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1. If Bozena participates and the 401(k) earns 10 percent annually, how much will she have accumulated in 45 years (to age 67) even if her salary does not change? 2. If she does not participate and...

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1. If Bozena participates and the 401(k) earns 10 percent annually, how much will she have accumulated in 45 years (to age 67) even if her salary does not change?
2. If she does not participate and annually saves $1,600 on her own, how much will she have accumulated if she earns 10 percent and is in the 20 percent federal income tax bracket?
3. If she retires at age 67, given the amounts in (1) and (2), how much can Bozena withdraw and spend each year for 20 years from each alternative? Assume she continues to earn 10 percent (before tax) and remains in the 20 percent federal income tax bracket.
4. If her salary grows, what impact will the increase have on the 40l (k) plan? To illustrate the effect on her accumulated funds, assume a $5,000 increment every five years so that she is earning $72,000 in years XXXXXXXXXXages 63-67).
5. What are the risks and potential returns associated with each of the six alternative funds?
6. Who bears the risk associated with Bozenas retirement income? 7. Why does Ken not have to make these investment decisions? What are the risks associated with his retirement plan?
8. At this point in Bozenas life, which alternative(s) do you suggest she select?


MINI CASE

Ken Saffafs 22-year-old daughter Bozena has just accepted a job with Doctor Medical Systems (DMS), a firm specializing in computer services for doctors. DMS offers employees a 401(k) plan to which employees may contribute 5 percent of their salary. DMS will match $0.50 for every dollar contributed. Bozenas starting salary is $32,000, so she could contribute up to $1,600 and DMS would contribute an additional $800. If she did decide to contribute to the plan, she has the following choices of funds, all managed by Superior Investments. She may select any combination of the funds and change the selection quarterly.
Answered Same Day Dec 22, 2021

Solution

David answered on Dec 22 2021
116 Votes
1
1. This first question illustrates the large amount to which a modest amount will grow over an extended time period.
    Bozena's contribution  $1,600
    Company's match            800
                                   _______
     Total contribution      $2,400
 PMT = -2400; N = 45; I = 10; PV = 0;
  FV = ? = __$1725372______(Qs 1)
  This is the terminal value.
The interest table for the future value of an annuity does not have 45 years. An alternative means to solve the problem is to compute the interest factor.
FVAIF = (1 + i)^n - 1 = (1 + .1)^45 - 1
          ---------------    -------------------
                i                     0.1
= 718.905
                     
The next step is $2,400 X 718.905 = $1,725,372
 
2. If Bozena does not participate in the 401(k) but saves $1,600 annually, she will have considerably less because (1) she does not get the matching funds and (2) her earnings are taxed. Unless she pays the tax obligation from another source of funds, she nets only 8 percent annually. The terminal value is reduced to ______$618,410_____(Qs 2).
(PMT = -1600; N = 45; I = 8; PV = 0; FV = $618408.99)  or  
FVAIF =(1 + i)^n - 1 = (1 + .08)^45 - 1
        ----------------    ---------------------
                   i                   .08
= 386.506
                               
and $1,600 x 386.506 = 618410
(Note: Its assumed that she would save $1600 on after tax basis that is by non contributing to 401(k) does not affect her taxes. If we assume that if she does contribute to 401(k) so her 1600 would be taxed so on after tax basis she would have 1600*(1-.20) = $1280 so the future value = 1280 x 386.506 = $494,728)
3. In this question Bozena withdraws the funds from...
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