Response to the following problem:
Aunt Sally wants to prepare for her retirement. She has decided that she would like to retire at age 65. Once she has retired, she feels that she will need $30,000 per year to cover her expenses. Current actuarial rates say that she will probably live 15 years past retirement. To be safe, she would like to have enough money in the bank to last her for 20 years.
a.) How much money will Aunt Sally need to accumulate by the time she retires at age 65 in order to be able to withdraw $30,000 per year for 20 years?
b.) If Aunt Sally is currently 45 years old and has no money in savings, how much will she have to put aside each year in order to have sufficient funds to retire at age 65.
Assume that Aunt sally will be able to maintain a 6% interest rate throughout the 40 years and that there will be 20 equal deposits to accumulate the funds and 20 equal withdrawals to then deplete the accumulated funds. (The deposits and the withdrawals will not be the same amounts)