Final answer:
The present value of both annuities is calculated at two different interest rates (10% and 20%) to determine which is the better investment. Annuity C, an ordinary annuity, and Annuity D, an annuity due, have different present values at each interest rate, with the value decreasing as the interest rate increases.
Step-by-step explanation:
The question asks to calculate the present value of two annuities, one being an ordinary annuity and the other being an annuity due, at interest rates of 10% and 20%, to determine which is the better investment for Md. Kushik Reza. The present value (PV) of an annuity can be found using the formula:PV ordinary annuity = Pmt * [(1 - (1 + r)^-n) / r]PV annuity due = Pmt * [(1 - (1 + r)^-n) / r] * (1 + r)Where Pmt is the payment amount per period, r is the interest rate per period, and n is the total number of periods.To calculate at 10% interest for annuity C, the ordinary annuity PV = BDT 3,500 * [(1 - (1 + 0.10)^-10) / 0.10] = BDT 3,500 * 6.14457 ≈ BDT 21,506 For annuity D, the annuity due:PV = BDT 2,300 * [(1 - (1 + 0.10)^-10) / 0.10] * (1 + 0.10) = BDT 2,300 * 6.14457 * 1.10 ≈ BDT 16,539 Repeating these calculations at 20% interest gives For annuity C PV = BDT 3,500 * [(1 - (1 + 0.20)^-10) / 0.20] = BDT 3,500 * 4.19203 ≈ BDT 14,672 For annuity D PV = BDT 2,300 * [(1 - (1 + 0.20)^-10) / 0.20] * (1 + 0.20) = BDT 2,300 * 4.19203 * 1.20 ≈ BDT 11,597 Conclusion: By comparing the present values, we can determine which annuity is more favorable for Md. Kushik Reza at different interest rates. Note that as the interest rate increases, the present value of both annuities decreases, which is expected due to the time value of money principle.