Question

In this problem we will assume all cash flows occur at the BEGINNING OF THE PERIOD (Annuity Due). Therefore, you need to set the calculator to BEGIN.

Problem:

Assume you are 32 years old and plan to retire in 35 years at age 67. You are currently earning $75,000/year and expect average annual salary increases of 4.0%/year over the next 35 years. You have $0 saved for retirement.

You are trying to determine how much money to save (invest) each year in your 401(k) Plan to fund your retirement in order to pay yourself 70% of your final salary each year (that increases with inflation). [Remember this is an Annuity Due, so your first annual investment is made in Year 0….and your final payment is in Year 34.] You plan to maintain an investment as a percent of your salary, which simply means your payment into the 401(k) will also increase by 4.0% per year as your salary increases 4.0% each year.

You believe that you can earn 8.0%/year over the next 35 years while saving for retirement.

Once you retire, you have a life expectancy of 25 years. You plan to be more conservative in your investments and expect to earn only 5.0%/year on your investments over the 25 years while in retirement. You also want to maintain your purchasing power by increasing your “annual retirement pay” by the expected inflation rate of 3.0% each year. [Remember, your first withdrawal will be made in Year 0 of retirement (i.e., Year 35 on the timeline.] Assume that after you withdraw the 25^th payment, you will have $0 left in the account.

Questions: [NOTE: there are obviously many steps to get to these answers…scoring is below.]

1. What is your final year’s salary? What is 70% of your salary? [Round to the dollar.]
2. How much will you need in your 401(k) at retirement in order to “pay yourself” 70% of your final year’s salary, AND have that payment to yourself increase at 3.0% each year to maintain purchasing power?
3. How much do you need to contribute each year (i.e., save, invest) over the next 35 years in order to fund your retirement. Remember, payment into the 401(k) is increasing by 4.0% each year.

Scoring:

1. Readability of your Exam. Is it organized, do you show all work, are your answers BOXED in, etc. (10 points)
2. Correctly work problem as an Annuity Due (10 points)
3. Calculate the FV of salary and 70% of salary as first withdrawal from your 401(k) in retirement. (15 points)
4. Do you show a Timeline and is it labeled properly? (15 points)
5. Calculate adjusted interest rate for Retirement Annuity section. (10 points)
6. Calculate the PVA for the Retirement Annuity. (10 points)
7. Calculate the adjusted interest rate for the saving/investing section of problem. (10 points)
8. Calculate the adjusted FVA correctly that is used to determine amount to save each year. (10 points)
9. Calculate the amount you need to save each year; where payment increases as salary increases. (10 points)

Answer 1

1. Final year salary when salary increases by 4% for 35 years is calculated as below

= 75000(1+4%)Power 35 = $295957

70% of salary is $207170

2.PV of payments of retirement to pay 70% of final salary for 25 years

=207170 + 207170(1.03)/1.05+207170(1.03)2/1.05+.......+207170(1.03)24/1.0524 = $4151549

3. Let X be the yearly percentage of salary he should invest in

X*75000*(1.08)35 + X*75000(1.04)(1.08)34+.....+x(1.04)34(1.08)= $4151549

X=$4151549/(292.68*75000) = 18.91%

Using the Future Value of Growing annuity

FV(GA)=Pmt.*(((1+r)power n-(1+g)power n)/(r-g))*(1+r)

Applying values in above formula,

4151549=Pmt.*(((1+0.08)power35-(1+0.04)power35)/(0.08-0.04))*(1+0.08)

By Solving we get annual savings =14186