Patrick Plans to retire in exactly 15 years' time, and he has a plan to create a fund that will allow him to receive $72,000 at the beginning of each year for the 15 years between retirement and death (a psychic has told him that he would die after 30 years from now). He is also been advised that his retirement savings will be able to earn 10% interest per year during the retirement period. 

(a) How large a fund will Patrick need when he retire in 15 years' time to provide the $72,000 retirement annuity? 

(b) How much will Patrick need today as a single amount to provide the fund calculated in part (a) if he can earn 5% interest per year during the 15 years preceding retirement? 

(c) What effect would a decrease in the interest rate Patrick can earn both during and prior to retirement have on the values found in parts (a) and (b)? Explain