© The McGraw-Hill Companies, Inc., 2008 McGraw-Hill/Irwin 7-1 Chapter 7 Retirement Plans STARTEXIT.

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© The McGraw-Hill Companies, Inc., 2008McGraw-Hill/Irwin

Chapter 7

Retirement Plans

START EXIT

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Chapter Outline

7.1 Basic Principles of Retirement Planning

7.2 Details of Retirement Plans

7.3 Assessing the Effect of Inflation

Chapter Summary

Chapter Exercises

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• Most retirement programs fall into one of two categories: defined benefit plans and defined contribution plans.

• A defined benefit (DB) plan is a retirement program that provides a set income in retirement, which may be calculated on the basis of pre-retirement earnings, years worked, retirement age, and/or the period of time for which benefits are guaranteed to be paid.

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Example 7.1.1• Problem

– A union retirement plan promises an income to union members beginning at age 65 and continuing until death. The formula states that retirees who have at least 5 years of service will receive a monthly income of $80 for each year of service, up to a maximum monthly income of $2,000.

– Find the benefit that would be payable to a member who retires at age 65 with (a) 4 years of service, (b) 10 years of service, and (c) 40 years of service.

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Example 7.1.1 Cont.

• Solution– Since the formula requires a minimum of 5 years

of service, someone retiring with fewer than 5 years would not receive any benefit.

– For someone with 10 years of service, the monthly benefit would be 10 x $80 = $800

– For someone with 40 years of service, the monthly benefit would be $2,000. Even though 40 x $80 = $3,200, the maximum benefit is $2,000.

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– The XYZ Corporation Pension Plan provides a lifetime income to its employees on retirement at age 65. The formula provides 2% for each year of service of the average of the employee’s earnings for the last 3 years on the job, up to a maximum of 70%.

– Jelena retired at 65 with 28 years of service. Her earnings for the last 3 years were $37,650, $39,525, and $40,187.

– What is her pension benefit?

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Example 7.1.2 Cont.• Solution

– Jelena is entitled to 28 x 2% = 56% of her final 3-year average income

– Her 3-year average income is

($37,650 + $39,525 + $40,187)/3 = $39,120.67

– So her annual pension benefit is

56% x $39,120.67 = $21,907.53 per year

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– The XYZ Corporation offers employees the choice to retire as early as age 60 or as late as age 72. Those retiring before age 65 have their calculated benefit reduced by 2.5% for each year they retire prior to age 65; those retiring later have their benefit increased by 1.9% for each year beyond age 65 that they work.

– Brooke plans to retire this year at age 63. She has 19 years of service to the company and her last 3 years’ earnings were $48,000, $52,000, and $54,000.

– Kurt plans to retire this year at age 69. He has 37 years of service and his last 3 years’ earnings were $41,500, $43,750, and $46,300.

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– Brooke’s 19 years of service entitle her to 38% of benefits.

– Her final 3-year average salary is $51,333.33. If she were 65, her annual benefits would be $19,506.67.

– Because she is retiring 2 years early, she will give up 2 x 2.5% = 5% of the benefit.

– So her annual benefits would be only $19,506.67 x 95% = $18,531.34.

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– Kurt’s 37 years of service would give him 74%, except that the maximum is 70%.

– His final 3-year average salary is $43,850.– If he were 65, his benefit would be $30,695 per

year.– Retiring 4 years later means he will get an extra 4

x 1.9% = 7.6%.– So he will get $30,695 x 107.6% = $33,027.82

per year.

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• Unlike defined benefit plans, defined contribution (DC) plans do not provide a fixed, guaranteed income in retirement.

• Instead, the employer contributes money to a retirement account for each employee on the basis of some set formula.

• The money is then invested and grows in value during the employee’s working years.

• Sometimes the contributions to the plan are made entirely by the employer. In most cases, though, the employee is either permitted or required to contribute money as well.

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Example 7.1.4 • Problem

– The company Jesse works for contributes 8% of each employee’s annual earnings to a defined contribution plan, provided that the employee contributes at least 3%. Jesse makes $32,500 per year. How much will go into his account this year if he contributes (a) nothing, (b) 3%, and (c) 10% of his income?

• Solution– If Jesse does not contribute anything, he is not qualified for

any employer’s contributions.– If Jesse contributes 3%, his employer will contribute 8%.

Therefore, the total contribution would be 11% x $32,500 = $3,575.

– If Jesse contributes 10%, his employer will contribute 8%. Therefore the total contribution would be 18% x $32,500 = $5,850.

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– Daxxilon Digital Devices has a defined contribution plan. The company matches 75% of each employee’s contributions up to a maximum of 10%.

– Hamid earns $60,000. How much will be deposited to this account this year if he contributes (a) nothing, (b) 5%, and (c) 15% of his earnings?

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– If Hamid contributes nothing, his company won’t contribute anything either.

– If Hamid contributes 5%, his portion would be 5% x $60,000 = $3,000. His employer will contribute 75% x $3,000 = $2,250. So the total contribution would be $3,000 + $2,250 = $5,250

– If Hamid contributes 15%, his portion would be 15% x $60,000 = $9,000. His employer will contribute 75% x (10% x $60,000) = $4,500. The total contribution would be $9,000 + $4,500 = $13,500.

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• After you have accumulated a certain number of years of service, you become vested in the plan, meaning that any benefits earned will not be lost, regardless of whether or not you continue working or even if the plan is discontinued.

• How quickly someone attains this vesting is determined by a vesting schedule.

• With cliff vesting, it is an all-or-nothing deal. After a certain number of years of service, you become fully vested in the plan; prior to that point, you have no vested benefit and will receive no benefits from the plan if you depart before that point.

• With step vesting, you may be entitled to a certain percent of your benefits, depending on your years of service when you leave.

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– Dave has just been laid off from hisjob. He was covered by the company’s defined benefit pension plan, which provides a benefit of 2% final year’s salary for each completed year of service, beginningat age 65.

– Dave earned $43,600 at this job in the last year, and had completed 6 years of service.

– The pension plan uses the 7-year 20% vesting schedule. What is Dave’s vested benefit?

Yrs of Service

Completed

Vesting Percent

< 3 years 0%

3-4 years 20%

4-5 years 40%

5-6 years 60%

6-7 years 80%

7+ years 100%

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– Dave is entitled to 6 x 2% = 12% ofsalary as a benefit.

– However, he has only 6 years ofservice and so he eligible for only80% of the benefits.

– Therefore, his vested benefit is (12% x $43,600) x 80% = $4,185.60per year, beginning at age 65.

Yrs of Service

Completed

Vesting Percent

< 3 years 0%

3-4 years 20%

4-5 years 40%

5-6 years 60%

6-7 years 80%

7+ years 100%

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– Kelly is leaving her job afterworking there for 3 ½ years.

– She has contributed a total of$5,722.16.

– The company contributed a totalof $4,810.33.

– Find her vested balance in thisplan.

Yrs of Service

Completed

Vesting Percent

< 3 years 0%

3-4 years 20%

4-5 years 40%

5-6 years 60%

6-7 years 80%

7+ years 100%

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– She is eligible for 20% of employer’s contribution, so thatportion is 20% x $4,810.33 =$962.07.

– Her own contribution is alwaysfully vested so she will keep$5,722.16 + $962.07 = $6,684.23

Yrs of Service

Completed

Vesting Percent

< 3 years 0%

3-4 years 20%

4-5 years 40%

5-6 years 60%

6-7 years 80%

7+ years 100%

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Section 7.1 Exercises

Problem 1: Defined Benefit Plans

Problem 2: Defined Contribution Plans

Problem 3: Vesting

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Problem 1

• Pacifica International has a defined benefit pension plan. On retirement at age 65, the plan provides 1.75% of the 3-year final average salary for each year of service, up to a maximum of 60%.

• Dave has 25 years of service and his 3-year final average salary is $48,734.

• Calculate his pension benefit.

CHECK YOUR ANSWER

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Solution 1• Pacifica International has a defined benefit pension plan.

On retirement at age 65, the plan provides 1.75% of the 3-year final average salary for each year of service, up to a maximum of 60%.

• Dave has 25 years of service and his 3-year final average salary is $48,734.

• Calculate his pension benefit.

• Dave qualifies for 1.75% x 25 = 43.75%• 43.75% x $48,734 = $21,321.13

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Problem 2

• Fischer’s Bakery offers its employees a defined contribution retirement plan with 40% matching up to 10% of salary. If Rhonda’s annual salary is $39,400, how much will be deposited to her account if she contributes 5% of her salary?

CHECK YOUR ANSWER

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Solution 2• Fischer’s Bakery offers its employees a defined

contribution retirement plan with 40% matching up to 10% of salary. If Rhonda’s annual salary is $39,400, how much will be deposited to her account if she contributes 5% of her salary?

• Rhonda’s Contribution: $39,400 x 5% = $1,970• Employer’s Contribution: $1,970 x 40% = $788• Total Contribution = $1,970 + $788 = $2,758

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Problem 3• Sally has $23,498 in her defined

contribution plan at work. Of thatbalance, $15,264 comes from heremployer.

• The plan uses the 7-year stepvesting schedule.

• How much of her balance wouldSally keep if she has 6 ½% yearsof service?

CHECK YOUR ANSWER

Yrs of Service

Completed

Vesting Percent

< 3 years 0%

3-4 years 20%

4-5 years 40%

5-6 years 60%

6-7 years 80%

7+ years 100%

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Solution 3• Sally has $23,498 in her defined contribution

plan at work. Of that balance, $15,264 comes from her employer.

• The plan uses the 7-year step vesting schedule.• How much of her balance would Sally keep if

she has 6 ½% years of service?• Her own contribution is $23,498 -- $15,264 =

$8,234 and she keeps the full amount.• However, she will be able to keep only 80% of

employer’s contribution so that comes to 80% x $15,264 = $12,211.20

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• An individual retirement account (IRA) is a special type of account that can be set up by an individual through almost any bank, brokerage firm, credit union, or other financial institution.

• The purpose of an IRA is to allow an individual to save for retirement, and the tax laws offer significant tax advantages to encourage people to set up and contribute to these sorts of accounts.

• There are limits, however, to how much an individual can contribute to an IRA in any one year.

• An IRA is not a type of investment in itself; it’s a type of account that can contain almost any sort of investment within it.

• Also, money invested in an IRA can’t usually be withdrawn until its owner reaches age 59 ½.

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• Roth IRAs are a special type of IRA. They get their name from the late Senator William Roth of Delaware, who championed their creation.

• Contributions to a Roth IRA are not tax deductible but, like ordinary IRAs, their investment growth is not taxed while the money is in the account.

• Roth IRAs have a unique advantage, though, because their investment growth is not taxed when money is withdrawn from the account either.

• In other words, all of the investment growth from a Roth IRA is income tax free, not just income tax deferred.

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– Sarah has $3,000 that she wants to invest in an IRA. She expects that this money will earn 9% and does not expect to withdraw the money from her IRA for another 40 years.

– Assuming that she will pay a 30% rate for combined state and federal income taxes, how much will she have after taxes if she invests in (a) a Roth IRA or (b) a traditional IRA.

• Solution– Compounded at 9% for 40 years, her $3,000 would grow to:

FV = PV(1 + i)n

FV = $3,000(1 + 0.09)40 = $94,288No taxes will be owed when she withdraws her money from a Roth IRA

– Her money would grow to the same amount in a traditional IRA. However, paying 30% in income taxes would leave her with 70% x $94,288 = $65,960.

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• 401(k)s are a type of retirement account offered as a benefit by employers. Workers contribute to their 401(k) accounts by payroll deductions and money contributed is not included in taxable income.

• As in a traditional IRA, the money grows tax-deferred, and is subject to income tax when it is withdrawn from the plan.

• When a company sets up a 401(k) plan for its employees, it generally selects a plan administrator such as a bank, insurance company, or mutual fund company.

• Employees control how their money is invested by choosing from a selection of mutual funds.

• In many, though not all, cases the employer offers some matching of the employee’s contributions.

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– Lisette makes $26,735 annually working for Shender Chemical Corp. The company offers a 401(k) plan with 75% matching up to 6% of salary. How much in total would Lisette have deposited to her 401(k) each year if she decides to contribute (a) 4% or (b) 10%.

• Solution– 5% of her annual salary is 5% x $26,735 = $1,336.75– The company will match 75% of this amount or

75% x $1,336.75 = $1,002.56– In total, this makes $1,336.75 + $1,002.56 = $2,339.51– 10% of her annual salary is 10% is $2,637.50– The company will match 75%(6% x $2,637.50) = $1,186.88– In total, this makes $2,637.50 + $1,186.88 = $3,824.38

7-32



– Curt is 24 years old and just started a new job which offers a 401(k) plan. He will be making $31,000 per year.

– Looking to the future, Curt is wondering what percent of his salary he should contribute to the 401(k) if he wants to have $750,000 in this account when he reaches age 65.

– He is paid biweekly, his company does not offer any matching, and he expects that his investments can earn 10%.

• SolutionFV = PMTsn/i

$750,000 = PMT x 15,305.57734PMT = $49.00

Curt’s biweekly pay will be $31,000/26 = $1,192.31. A $49 contribution amounts to $49.00/$1,192.31 = 4.11%

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– Nancy earns $26,000 per year and is paid biweekly. She wants to have $250,000 in her 401(k) 30 years from now, and thinks that her investments can earn 8 ½%. Her employer matches the contributions 50% up to 8% of salary. How much of her salary should she contribute?

• SolutionFV = PMT x sn/i

$250,000 = PMT x 3,595.324968PMT = $69.53This total includes both her and her employer’s contributions, so150% x Nancy’s Contribution = $69.53Nancy’s Contribution = $46.35Her biweekly pay will be $26,000/26 = $1,000.A $46.35 contribution amounts to $46.35/$1,000 = 4.64%

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Section 7.2 Exercises

Problem 1:

Traditional and

Roth IRAs

Problem 2:

401(k) Plan Projections

7-35

Problem 1

• Suppose Misty deposits $2,000 into a Roth IRA which earns an average rate of 9% for the next 30 years. What is the future value of this deposit?

CHECK YOUR ANSWER

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Solution 1• Suppose Misty deposits $2,000 into a

Roth IRA which earns an average rate of 9% for the next 30 years. What is the future value of this deposit?

• FV = PV(1 + i)n

FV = $2,000(1 + 9%)30

FV = $26,535.36

BACK TO GAME BOARD

7-37

Problem 2

• Jolanda’s company offers a 401(k) plan with no employer match. She would like to have $500,000 in her account in 30 years. Her annual salary is $48,000. She believes her investments can earn 7%.

• How much should she be depositing with each paycheck if she gets paid monthly?

CHECK YOUR ANSWER

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Solution 2• Jolanda’s company offers a 401(k) plan with no employer match.

She would like to have $500,000 in her account in 30 years. Her annual salary is $48,000. She believes her investments can earn 7%.

• How much should she be depositing with each paycheck if she gets paid monthly?

• FV = PMTsn/i

$500,000 = PMT x 1219.008563

PMT = $410.17

BACK TO GAME BOARD

008563.12190.00583

1)0.005831(

i

1)i1( 360

/

n

ins

7-39



– Loosely speaking, inflation is the tendency of prices to rise over time.

– Suppose that a lawnmower costs $189.95 today and that you expect lawnmower prices to rise at a 4% effective rate in the future. If your assumption is correct, how much would this mower cost 20 years from now?

• Solution– FV = PV(1 + i)n

FV = $189.95(1 + 4%)20 = $416.20

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– Suppose you want to have $1,000,000 in your 401(k) account in 40 years. How much do you need to deposit into this account each week to achieve your goal if you expect to earn 9% on your investments?

– Also assume that your goal is not $1,000,000 in actual dollars but instead in today’s dollars.

7-41


Example 7.3.2• Solution

– Our first step is to figure out what the actual goal is. Of course, since we can’t know what inflation will be over the next 40 years, there is now way to know this for sure. We will assume a 3.5% inflation rate.FV = PV(1 + i)n

FV = $1,000,0000(1 + 3.5%)40 = $3,959,260– So the goal is to actually have $3,959,260.

FV = PMTsn/i

$3,959,260 = PMT x 20502.17PMT = $193.11

17.205020.0017307

1)0.00173071(

i

1)i1( 2080

/

n

ins

7-42

Chapter 7 Summary

• Defined Benefit Plans• Defined Contribution Plans• Vesting• IRAs• Roth IRAs• 401(k)s• Projections with Inflation

7-43

Chapter 7 Exercises

Section 7.1 Section 7.2 Section 7.3

$100 $100 $100

$200 $200 $200

EXIT

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Section 7.1 -- $100• The Reynolds Enterprises, Inc. provides a lifetime income to its

employees on retirement at age 65. The formula provides 1.5% for each year of service of the average of the employee’s earnings for the last 3 years of service, up to a maximum of 75%.

• However, employees can retire as early as 60 or as late as 70. Those retiring before age 65 have their calculated benefit reduced by 1.5% for each year they retire prior to age 65. Those retiring later have their benefit increased by 1.5% for each year beyond age 65.

• Linda plans to retire this year at age 67. She has 30 years of service and her average salary for the last 3 years was $49,371.

• What is her pension benefit?

CHECK YOUR ANSWER

7-45

Section 7.1 -- $100• The Reynolds Enterprises, Inc. provides a lifetime income to its employees

on retirement at age 65. The formula provides 1.5% for each year of service of the average of the employee’s earnings for the last 3 years of service, up to a maximum of 75%.

• However, employees can retire as early as 60 or as late as 70. Those retiring before age 65 have their calculated benefit reduced by 1.5% for each year they retire prior to age 65. Those retiring later have their benefit increased by 1.5% for each year beyond age 65. Linda plans to retire this year at age 67. She has 30 years of service and her average salary for the last 3 years was $49,371.

• 30 x 1.5% = 45%

• 45% x $49,371 = $22,216.95

• 2 x 1.5% = 3%

• $22,216.95 x 103% = $22,883.46

BACK TO GAME BOARD

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Section 7.1 -- $200• Fabrics Galore, Inc. contributes 5% of

each employee’s annual earnings to a defined contribution plan. In addition, employees can contribute up to 20% of their annual pay.

• Shalonda makes $52,397 per year. How much will go into her account this year if she contributes 10%?

CHECK YOUR ANSWER

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Section 7.1 -- $200

• Fabrics Galore, Inc. contributes 5% of each employee’s annual earnings to a defined contribution plan. In addition, employees can contribute up to 20% of their annual pay.

• Shalonda makes $52,397 per year. How much will go into her account this year if she contributes 10%?

• 5% x $52,397 = $2,619.85

• 10% x $52,397 = $5,239.70

• Total Contributions = $7,869.55

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7-48

Section 7.2 -- $100

• Jasmine would like to invest last year’s income tax refund, $1,849, in an IRA. She expects that this money will earn 8% for the next 35 years.

• Assuming that Jasmine will pay a 32% combined state and federal income taxes, how much will she have after taxes?

CHECK YOUR ANSWER

7-49

Section 7.2 -- $100• Jasmine would like to invest last year’s income tax

refund, $1,849, in an IRA. She expects that this money will earn 8% for the next 35 years.

• Assuming that Jasmine will pay a 32% combined state and federal income taxes, how much will she have after taxes?

• FV = PV(1 +i)n

FV = $1,849(1 + 8%)35

FV = $27,338.10Taxes = 32% x $27,338.10 = $8,748.19Therefore, Jasmine will have a total of $27,338.10 -- $8,748.19 = $18,589.91

BACK TO GAME BOARD

7-50

Section 7.2 -- $200

• Gerard makes $82,400 annually working for Chesapeake Bay Accounting Services. The company offers a 401(k) plan with 70% matching up to 10% of salary. How much would be deposited to Gerard’s account if he contributes 5%?

CHECK YOUR ANSWER

7-51

Section 7.2 -- $200

• Gerard makes $82,400 annually working for Chesapeake Bay Accounting Services. The company offers a 401(k) plan with 70% matching up to 10% of salary. How much would be deposited to Gerard’s account if he contributes 5%?

• $82,400 x 5% = $4,120

• $4,120 x 70% = $2,884

• Total = $4,120 + $2,884 = $7,004

BACK TO GAME BOARD

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Section 7.3 -- $100

• Suppose a refrigerator costs $1,200 today and you suspect the prices will rise at 3.5% effective rate in the future. How much would an equivalent refrigerator cost in 10 years?

CHECK YOUR ANSWER

7-53

Section 7.3 -- $100• Suppose a refrigerator costs $1,200 today and

you suspect the prices will rise at 3.5% effective rate in the future. How much would an equivalent refrigerator cost in 10 years?

• FV = PV(1 + i)n

FV = $1,200(1 + 3.5%)10 = $1,692.72

BACK TO GAME BOARD

7-54

Section 7.3 -- $200• Jennifer would like to have $500,000 in her

401(k) account in 30 years. How much would she really need to deposit into this account over the period of 30 years if her goal is not $500,000 in actual dollars but instead $500,000 in today’s dollars (expected inflation rate is 3.5%).

CHECK YOUR ANSWER

7-55

Section 7.3 -- $200• Jennifer would like to have $500,000 in her 401(k)

account in 30 years. How much would she really need to deposit into this account over the period of 30 years if her goal is not $500,000 in actual dollars but instead $500,000 in today’s dollars (expected inflation rate is 3.5%).

• FV = PV(1 + i)n

FV = $500,000(1 + 3.5%)30 = $1,403,396.85

BACK TO GAME BOARD

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