Benny, aged 40, is now planning for his retirement. After doing some research, he has decided that once he retires, he will put all his wealth into a retirement account earning 1.2% per month with Kowloon Bank. In order to cope with living while retired, Benny needs to withdraw a regular amount from this retirement account every month during his retirement. Answer the following questions:
a) If Benny lives for 20 years after he retires and wants to withdraw $40,000 at the end of each MONTH during his retirement, how much does he need to accumulate in his retirement account at the time he retires?
b) If Benny wants to receive $120,000 at the end of each QUARTER during his retirement instead, how much does he need to have in his account at the time of retirement? (Hint: You need to find out the EAR first and use the quarterly rate to calculate.)
c) Benny is celebrating his 40th birthday today and he wants to start his retirement plan now. In order to obtain the retirement sum in part (b) at his retirement age of 55, Benny decides to make equal deposits into a mutual fund account every year on his birthday. The mutual fund account provides 20% per annum return to investors. Benny makes his deposits today and will continue to deposit until he is 54. In other words, the last deposit will be on his 54th birthday. With the above information, calculate the amount that Benny should deposit every year so that he is able to make the desired withdrawals during his retirement. (Hint: This is an annuity due problem.)