## Current and future planned savings will provide adequate future retirement income

Part 3: Financing Retirement Prof. Finance has a self-managed retirement plan through her University and would like to retire in 10 years and wonders if her current and future planned savings will provide adequate future retirement income. Here’s her information and goals.  Prof. Finance wants a 23-year retirement annuity that begins 10 years from today with an equal annual payment equal to \$90,000 today inflated at 2.5% annually over 10 years. Her first retirement annuity payment would occur 10 years from today. She realizes her purchasing power will decrease over time during retirement

. Prof. Finance currently has \$520,000 in her University retirement account. She expects these savings and any future deposits into her University and any other retirement account will earn 7% compounded annually. Also, she expects to earn this same 7% annual return after she retires. Answer the following questions to help Prof. Finance finalize her retirement planning. 1. What is Prof. Finance’s desired annual retirement income? 2. How much will Prof. Finance need 10 years from today to fund her desired retirement annuity? 3. In addition to the \$520,000 balance today, Prof. Finance will fund her future retirement goal from question 2 by making 10 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. Finance retires). How large does this annual deposit need to be in addition to the initial \$520,000 invested in Prof. Finance’ retirement fund? 4. This annual figure from #3 makes Prof. Finance feel a little anxious about her future planned retirement since her current annual contribution is \$18,200. Also, Prof. Finance’ annual retirement account contribution is based on a percentage of her salary and will increase as her salary increases.

However, Prof. Finance 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. Finance need now at retirement given Prof. Finance’s 7% expected return? 5. In addition to the \$520,000 balance today, Prof. Finance will fund her adjusted future retirement goal from question 4 by making 10 annual equal deposits at 7% compounded annually into her retirement accounts starting a year from today (the last deposit will be made when Prof. Finance retires). How large does this annual deposit need to be in addition to the initial \$520,000 invested in Prof. Finance’s retirement fund? 6. Wow, the annual deposit required to fund the growing retirement annuity in question 5 gives Prof. Finance 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.

Let’s account for the fact that her and the University’s contributions to Prof. Finance’ 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 \$19,000 and let’s assume that her annual deposit and salary will  grow at a 2.5% annual rate over the remaining 9 years (10 total deposits) to Prof. Finance’ retirement. Also, she plans to contribute an additional \$9,600 at the end of the year and will increase this additional deposit 2.5% each year until she retires. This will make her first year total deposit \$28,600 which will increase 2.5% annually. These deposits are in addition to the \$520,000 she currently has today in the University retirement plan. Answer the following based on these assumptions. a) How much money will Prof. Finance have in her retirement account immediately after her last deposit 10 years from today? b) What would be the equal annual payment from her 23-year retirement annuity whose first payment occurs exactly 10 years from today?