Question: Your friend is now 55 years old. He is planning to retire when he is 65 years old. He has currently $100,000 in a savings account at a bank paying an annual interest rate of 9 percent compounded monthly until he retires. In addition, he plans to deposit in the same savings account monthly amounts with a first amount one month from now equal to $1,000 and the last amount with be deposited on his 65th birthday. The monthly deposit will grow at a monthly rate of 1/4 percent. When your friend retires, he will get a lump sum of $200,000 as an indemnity. He will deposit the amount also in the savings account.
A. Your friend's retirement income will come only from his savings. He plans to withdraw monthly a certain amount of money from the savings account starting exactly one month after his 65th birthday. Assume that your friend's last monthly withdrawal will be on his 85th birthday. Determine the Value of each monthly withdrawal.
B. Assume now that inflation is projected at 3 percent annually after your friend retires. Assume also that your friend is planning to withdraw a monthly amount with the same real value to maintain the same standard of living. Assume also that he can still earn 9% nominal return on his savings account after he retires. Determine the value of the first monthly amount he will withdraw after he retires and the last amount he withdraws. Assume again that your friend's last monthly withdrawal will be on his 85th birthday.