Despite having secured good grades in FINN 100 and FINN 200, your mother, who happens to be a doctor at National Hospital, still does not trust you on financial matters. You recommend her to seek financial advice from your TA Ahmad Raza. Ahmad works part-time at SAROH Investment Advisory as financial analyst. Your mother, 45 years old, tells Ahmad that she has PKR 100,000 in her savings account at Faisal Bank, Lalak Chowk Branch. She plans to sell your current Honda Atlas Motorcycle for PKR 80,000 in ten years as she hopes that you would have purchased your own car by then. Despite the low pay, your mother plans work for 20 years more at National Hospital, and expects to save PKR 10,000 a year for the next 10 years, and PKR 15,000 a year for the following 10 years.

(a) You and Ahmad both know that your mother earns 5% on both her current and future savings. Your mother is trying to find out how much should she expect to have in savings, when she retires in 20 years. Before Ahmad answers, you want to do the calculations yourself. What would be the correct answer to this question, show complete working. [10 Marks]

(b) If your mother plans to withdraw the money in equal annual installments over the 15 years following her retirement, how much can each withdrawal be? You and Ahmad assume that the interest rate continues to be 5% after the twentieth year. Show complete working. [10 Marks]

(c) How would your answer to (a) change if interest rates are expected to rise to 6% after ten years? Show complete working.