Question

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 25h payment, you will have S0 left in the account. Set up and show your Timeline with payments Carry your adjusted interest rates out to 6 decimal places to reduce rounding errors. Questions: NOTE: there are obviously many steps to get to these answers...scoring is below.] What is your final year's salary? What is 70% of your salary? Round to the dollar.] 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? 1. 2. 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

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Answer 1

ANSWER:

1. (a) Final year's salary when salary increase by 4% for 35 years= 75000(1 + 4%)³⁵=$295,957

(b) 70% of salary= 0.7*295957=$207,170

2.so to pay 70% of the fianl salary for 25 years you need to have the present value of those payments at retirement

= 207170 + 207170(1.03)/1.05 + 207170(1.03)²/1.05 + ...................+ 207170(1.03)²⁴/1.05²⁴=$4,151,549

3. So get the yearly percentage of salary that he should put in be x

=> x * 75000*(1.08)³⁵+ x* 75000 ( 1.04)(1.08)³⁴+..........+ x(1.04)³⁴(1.08)=4,151,549

=> x= 4151549/(292.68*75000)= 18.91%

Answer 2

Q#1

The final year’s salary after the increase of 4% every year for the next 35 years will be calculated as below:

= $75,000 * (1 + 4%) ³⁵

= $75,000 * 3.95

= $295,957

The second part of the question is what will the 70% of your salary:

= $295,957 * 70%

= $295,957 * 0.7

= $207,170

Q#2

To ‘pay myself’ 70 percent of my last year’s salary along with 3 percent increase my purchasing power, the amount that I should have in my 401(k) at retirement is calculated as below.

Since the life expectancy remaining is 25 years, we need the present values of all these payments for retirement:

= 207170 + 207170 * (1+3%)/1.05 + 207170(1+3%) ² /1.05 + ............+ 207170(1+3%) ²⁴/1.05²⁴

⁼ $4,151,549

 

Q#3

In order to fund my retirement, along with the increase of 4% every year in my 401(k), the amount that I would have to contribute each year will be calculated as below:

Let’s suppose that the amount to be contributed to be x.

Then

= x * $75,000*(1.08)³⁵+ x * $75,000 (1.04) (1.08)³⁴+.......+ x * $75,000(1.04)³⁴   (1.08) =$4,151,549

x = $415,1549 / (292.68 * $75,000)= 18.91%