Lesson 9-1 Retirement Income
from Savings
Check Your Understanding (Example 1)
12(25)
0.038
$250 1 1
12
⎛⎞
⎛⎞
⎜⎟
+−
⎜⎟
⎜⎟
⎝⎠
B =
12
⎜⎟
⎜⎟
⎝⎠
⎝⎠
= $191,813.77
Check Your Understanding (Example 2)
Check Your Understanding (Example 3)
Half the interest:
Check Your Understanding (Example 4)
Add her taxable income to her withdrawal to get her
Check Your Understanding (Example 5)
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.
100
P
D×
Applications
1. Retirement requires advanced planning and
2. Use the future value of a periodic investment
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.
25 for t.
B =
1( 2 5 )
0.05
$10,000 1 1
⎛⎞
+
= $33,863.55
6a. Use the future value of a periodic investment
formula and substitute $500 for P, 0.04 for r,
6b. $11,044 × 0.23 ≈ $2,540
6c. $11,044 × 0.1 ≈ $1,104
7. Use the present value of a periodic investment
8a. $88,000 × 0.6 = $52,800
8b. B = pert = $400,000e(0.029)(1) = $411,769.84
12 for n, and $200,000 for B. Solve for t.
12
0.039
t
⎛⎞
⎛⎞
13
8 =
12
0.039
11
12
t
⎛⎞
+−
⎜⎟
⎝⎠
12
0.039
t
⎛⎞
0.039
log 1 12
⎛⎞
+
⎜⎟
⎝⎠
12.785 =
t
10c. $13,138 – $11,938 = $1,200
11a. Use the future value of a periodic investment
12a. Since Jhanvi’s income is between $100,000 and
12b. ($155,550 × 0.28) – $8,317 = $35,237
12c. $35,237 – $22,700 = $12,537
12d. $45,000 × 0.1 = $4,500
14. The maximum contribution from the employer is
P percent of Mike’s salary, Y, or 100
YP up to M
YP • 100
M = 10,000
YMP .
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)
Check Your Understanding (Example 6)
Applications
1. When people retire, their income falls and their
2a. $102,000 × 0.062 = $6,324
2b. $67,010 × 0.062 = $4,154.62
3a. Multiply the maximum taxable income by the tax
rate expressed as a decimal, 0.062x.
3b. Multiply the combined income by the tax rate
and subtract the maximum tax payable
computed in part a, 0.062(y + p) − 0.062x.
−$, $
7. The problem does not state what year Stacy
8b. Rachael’s benefits will be reduced by 6.7%.
$4,100
− $680 = $3,420
x − 0.133x, or 0.867x
11c. $67,649 − $3,211 = $64,438
11d. Sascha is single so enter $25,000.
11i. $9,000 ÷ 2 = $4,500
11j. The smaller amount is $4,500.
64, her full benefit is reduced by 20%.
$2,101 × 0.2 = $420.20
$32,000.
13m. $33,191 × 0.85 = $28,212.35
13n. Line 17 is smaller so enter $28,212.35.
13p. The amount found in line 18, $28,212.35.
Lesson 9-3 Pensions
Check Your Understanding (Example 1)
benefit; (x + y)z or xz + yz.
Check Your Understanding (Example 2)
Check Your Understanding (Example 3)
Check Your Understanding (Example 4)
Check Your Understanding (Example 5)
Applications
1. Although this quote is more likely to be seen on
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
$901,860 ÷ 24 = $37,577.50
5b. $37,577.50 × 0.0235 × 24 = $21,193.71
5c. $, .
$,
21193 71
52 000 × 100 = 40.7 or 41%
= $78,302.80
years of service: 2010 – 1988 = 22
7a. $72,000 + 2($74,780) + $76,000
2nd-year salary: $80,000 × 1.025 = $82,000
3rd-year salary: $82,000 × 1.025 = $84,050
annual benefit: $83,050.31 × 4 × 0.02 × 0.7
= $4,650.82
= $79,000
12a. $35(1.001)25 = $35.89
12b. $35.89(45) = $1,615.05
14. average salary: $90,000 + $92,598 + $93,000
3
= $91,866
$91,866 ÷ 12 = $7,655.50
15. average salary: $50,000 + $50,000 + $52,100
3
16. $60,000 × 1.02 = $61,200
17. $100,000 × 0.0212 × 15 = $31,800
them together; 0.0212 × 15 × ()
Lesson 9-4 Life Insurance
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)
Check Your Understanding (Example 6)
Applications
1. We get preoccupied with day-to-day
2a. Using the table, the monthly premium would be
2b. Using the table, the monthly premium would be
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
is 55.
8c. The greatest integer less than or equal to 0.65
is 0.
is –9.
8g. The greatest integer less than or equal to 19
is 19.
is –9.
8j. The greatest integer less than or equal to 2
3
10a. 3.25 × 12 = 39 payments
10b. Multiply the number of payments by the
11c. Since the term has not expired, they receive the
face value of the policy, $100,000.
11d. $100,000 – $945 = $99,055
Death after 51: 5($756) = $3,780
11h. (–99,244)(0.0032) + (–98,488)(0.0034)
+ (–97,732)(0.0038) + (–96,976)(0.0043)
12d.
12e. (0.1)(–$3) + (0.9)($2) = –$0.30 + $1.80 = $1.50
Assessment
Really? Really! Revisited
1. 24 hours × 60 minutes × 60 seconds = 86,400
seconds per day
4,300,000 ≈ 7.3
One baby was born every 7.3 seconds.
Applications
1a. $106,800 × 0.062 = $6,621.60
1b. $77,090 × 0.062 = $4,779.58
the maximum credits of 4.
3. 0.90 × $680 = $612
$2,128 – $283.02 = $1,844.98
6. Line 1: $38,121 is given
Line 2: $38,121 ÷ 2 = $19,060.50
Line 3: $23,907 is given
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
10a. [10,000 × 0.015312] = [153.12] = 153
10b. 1 – 0.015312 = 0.984688
11a. Death at 40: $973 – $250,000 = –$249,027
Death at 41: 2($973) – $250,000 = –$248,054
11b. (–$249,027)(0.0008) + (–$248,054)(0.0009)
+ (–$247,081)(0.0011) + (–$246,108)(0.0012)
12b. Use the future value of a periodic investment
formula and substitute $300,000 for P,
0.0225 for r, 12 for n, and 1, 2, and 3 for t.
B = 1( 1 3 )
0.042
⎛⎞
= $59,390.48
approximately $60,000.
14a. 5($26,745) + $29,000 + $29,400 + $30,100
+ 4($35,000) + $36,700 + $38,000 + $39,000
+ $39,500 = $681,725
14c. $18,140.38
$39,500 ≈ 0.459
Rounded to the nearest percent, 46%.
15a. $300 × 12 = $3,600
15c. $15,250 – $14,350 = $900
16a. Since Regina’s salary was $100,040, use the
+ $61,700 + $62,000 + $63,000 + $63,500
= $937,500 19. Mike’s average:
$84,780 $84,900 $85,000
3
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