Letterman is currently 35 years old and would like to retire at age 60 (i.e. 25 years later). He wants to have enough saving when reaching 60 to support his post retirement life for 22 years (assuming the average life expectancy of males in HK to be 82 years). He would like to seek for your assistance in formulating his retirement plan.

1. Based on the budget constructed, Letterman estimated that he would spend $350,000 every year during his post retirement life. Assuming he could earn a 8% return per annum during his post retirement period, calculate how much retirement saving Carlson needs to have when he reaches 60 years old.

2. At the moment Letterman has a saving of $700,000. Assuming he could earn a 5% return per annum for the next 25 years:

(a) Would Letterman have enough retirement saving at age 60? (3 marks)

(b) If not, how much is the shortfall amount?

3. Letterman would like to make use of his current saving of 700,000 plus contributing a fixed amount of annual saving over the next 25 years to achieve the retirement saving as calculated in Part (1) above. Calculate the annual saving Letterman needs to contribute during the next 25 years, assuming both the initial saving of $700,000 and the annuity could earn a 5% return per annum.

4. Independent of Parts 1-3 above, suppose Letterman revises his plan and wishes to have $850,000 in savings and investment when he retires at age 60. Assuming that he can earn an average of 10% on his portfolio, what is the maximum annual withdrawal he can make over a 22-year period of retirement?