Prudence has just finished her course on financial management and would like to apply what she has learnt for her retirement planning. She would like to retire 30 years from today. She estimates she will need $50,000 a year to live comfortably, with the first retirement funds to be withdrawn a year from the day she retires until the 20th year post-retirement. Prudence estimates that she can earn 5% per year on her funds for retirement.

Her financial planner, Anthony, would like her to consider a regular savings plan to help her to achieve her retirement goals. The savings plan requires Prudence to deposit monthly into an account with a quoted rate of 5%, compounded monthly. Prudence will only look at this after she has done her own calculations.

(a) Compute the amount that Prudence must deposit in her account today so that she will have enough funds for her retirement.

(b) Calculate the amount that Prudence must deposit in her account each year, starting one year from today, so that she will have enough funds for her retirement.

(c) Examine the savings plan proposed by Anthony and discuss whether Prudence should take up her planner's suggestion.