1. **Problem Statement:** Shaam makes a 1200 deposit every six months into a mutual fund that earns 7% interest per annum compounded semi-annually. We need to find the total value of his investment after 20 years. 2. **Understanding the Problem:** This is a problem of finding the future value of an annuity with regular deposits and compound interest. 3. **Formula Used:** The future value of an annuity compounded periodically is given by: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $P$ is the periodic deposit (1200), - $r$ is the interest rate per period, - $n$ is the total number of deposits. 4. **Calculate Parameters:** - Interest rate per period $r = \frac{7}{100} \div 2 = 0.035$ (since interest is compounded semi-annually) - Number of periods $n = 20 \times 2 = 40$ (20 years, 2 deposits per year) 5. **Substitute Values:** $$FV = 1200 \times \frac{(1 + 0.035)^{40} - 1}{0.035}$$ 6. **Calculate $(1 + 0.035)^{40}$:** $$1.035^{40} \approx 3.946$$ 7. **Calculate numerator:** $$(3.946 - 1) = 2.946$$ 8. **Calculate fraction:** $$\frac{2.946}{0.035} = 84.1714$$ 9. **Calculate future value:** $$FV = 1200 \times 84.1714 = 101005.68$$ 10. **Conclusion:** After 20 years, Shaam's investment will be worth approximately **101005.68**.