Investments & Securities Chapter 9 Using The Formula For Social Security Benefits Check Your Understanding Example Rachael S

Chapter 9

Lesson 9-1 Retirement Income

from Savings

B =

12(25)

0.038

$250 1 1

12

⎛⎞

⎜⎟

+−

⎜⎟

⎝⎠

= $124,881.43

+

Check Your Understanding (Example 2)

Check Your Understanding (Example 3)

Half the interest:

0.01125

$300,000 12

0.01125

11

12

⎛⎞

⎜⎟

⎝

⎛⎞

+−

⎜⎟

⎝⎠

Financial Algebra Solutions Manual Chapter 9 Page 132

⎠

Half the years:

0.0225

$300,000 12

⎛⎞

number of years would require a larger monthly

income is between $100,150 and $178,850,

Check Your Understanding (Example 5)

Express P as a decimal by dividing by 100. Then

multiply the result by Robin’s salary, D, to get the

amount her company will match. To express this as

a monthly amount, divide by 12.

P

D×

Applications

1. Retirement requires advanced planning and

B =

0.032

⎝⎠

= $217,029.69

3. Use the future value of a periodic investment

formula and substitute $100 for P, 0.0175 for r,

12 for n, and 42 for t.

12(42)

0.0175

$100 1 1

12

0.0175

12

⎛⎞

⎜⎟

+

−

⎜⎟

⎝⎠

4. Use the compound interest formula and

substitute $50,000 for P, 0.04 for r, 2 for n, and

5a. Use the compound interest formula and

5b. 100% – 22% = 78%

B =

0.039

$10,000 1 1

⎛⎞

+

⎜⎟

⎝⎠

= $26,024.88

6a. Use the future value of a periodic investment

6b. $11,044 × 0.23 ≈ $2,540

6c. $11,044 × 0.1 ≈ $1,104

7. Use the present value of a periodic investment

formula and substitute $600,000 for P, 0.06 for r,

Financial Algebra Solutions Manual Chapter 9 Page 133

8b. B = pert = $400,000e(0.029)(1) = $411,769.84

B = pert = $411,769.84e(0.029)(1) = $423,886.00

formula and substitute $400 for P, 0.039 for r,

12 for n, and $200,000 for B. Solve for t.

12

t

⎛⎞

13

8 =

11

12

+−

⎜⎟

⎝⎠

21

12

0.039

112

t

⎛⎞

+

⎜⎟

12.785 =

t

It will take Bob about 25 years to reach his goal.

0.05

2

11b. 67.40X × 0.2 = 13.48X

11c. penalty amount = 13.48X × 0.1 = 1.348X

T

⎛⎞

XT

12a. Since Jhanvi’s income is between $100,000 and

$112, 650, use the first row of the worksheet.

($110,550 × 0.25) – $4,937.50 = $22,700

12b. ($155,550 × 0.28) – $8,317 = $35,237

12c. $35,237 – $22,700 = $12,537

13. $200 × 26 = $5,200 in contributions; $5,200 ÷

14. The maximum contribution from the employer is

P percent of Mike’s salary, Y, or 100

YP up to M

Lesson 9-2 Social Security Benefits

Check Your Understanding (Example 1)

Check Your Understanding (Example 2)

Check Your Understanding (Example 3)

Check Your Understanding (Example 4)

Check Your Understanding (Example 5)

Divide the taxable amount by the Social Security

Check Your Understanding (Example 6)

Multiply the premium, p, by 12 to get the annual

amount spent; 12p.

Applications

1. When people retire, their income falls and their

also increase with inflation. President Roosevelt

2a. $102,000 × 0.062 = $6,324

2b. $67,010 × 0.062 = $4,154.62

3b. Multiply the combined income by the tax rate

and subtract the maximum tax payable

computed in part a, 0.062(y + p) − 0.062x.

4. 1050 250

−$, $

7. The problem does not state what year Stacy

10 years to qualify for benefits. She must work

until age 46 + 10 = 56.

8b. Rachael’s benefits will be reduced by 6.7%.

$4,100

− $680 = $3,420

0.32 × $3,420 = $1,094.40

x − 0.133x, or 0.867x

11d. Sascha is single so enter $25,000.

11j. The smaller amount is $4,500.

64, her full benefit is reduced by 20%.

$2,101 × 0.2 = $420.20

$32,000.

13e. $123,889.50 − $32,000 = $91,889.50

13f. Linda and Rob are married filing jointly so enter

13k. $79,889.50 × 0.85 = $67,906.08

13l. $6,000 + $67,906.08 = $73,906.08

amount spent; 12x.

15. m + 0.123m = 1.123m

16a. 28 – 21 = 7 ÷ 2 = 3.5 × 4 = 14 credits

Financial Algebra Solutions Manual Chapter 9 Page 135

Check Your Understanding (Example 1)

Check Your Understanding (Example 2)

Check Your Understanding (Example 3)

Check Your Understanding (Example 4)

Since Marina’s pension is based on an average

Check Your Understanding (Example 5)

Calculate Ralph’s annual pension by multiplying his

Applications

1. Although this quote is more likely to be seen on

a T-shirt given to a newly retired person, it

2. 27 × $55 = $1,485

3a. 20 × $50 = $1,000

4. Regardless of the method, all three items are

5a. $28,800 + $28,800 + $29,210 + $29,300

+ $29,900 + $29,900 + $30,250 + $30,350

5b. $37,577.50 × 0.0235 × 24 = $21,193.71

5c. $, .

$,

21193 71

52 000 × 100 = 40.7 or 41%

5d. $21,193.71 ÷ 12 = $1,766.14

6. 2009 salary: $76000 × 1.03 = $78,280

7a. $72,000 + 2($74,780) + $76,000

7b. 2($81,000) + $81,400 + $81,900

2nd-year salary: $80,000 × 1.025 = $82,000

3rd-year salary: $82,000 × 1.025 = $84,050

4th-year salary: $84,050 × 1.025 = $86,151.25

annual benefit: $83,050.31 × 4 × 0.02 × 0.7

= $4,650.82

= $79,000

12b. $35.89(45) = $1,615.05

12c. $1,615.05 × 12 = $19,380.60

14. average salary: $90,000 + $92,598 + $93,000

3

= $91,866

$91,866 ÷ 12 = $7,655.50

$7,655.50 – $600 = $7,055.50

$7,055.50 × 0.30 = $2,116.65

16. $60,000 × 1.02 = $61,200

average salary:

3

17. $100,000 × 0.0212 × 15 = $31,800

18. Substitute the variables noted in the 15 year

formula and the over 15 year formula and add

DEF++

Lesson 9-4 Life Insurance

Check Your Understanding (Example 1)

Check Your Understanding (Example 2)

Check Your Understanding (Example 3)

Multiply the premium, m, by 12 to get the annual

Check Your Understanding (Example 4)

Check Your Understanding (Example 5)

Applications

major events such as births, graduations,

2b. Using the table, the monthly premium would be

$51. $51 × 12 = $612

2d. Using the table, the monthly premium would be

$x. $x × 12 = $12x

4. $780 × 0.40 = $312

$312 × 1.022 = $318.86

5. The probability of death is less for the 20-year-

6a. $134 × 12 = $1,608

$11,260 – $1,608 = $9,652

7b. A 56 year old male has a life expectancy of

23.52 years, so he is expected to live to

56 + 23.52 = 79.52 or 80 years.

is 55.

8b. The greatest integer less than or equal to 55.001

is 0.

8g. The greatest integer less than or equal to 19

is –1.

8j. The greatest integer less than or equal to 2

3

9. Add the interest earned to the cash value and

the number of months the cash value will pay for

x

y

+.

11c. Since the term has not expired, they receive the

face value of the policy, $100,000.

Death at 48: 2($756) – $100,000 = –$98,488

Death at 49: 3($756) – $100,000 = –$97,732

= $1,793.62

12c. $2

1. 24 hours × 60 minutes × 60 seconds = 86,400

seconds per day

day

3. 365 × 24 × 60 × 60 = 31,536,000 seconds in one

year

Applications

1a. $106,800 × 0.062 = $6,621.60

2. $187 × 26 = $4,862

$4,862 ÷ $520 = 9.35

4. $350 × 26 = $9,100

5. $2,128 × 0.133 = $283.02

$2,128 – $283.02 = $1,844.98

6. Line 1: $38,121 is given

Line 4: $450 is given

Financial Algebra Solutions Manual Chapter 9 Page 139

Line 6: $3,211 is given

Line 9: $40,206.50 – $25,000 = $15,206.50

Line 16: $4,500 + $5,275.53 = $9,775.53

7. Convert 4.1 percent to a decimal and add 1 to

8. Multiply the monthly payments by 18 and

9. Add the interest to the cash value and divide by

the monthly payments, then take the greatest

Death at 41: 2($973) – $250,000 = –$248,054

Death at 42: 3($973) – $250,000 = –$247,081

+ (–$245,135)(0.0013) + ($4,865)(0.9947)

= –$199.2216 – $223.2486 – $271.7891

– $295.3296 – $318.6755 + $4,839.2155

12b. Use the future value of a periodic investment

12(1)

0.0225

⎛

⎞

0.0225

⎛

⎞

B

1 = $300,000

0.0225

112

⎛

+

⎜

⎞

⎟

= $320,928.79

0.042 for r, 1 for n, and 13 for t.

B = 1( 1 3 )

0.042

11

⎛⎞

+

−

⎜⎟

= $59,390.48

14a. 5($26,745) + $29,000 + $29,400 + $30,100

+ $39,500 = $681,725

$681,725 ÷ 21 = $32,463.10

15a. $300 × 12 = $3,600

$3,600 + $72,000 = $75,600

15b. pre-tax: Use the table to find tax on $72,000 for

first line of the worksheet.

$100,040 × 0.28 – $5,628 = $22,383.20

17. $57 × 23 × 1.0205 = $1,337.88

18a. 2($54,000) + $55,100 + 2($55,800) + $56,200

+ $56,400 + $57,000 + $60,000 + 3($61,000)

20. Using the table, for 3 years of service he will