$$I only get one shot at this?$$ you wonder aloud. Martina, human resources manager at Covington State University, has just explained that newly hired assistant professors must choose between two retirement plan options. $$Yes$,$ I$$m afraid so$,$ Martina concedes. $$But you do have a week to decide.$$

Martina's explanation was that your two alternatives are $(1)$ the state$$s defined benefit plan and $(2)$ a defined contribution plan under which the university will contribute each year an amount equal to $8\%$ of your salary. The defined benefit plan will provide annual retirement benefits determined by the following formula: $1\mathrm{.}5\%\backslash$times years of service $\backslash$times salary at retirement.

$$It$$s a good thing I studied pensions in my accounting program,$$ you tell Martina. $$Now let$$s see. You say the state is currently assuming our salaries will rise about $3\%$ a year, and the interest rate they use in their calculations is $6\%?$ And, for someone my age, you say they assume I$$ll retire after $40$ years and draw retirement pay for $20$ years. I$$ll do some research and get back to you.$$

Note: Use tables, Excel, or a financial calculator. $($FV of $$1,$ PV of $$1,$ FVA of $$1,$ PVA of $$1,$ FVAD of $$1$ and PVAD of $$1)$

Hint: The calculations are greatly simplified using an electronic spreadsheet such as Excel. There are many ways to set up the spreadsheet. One relatively easy way is to set up the first few rows with the formulas as shown below, then use the $$fill down$$ function to fill in the remaining $38$ rows, and use the Insert: Name: Define: function to name column B $$n$.$ Since contributions are assumed made at the end of each year, there are $39$ years remaining to maturity at the end of $2024.$ Note that multiplying each contribution by $(1\mathrm{.}06)$n$,$ where n equals the remaining number of years to retirement, calculates the future value of each contribution invested at $6\%$ until retirement.

End of Year Years to Retirement Salary Contribution Future Value at Retirement

$202439100,000=$ C$3\backslash$times $0\mathrm{.}08=$ D$3\backslash$times $1\mathrm{.}06^$n

$=$A$3+1=$ B$31=$ C$3\backslash$times $1\mathrm{.}03=$ C$4\backslash$times $0\mathrm{.}08=$ D$4\backslash$times $1\mathrm{.}06^$n

Suppose instead that you choose the defined contribution plan. Assuming that the rate of increase in salary is the same as the state assumes and that the rate of return on your retirement plan assets will be $6\%$ compounded annually, what will be the future value of your plan assets as of the anticipated retirement date $($end of $2063)?$ What will be your annual retirement pay $($assuming continuing investment of remaining assets at $6\%)?$Required information

$[$The following information applies to the questions displayed below.$]$

"I only get one shot at this?" you wonder aloud. Martina, human resources manager at Covington State University, has just

explained that newly hired assistant professors must choose between two retirement plan options. "Yes, I$\text{'}$m afraid so$,"$

Martina concedes. "But you do have a week to decide."

Martina's explanation was that your two alternatives are $(1)$ the state's defined benefit plan and $(2)$ a defined contribution

plan under which the university will contribute each year an amount equal to $8\%$ of your salary. The defined benefit plan

will provide annual retirement benefits determined by the following formula: $1\mathrm{.}5\%$ years of service $$ salary at retirement.

"It's a good thing I studied pensions in my accounting program," you tell Martina. "Now let's see. You say the state is

currently assuming our salaries will rise about $3\%$ a year, and the interest rate they use in their calculations is $6\%?$ And, for

someone my age, you say they assume l$\text{'}$ll retire after $40$ years and draw retirement pay for $20$ years. I'll do some research

and get back to you."

Note: Use tables, Excel, or a financial calculator. $($FV of $$1,$ PV of $$1,$ FVA of $$1,$ PVA of $$1,$ FVAD of $$1$ and PVAD of $$1)$

Hint: The calculations are greatly simplified using an electronic spreadsheet such as Excel. There are many ways to set up

the spreadsheet. One relatively easy way is to set up the first few rows with the formulas as shown below, then use the "fill

down" function to fill in the remaining $38$ rows, and use the Insert: Name: Define: function to name column $B"n".$ Since

contributions are assumed made at the end of each year, there are $39$ years remaining to maturity at the end of $2024.$

Note that multiplying each contribution by $(1\mathrm{.}06{)}^n,$ where $n$ equals the remaining number of years to retirement, calculates

the future value of each contribution invested at $6\%$ until retirement.

Required:

You were hired at the beginning of $2024$ at a salary of $$100,000.$ If you choose the state's defined benefit plan and projections hold

true, what will be your annual retirement p