Financing RetirementProf. Business has a self-managed retirement plan through her University and would like toretire in 13 years and wonders if her current and future planned savings will provide adequatefuture retirement income. Here's her information and goals.

Prof. Business wants a 23-year retirement annuity that begins 13 years from today withan 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 herpurchasing power will decrease over time during retirement.

Prof. Business currently has $400,000 in her University retirement account. She expectsthese savings and any future deposits into her University and any other retirement accountwill earn 7.5% compounded annually. Also, she expects to earn this same 7.5% annualreturn after she retires.Answer the following questions to help Prof. Business finalize her retirement planning.

1. What is Prof. Business' desired annual retirement income?

2. How much will Prof. Business need 13 years from today to fund her desired retirementannuity?

3. In addition to the $400,000 balance today, Prof. Business will fund her future retirementgoal from question2 by making 13 annual equal deposits at 7.5% compounded annuallyinto her retirement accounts starting a year from today (the last deposit will be madewhen Prof. Business retires). How large does this annual deposit need to be in additionto the initial $400,000 invested in Prof. Business' retirement fund?

4. This annual figure from #3 makes Prof. Business feel a little anxious about her futureplanned 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 herpurchasing power eroding during retirement. She would like her first retirementwithdrawal to be equal to the amount you found in #1, and then she increase eachsuccessive 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?

5. In addition to the $400,000 balance today, Prof. Business will fund her adjusted futureretirement 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 lastdeposit will be made when Prof. Business retires). How large does this annual depositneed to be in addition to the initial $400,000 invested in Prof. Business' retirementfund?

6. Wow, the annual deposit required to fund the growing retirement annuity in question 5gives Prof. Business some sticker shock. However, she may be willing to accept a lowerannual retirement annuity than described in question 4 that loses purchasing powerover time but that is hopefully higher than the retirement annuity in questions 1 and 2.Let's account for the fact that her and the University's contributions to Prof. Business'University retirement plan are based on a certain percentage of her salary and willincrease as her salary increases. Based on this formula, her first upcoming end of theyear deposit will be $14,600 and let's assume that her annual deposit and salary willgrow 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 ofeach year until she retires. This will make her first year total deposit $20,600, but onlythe $14,600 part of this deposit will increase 2.5% annually, the $6000 part of thedeposit will remain fixed each year under current laws. These deposits are in additionto the $400,000 she currently has today in the University retirement plan. Answer thefollowing based on these assumptions.

a) How much money will Prof. Business have in her retirement account immediatelyafter her last deposit 13 years from today?

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