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 Muneeba Qayyum. Muneeba works part-time at SAROH Investment Advisory as financial analyst. Your mother, 50 years old, tells Muneeba that she has PKR 250,000 in her savings account at Faisal Bank, Lalak Chowk Branch. Despite the low pay, your mother plans work for 10 years more at National Hospital, and expects making PKR 100,000 a year. Besides being a medical doctor, your mother also has financial know-how and expects to make return of five percent on her investments for the foreseeable future. In order to pay tribute to doctors for their selfless work during COVID crisis, Prime Minister of Pakistan has decided to give complete tax exemption to doctors, so you can safely ignore taxes.

(a) Once your mother retires in ten years from now, she wants to be able to withdraw PKR 80,000 for the following five years. In addition to being an ACF major, Muneeba has also done minors in actuarial sciences. She has told your mother that she will live to be ninety years old. Question is, how much your mother needs to have in Faisal Bank ten years from now to be able to do this? Show complete working.

(b) How much of income your mother needs to save each year for the next ten years to be able to afford her planned withdrawals of PKR 80,000 per year after year ten? Show complete working.

(c) Due to changes in economy, now assume that interest rate declines to four percent ten years from now. How much would she have to lower her annual withdrawals by, assuming she still plans to withdraw cash each year for the following twenty five years? Show complete working.