45. Mr. Ali invests Rs. 400,000 at the start of each quarter @ \( 12 \% \) for 8 years. What will be the total amount after 8 years? A) Rs. \( 4,919,877 \) B) Rs.5,510,263 C) Rs. \( 211,001,103 \) D) Rs. 21631137

To find the total amount Mr. Ali will have after 8 years of investing Rs. 400,000 at the start of each quarter at an annual interest rate of \( 12\% \), we can use the Future Value of an Annuity formula. Given: - Quarterly investment (P) = Rs. 400,000 - Interest rate per quarter (r) = \( \frac{12\%}{4} = 3\% = 0.03 \) - Total number of quarters (n) = 8 years * 4 quarters/year = 32 quarters The future value (FV) of the annuity can be calculated using the formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Substituting the values: \[ FV = 400,000 \times \frac{(1 + 0.03)^{32} - 1}{0.03} \] Calculating \( (1 + 0.03)^{32} \): \[ (1 + 0.03)^{32} \approx 2.5751 \] Then we calculate: \[ FV = 400,000 \times \frac{2.5751 - 1}{0.03} \approx 400,000 \times \frac{1.5751}{0.03} \approx 400,000 \times 52.5033 \approx 21,001,329 \] So, Mr. Ali's total amount after 8 years, rounded, is approximately Rs. 21,001,329. Thus, the closest option is: C) Rs. \( 211,001,103 \)