + \frac{x}{100} $$ 9. Calculate $\sqrt[11]{2}$: $$ \sqrt[11]{2} \approx 1.065 $$ 10. Solve for $x$: $$ 1.065 = 1 + \frac{x}{100} \Rightarrow \frac{x}{100} = 0.065 \Rightarrow x = 6.5 $$ **Final answers:** - (a) $1842$ - (b) $6.5$