Your cousin is asking you to help him with his retirement planning. You know he's coming just celebrated his 24th birthday and he wants to retire in exactly 41 years, that is to say, his 65th birthday. Specifically, he wishes to withdraw $35,000 in 41 years, then the same amount at the end of each of the next nine years (42,43 years old, ..., 50 years old). Subsequently, in 51 years, he wants to withdraw $ 40,000 as well a similar amount at the end of each of the following 9 years (52, 53, ...,60 years). There would be 10 withdrawals of $ 35,000 and 10 other withdrawals of $ 40,000 expected during the anticipated 20 years of retirement.

In order to accumulate enough money and allow him to achieve his goals, he has already $ 10,000. In addition, he would be willing to make equal annual payments, from the end of this year until his 64th birthday (in 40 years). He thinks he can get an average annual rate of return of 7% for all these years.

a) Illustrate the flow diagram related to this problem (make a representation graphic).

b) Determine how much your cousin will have to hold in 40 years, if he wants to reach his retirement income goals.

c) Calculate the amount of equal annual payments to be made.

d) Answer again to question b), but assuming that your cousin would get rather the equivalent of a rate of return of 0.5% per month.