Prof. Business realizes she is entering the last third of her career and is considering retirement in 12 years. She is in a self-managed defined contribution pension plan and through automatic payroll deduction and University matching both based on mandated percentages of her salary $1250/month is currently deposited into her pension plan. Due to the lack of recent raises at her public university, she doesn't plan on these monthly contributions increasing much if any over the next 12 years. Prof. Business currently has $500,000 in her pension plan account and is somewhat concerned if this along with her mandated future $1250 monthly deposits will adequately fund her retirement in 12 years. She is considering supplementing her pension plan by having automatic additional monthly deposits deducted into a 403c retirement plan which is like a 401k plan for employees of non-profit organizations like public universities. She is comfortable that this 403c plan since it has the same investment management companies and investment options as her current pension plan and it also has a Roth option where she won't get a tax break for her deposits but her retirement withdrawals will be tax free. Prof. Business has a monthly deposit amount in mind, but wants your help in trying to figure out if this amount will be adequate. Given her current pension plan portfolio investment mix, she estimates a nominal annual expected return of 7.2% which translates to a 0.6% monthly expected return.

1. Prof. Business is considering having $900/month, which is about 10% of her monthly gross (pre-tax) salary deducted and deposited into the 403c for the next 12 years. This is addition to the $500,000 already in her pension plan today and the estimated $1250 monthly deposits into her current pension plan. What is the expected total value of Prof. Business' retirement accounts after making end of the month deposits of $2150 for 10 years on top of her current retirement savings of $500,000 at her expected monthly return?

2. Prof. Business estimates she will live for 23 years after her planned retirement in 12 years and wants a monthly retirement annuity with the withdrawals at the end of each month once she retires. What is her expected monthly retirement income using your answer from #1 and assuming she will continue to earn her expected monthly return after retirement?

3. Upon hearing the amount of this monthly retirement annuity, Prof. Business is happy with this figure because it's higher her current pre-tax income. However, she wonders if her expected monthly investment return is too optimistic and wants to change it to a 6% nominal annual rate, or 0.5% per month before and after retirement. Also, she wants a monthly income of $11,000 once she retires (for 23 years). How much extra above her estimated mandated $1250 monthly pension plan amount would Prof. Business need to deposit monthly into the 403c plan over the next 12 years to fund this retirement income goal?

4. Prof. Business feels like the required 403c monthly deposit is too much of a financial stretch for her and wants you to re-figure her potential monthly retirement income using the same investment rate assumptions as #3 (6% nominal annual rate, 0.5% monthly rate before and after retirement), but with the following deposit assumptions. One, she thinks she can deposit an extra $200/month into the 403c plan for a monthly deposit of $1100 into the 403c plan for the next 12 years which makes for a total monthly deposit of $2350 the upcoming year. Also, she thinks her salary and her mandated monthly pension plan deposit will increase 2% annually from the current monthly deposit of $1250 this upcoming year (deposits 1-12). For example, her mandated monthly pension plan deposit for year 2 (deposits 13-24) will be $1275 and will increase 2% each year until retirement. This will be in addition to the flat $1100 deposit into the 403C plan. Also remember these monthly deposits are on top of the $500,000 Prof. Business has invested today. Answer the following.

a. How much will Prof. Business have at retirement under these assumptions?

b. What will Prof. Business' monthly retirement withdrawal be for 23 years once she retires?