Prof. Business wants a 23-year retirement annuity that begins 13 years from today with an equal annual payment equal to $90,000 today inflated at 2.5% annually over 13 years. Her first retirement annuity payment would occur 13 years from today. She realizes her purchasing power will decrease over time during retirement.

Prof. Business currently has $400,000 in her University retirement account. She expects these savings and any future deposits into her University and any other retirement account will earn 7.5% compounded annually. Also, she expects to earn this same 7.5% annual return after she retires.

In addition to the $400,000 balance today, Prof. Business will fund her future retirement goal from question 2 by making 13 annual equal deposits at 7.5% compounded annually into her retirement accounts starting a year from today (the last deposit will be made

when Prof. Business retires). How large does this annual deposit need to be in addition to the initial $400,000 invested in Prof. Business retirement fund?

This annual figure from #3 makes Prof. Business feel a little anxious about her future planned retirement since her current annual contribution is $14,600. Also, Prof. Business annual retirement account contribution is based on a percentage of her salary

and will increase as her salary increases. However, Prof. Business is worried about her purchasing power eroding during retirement. She would like her first retirement withdrawal to be equal to the amount you found in #1, and then she increase each successive retirement withdrawal by 2.5% annually over the remaining 22 withdrawals. How much will Prof. Business need now at retirement given Prof. Business 7.5% expected return?

In addition to the $400,000 balance today, Prof. Business will fund her adjusted future retirement goal from question 4 by making 13 annual equal deposits at 7.5% compounded annually into her retirement accounts starting a year from today (the last deposit will be made when Prof. Business retires). How large does this annual deposit need to be in addition to the initial $400,000 invested in Prof. Business retirement fund?

Wow, the annual deposit required to fund the growing retirement annuity in question 5 gives Prof. Business some sticker shock. However, she may be willing to accept a lower annual retirement annuity than described in question 4 that loses purchasing power over time but that is hopefully higher than the retirement annuity in questions 1 and 2. Lets account for the fact that her and the Universitys contributions to Prof. Business University retirement plan are based on a certain percentage of her salary and will increase as her salary increases. Based on this formula, her first upcoming end of the year deposit will be $14,600 and lets assume that her annual deposit and salary will grow at a 2.5% annual rate over the remaining 12 years (13 total deposits) to Prof. Business retirement. Also, she plans to contribute an additional $6,000 at the end of each year until she retires. This will make her first year total deposit $20,600, but only the $14,600 part of this deposit will increase 2.5% annually, the $6000 part of the deposit will remain fixed each year under current laws. These deposits are in addition to the $400,000 she currently has today in the University retirement plan. Answer the following based on these assumptions.

Wow, the annual deposit required to fund the growing retirement annuity in question 5 gives Prof. Business some sticker shock. However, she may be willing to accept a lower annual retirement annuity than described in question 4 that loses purchasing power over time but that is hopefully higher than the retirement annuity in questions 1 and 2. Lets account for the fact that her and the Universitys contributions to Prof. Business University retirement plan are based on a certain percentage of her salary and will increase as her salary increases. Based on this formula, her first upcoming end of the year deposit will be $14,600 and lets assume that her annual deposit and salary will grow at a 2.5% annual rate over the remaining 12 years (13 total deposits) to Prof. Business retirement. Also, she plans to contribute an additional $6,000 at the end of each year until she retires. This will make her first year total deposit $20,600, but only the $14,600 part of this deposit will increase 2.5% annually, the $6000 part of the deposit will remain fixed each year under current laws. These deposits are in addition to the $400,000 she currently has today in the University retirement plan. Answer the following based on these assumptions.

b) What would be the equal annual payment from her 23-year retirement annuity whose first payment occurs exactly 13 years from today?