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1

Retirement: 1-3,4 Retirement Planning Calculations

If an individual is projected to have an annual retirement income deficit of $50,000 (in first retirement-year dollars) and expects to earn an average annual 7% investment return over a 30-year retirement period, what is the lump-sum retirement fund required? Assume a 4% inflation rate.

1-3,4

Period = 1
Mode = BEG
N = 30
I/YR = 2.8846%
PV = ?
PMT = $50,000
FV = N/A

PV = $1,023,500

2

Retirement: 1-3,4 Retirement Planning Calculations

John and Betty are both age 47, and anticipate retiring when they are both age 66. With your help they have determined that their retirement income shortfall, in today’s dollars, is $35,000. They want to plan for a 30-year retirement period since longevity runs in their families. Assuming a 6.5% rate of return, and an inflation rate of 3%, what lump-sum amount would they need at the beginning of retirement to fund this income shortfall using the capital utilization method?

1-3,4

Step 1:
Period = 1
Mode = BEG
N = 19
I/YR = 3%
PV = $35,000
PMT = N/A
FV = ?

FV = $61,373

Step 2:
Period = 1
Mode = BEG
N = 30
I/YR = 3.3981%
PV = ?
PMT = $61,373
FV = N/A

PV = $1,182,176

3

Retirement: 1-3,4 Retirement Planning Calculations

The Cornells plan to retire in 15 years, and have determined that they will need an additional $ 70,000 per year in retirement year one dollars in order to enjoy the type of retirement they envision. They want to plan for a 25-year retirement period, expect to achieve a blended rate of return on their investments of 6%, and expect inflation to run at 3.5%. They have asked you to calculate the lump-sum amount they will need at the beginning of retirement to fund this shortfall.

1-3,4

Period = 1
Mode = BEG
N = 25
I/YR = 2.4155%
PV = ?
PMT = $70,000
FV = N/A

PV = $1,333,716

4

Retirement: 1-3,4 Retirement Planning Calculations

Module Check Summary

10. John and Sally have assets worth $84,000 that they plan to use to fund their retirement in 17 years. If they expect the assets to continue to grow at an annual rate of 7%, what will the assets be worth in 17 years?

a. $235,647

b. $245,762

c. $255,879

d. $265,340

(LO 1-3)

d. $265,340

Period = 1
Mode = BEG
N = 17
I/YR = 7%
PV = 84,000
PMT = $0
FV = ?

FV = $265,340

5

Retirement: 1-3,4 Retirement Planning Calculations

Module Check Summary

11. You have determined with Bob and Jill that their current resources will provide an annual retirement income deficit of $37,000 (in first-retirement-year dollars). They expect to earn an average yearly return on their investments of 6%. They also assume inflation will average 4% during their retirement. Using a 27-year retirement period, what is the lump-sum retirement fund required?

$773,603

$788,482

$1,318,712

$2,498,540

(LO 1-4)

$788,482

Period = 1
Mode = BEG
N = 27
I/YR = 1.9231%
PV = ?
PMT = 37,000
FV = N/A

PV = $788,482


6

Retirement: 1-3,4 Retirement Planning Calculations

Module Check Summary

12. After meeting with your clients, the Smiths, you have determined that their annual retirement income need, net of expected Social Security benefits, will be $22,000 in today’s dollars. They anticipate an annual after-tax return of 6% on their investments, and they expect inflation to average 4% over the long term. They also plan to retire in 25 years, and they want their projected retirement income to last for 30 years. Based upon this information, determine the lump-sum amount (plus or minus $25) that the Smiths will need at the beginning of retirement to fund their retirement.

$1,313,507

$1,327,503

$1,339,777

$1,353,036

(LO 1-4)

$1,353,036

Step 1:
Period = 1
Mode = BEG
N = 25
I/YR = 4%
PV = $22,000
PMT = $0
FV = ?

FV = $58,648

Step 2:
Period = 1
Mode = BEG
N = 30
I/YR = 1.9231%
PV = ?
PMT = $58,648
FV = $0

PV = $1,353,036

7

Retirement: 1-3,4 Retirement Planning Calculations

Module Check Summary

13. Bill and Mary Parker are projected to need a lump-sum retirement fund of $4,353,036. Their assets will amount to $4 million at the beginning of the first retirement year, leaving $353,036 to be saved over the pre-retirement period. The Parkers have 25 years until they plan to retire. Based upon an expected 4% inflation rate and a 6% after-tax return on their investments, calculate the Parkers’ first end-of-year (increasing) savings requirement.

$4,215

$4,260

$4,299

$4,342

(LO 1-4)

$4,342

Step 1:
Period = 1
Mode = BEG
N = 25
I/YR = 4%
PV = ?
PMT = $0
FV = $353,036

PV = $132,430

Step 2:
Period = 1
Mode = END
N = 25
I/YR = 1.9231%
PV = $0
PMT = ?
FV = $132,430

PMT = $4,175

Step 3:
$4,175
+ 4%
= $4,342

8

Retirement: 1-3,4 Retirement Planning Calculations

Module Check Summary

14. The Simsons need to save an additional $300,000 (in retirement year 1 dollars) to build a retirement fund that is capable of supporting their targeted retirement lifestyle. They expect to earn a 7% after-tax return on their retirement savings and are assuming a 5% long-term inflation rate. Their preference is to allocate a level annual savings amount to build this fund. What level annual end-of-year savings amount will the Simsons need to deposit at the end of each year during their 20-year pre-retirement period?

$4,698

$7,318

$9,073

$12,347

(LO 1-3,4)

$7,318

Period = 1
Mode = END
N = 20
I/YR = 7%
PV = $0
PMT = ?
FV = $300,000

PMT = $7,318

9

Retirement: 1-3,4 Retirement Planning Calculations

The following is the formula for what?

Period = 1
Mode = BEG
N = number of periods (years) until retirement
I/YR = growth/appreciation rate
PV = current market value
PMT = N/A
FV = ?

FV = ?

a. Estimate future value of available resources at retirement.

b. Estimate future value of future savings/investment program at retirement.

c. Determine retirement fund needed to meet income deficit.


(LO 1-3,4)

a. Estimate future value of available resources at retirement.

10

Retirement: 1-3,4 Retirement Planning Calculations

The following is the formula for what?

Period = 1
Mode = BEG
N = number of periods (years) until retirement
I/YR = fund earnings rate
PV = N/A
PMT = annual level savings amount
FV = ?

FV = ?

a. Estimate future value of available resources at retirement.

b. Estimate future value of future savings/investment program at retirement.

c. Determine retirement fund needed to meet income deficit.

(LO 1-3,4)

b. Estimate future value of future savings/investment program at retirement.

11

Retirement: 1-3,4 Retirement Planning Calculations

Fred and Wilma are both age 40 and plan to retire at age 62, so they have 22 years until retirement. The anticipate inflation at 3%. The PV of their deficit is $22,000. So the future value of the income amount they would need in the first year of retirement is:

(LO 1-3,4)

Period = 1
Mode = BEG
N = 22
I/YR = 3%
PV = $22,000
PMT = $0
FV = ?

FV = $42,154

12

Retirement: 1-3,4 Retirement Planning Calculations

When calculating an income stream in retirement you should always have your calculator set in the ____ mode. This is because when clients retire they will always need the money at the beginning of each year to then pay for retirement.

a. BEG

b. END

(LO 1-3,4)

a. BEG

13

Retirement: 1-3,4 Retirement Planning Calculations

Keep in mind that unless otherwise indicated, retirement income payments are assumed to be made at the _____ of the year, while savings to build the retirement fund are deposited at the _____ of the year

BEG

END

(LO 1-3,4)

Keep in mind that unless otherwise indicated, retirement income payments are assumed to be made at the BEG of the year, while savings to build the retirement fund are deposited at the END of the year

14

Retirement: 1-3,4 Retirement Planning Calculations

The following is the formula for what?

Period = 1
Mode = BEG
N = number of periods (years) until retirement
I/YR = Inflation rate
PV = present value of retirement income deficit
PMT = N/A
FV = ?

FV = ?

a. Estimate future value of available resources at retirement.

b. Estimate future value of future savings/investment program at retirement.

c. Determine retirement fund needed to meet income deficit.

(LO 1-3,4)

c. Determine retirement fund needed to meet income deficit.

15

Retirement: 1-3,4 Retirement Planning Calculations

Fred and Wilma need to save an additional $768,064 by the beginning of retirement to make up for their
shortfall from Social Security and any inflation-adjusted pensions to achieve the level of retirement income ($22,000 in today’s dollars, $42,154 in retirement year one dollars) that they desired. Fred and Wilma have 22 years until retirement and they assume to earn 7% on their investments, so the annual level savings amount would be:

a. $13,673

b. $14,673

c. $15,673

1-3,4

c. $15,673

Period = 1
Mode = END
N = 22
I/YR = 7%
PV = N/A
PMT = ?
FV = $768,064

PMT = $15,673

Note that this is done in the “end” mode, not the “begin” mode. As stated before, unless otherwise indicated, retirement income payments are assumed
to be made at the beginning of the year to pay for that year’s expenses, while savings to build the retirement fund are deposited at the end of the year. If Fred and Wilma deposit $15,673 at the end of each year for the next 22 years, and earn a 7% return on their savings, they will get to the $768,064 that they need. We have already taken inflation into account when we calculated the $768,064, so we do not concern ourselves with it in this calculation; all that is needed is the rate of return.

16

Retirement: 1-3,4 Retirement Planning Calculations

Which of the following is the 2nd step in the Serial Payment approach?

a. calculate the payment using the discounted lump sum from step (1) as a future value and an inflation-adjusted return as the interest rate

b. once payment has been solved for it will need to be inflated by the inflation rate in order to arrive at the end of first year payment

c. deflate the lump sum needed at retirement into today’s dollars, using the inflation rate as the discount rate

1-3,4

a. calculate the payment using the discounted lump sum from step (1) as a future value and an inflation-adjusted return as the interest rate

17

Retirement: 1-3,4 Retirement Planning Calculations

Which of the following is the 3rd step in the Serial Payment approach?

a. calculate the payment using the discounted lump sum from step (1) as a future value and an inflation-adjusted return as the interest rate

b. once payment has been solved for it will need to be inflated by the inflation rate in order to arrive at the end of first year payment

c. deflate the lump sum needed at retirement into today’s dollars, using the inflation rate as the discount rate

1-3,4

b. once payment has been solved for it will need to be inflated by the inflation rate in order to arrive at the end of first year payment

18

Retirement: 1-3,4 Retirement Planning Calculations

Which of the following is the 1st step in the Serial Payment approach?

a. calculate the payment using the discounted lump sum from step (1) as a future value and an inflation-adjusted return as the interest rate

b. once payment has been solved for it will need to be inflated by the inflation rate in order to arrive at the end of first year payment

c. deflate the lump sum needed at retirement into today’s dollars, using the inflation rate as the discount rate

1-3,4

c. deflate the lump sum needed at retirement into today’s dollars, using the inflation rate as the discount rate

19

Retirement: 1-3,4 Retirement Planning Calculations

Fred and Wilma need a lump-sum of $768,064 at the beginning of retirement 22 years from now, and that the inflation rate is 3%, and the rate of return 7%. There are three steps in the serial payment calculation:

Step 1
Period = 1
Mode = BEG
N = 22
I/YR = 3%
PV = ?
PMT = $0
FV = $768,064

PV = $400,847

Step 2:
Period = 1
Mode = END
N = 22
I/YR = 3.8835%
PV = $0
PMT = ?
FV = $400,847

PMT = $11,863.24

Step 3:
$11,863.24 * 1.03 = $12,219.14