Chapter 3
Lesson 3-1 Checking Accounts
Check Your Understanding (Example 1)
Check Your Understanding (Example 2)
amount from the old balance: $2,499.90 – $150.32
= $2,349.58.
Extend Your Understanding (Example 2)
Applications
1. Will Rogers indicates that banking is as
3. Add the deposits w, h, and v. Subtract the
4. $630 = 3($50) + 18($20) + t($10)
6. $5,195.65 + $6,873.22 – c – $15 + $6.05
7. 12($13) + 289($0.07) = $156 + $20.23
9. $245 = 2($50) + 6($20) + f($5)
$25 = $5f
10. $113 = 4($20) + x($10) + 3($1)
$113 = $80 + $10x + $3
$113 = $83 + $10x
$30 = 10x
3 = x
11. Let a represent the number of twenty dollar bills
dollar bills. b = 4a = 4(3) = 12, which means
12. Speaker Cabinets: $400.00 × 2 = $800.00
Speaker Cabinets: $611.00 × 2 = $1,222.00
Microphone Stands: $32.50 × 8 = $260.00
Total: $800.00 + $1,222.00 + $380.00 +
Sales Price: $6,956.36 – $904.33 = $6,052.03
Total Cost: $6,052.03 + $484.16 = $6,536.19
the transaction description: Fox High School,
13c. Write the date: 10/30, the transaction
13d. Write the date: 11/4, the transaction description:
13e. Write the date: 11/5, the transaction description:
13f. Write the check number: 116, the date: 11/7, the
$20.00. Add: $338.81 + $20.00 = $358.81.
13h. Write the date: 11/12, the transaction
$25.00. Subtract: $358.81 – $25.00 = $333.81.
fee, and the payment amount: $2.25. Subtract:
$333.81 – $2.25 = $331.56.
13j. Write the date: 11/17, the transaction
14. $1,400.00 – $1,380.15 = $19.85
–$745.82 – $130 = –$875.82
16a. Write the date 12/15 and the balance of
16c. Write the date: 12/17, the transaction
description: deposit, and the deposit amount:
16d. Write the date: 12/20, the transaction
16e. Write the check number: 2346, the date: 12/22,
the transaction description: Best Buy, and the
description: Macy’s, and the payment amount:
16h. Write the code: EFT, the date: 12/28, the
16i. Write the date: 12/29, the transaction
description: ATM, and the payment amount:
$200.00. Subtract: $1,154.75 – $200.00 =
$954.75. There is also an ATM fee of $1.50.
Write the date: 12/29, the transaction
description: ATM fee, and the payment amount:
$1.50. Subtract: $954.75 – $1.50 = $953.25.
17a. The check number after 622 is 623.
17h. $1,292.80 – $51.12 = $1,241.68
17i. Subtract the amount for check 624: –$25.00.
17l. $1,216.68 + $650.00 = $1,866.68
17t. Subtract the amount for check 628: –$65.00.
17u. $1,527.68 – $65.00 = $1,462.68
17v. Subtract the amount for check 629: –$300.00.
17x. Add the deposit amount: $400.00.
17z. $1,562.68 – $371.66 = $1,191.02
Lesson 3-2 Reconcile a Bank
Statement
Check Your Understanding (Example 1)
Check Your Understanding (Example 2)
Check Your Understanding (Example 3)
Applications
1. Errol Flynn used the word reconcile in the same
2. yes; $725.71 + $610.00 – $471.19 = $864.52
4. Add the deposits and subtract the outstanding
5b. 20($0.20) + $12.50 = $4
5c. $4 + $12.50 = $16.50
6a. The statement shows that the ending balance is
6b. The deposit of $700.00 is not on the bank
6d. $1,434.19 + $700.00 – $89.00 = $2,045.19
6e. The check register shows a balance of
6f. $2,046.19 = $2,046.19, so the account is
7. Let x = the number of checks Donna writes each
9. On the statement, you can still see that the
10. Outstanding deposit: $150; outstanding checks:
which reconciles with the statement balance.
11. $728.30 – $75.00 = $653.30
$516.80 – $120.00 = $396.80
$396.80 – $56.73 = $340.07
$340.07 – $100.00 = $240.07
$240.07 – $85.00 = $155.07
$155.07 + $1,000.00 = $1,155.07
13a. When d > c, the amount of the deposits is
13b. When d < c, the amount of the deposits is less
Lesson 3-3 Savings Accounts
Check Your Understanding (Example 1)
5.51% = 0.0551
Check Your Understanding (Example 2)
Check Your Understanding (Example 3)
Check Your Understanding (Example 4)
365 . Substitute $800 for p,
I = prt = ($800)(0.0571) 300
⎛
⎜
⎞
⎟
= $37.55
Applications
2. 3.4% = 0.034
3
1
2% = 3. 5% = 0.035
3. Because $1,203.44 – $300 = $903.44 is less
4. Let m = the number of months for the balance to
9a. I = prt = ($2,000)(0.0335)(4) = $268
9b. I = prt = ($3,500)(0.041) 15
12
⎛
⎜
⎝⎠
⎞
⎟
= $179.38
p
p
is about 21 months
9f. r = I
p
t = $500
($3,000)(3) = 0.0556 = 5.56%
9g. p = I
⎝⎠
$500
= $4,545.45
9h. t = I
p
p
x
p
p
13. r = I
p
$900
= 0.0598 = 5.98%
14. Bedford Bank: I = prt = ($20,000)(0.04)(5) =
15. Blank Bank: I = prt = ($x)(0.01r)(y) = $0.01xry
16. I = prt = ($3,450)(0.05)(18) = $3,105
$3,450 + $3,105 = $6,555
p
18a. I = prt, so the formula for cell A2 is =B2*C2*D2.
=A2/(C2*D2).
18c. r = I
p
t, so the formula for cell C2 is
Lesson 3-4 Explore Compound
Interest
Check Your Understanding (Example 1)
Check Your Understanding (Example 2)
The amount of interest is I = prt =
Check Your Understanding (Example 3)
Add the interest to the principal: $3,000 + $30 =
$30.30.
Check Your Understanding (Example 4)
I = prt = (x)(0.05) ⎛⎞
⎜⎟
1
365 = 0.5
365
x
Check Your Understanding (Example 5)
The amount of interest on January 7 is I = prt =
Financial Algebra Solutions Manual Chapter 3 Page 46
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Applications
1. Compound interest is better than simple interest
2. I = prt = ($3,700)(0.065)(1) = $240.50
3. I = prt = ($4,000)(0.0675)(1) = $270
4. I = prt = ($9,000)(0.08)(0.5) = $360
6a. I = prt = ($3,500)(0.075)(0.5) = $131.25
6b. $3,500 + $131.25 = $3,631.25
6f. I = prt = ($3,500)(0.075)(1) = $262.50
6g. $267.42 – $262.50 = $4.92
7c. I = prt = ($3,565.63)(0.075)(0.25) = $66.86
7h. $3,700.60 + $69.39 = $3,769.99
10a. $0
10b. $4,550.00
10j. $4,850.50 + $0.53 = $4,851.03
10k. $4,851.03
10p. $3,951.03 + $0.43 = $3,951.46
11a. $0
11c. $0
11f. $6,000.00 + $0.57 = $6,000.57
11g. $6,000.57
11k. I = prt = ($6,500.57)(0.0345) 1
⎛⎞
⎜
⎟
= $0.61
11n. $0
366
⎝⎠
11s. $4,001.18 + $0.38 = $4,001.56
13. I = prt = (d – y)(0.034) ⎛⎞
1
=
−
0.034( )
dy
14b. I = prt = (P + D)(0.02) ⎛⎞
⎜⎟
⎝⎠
1
365 = +0.02( )
365
PD
14c. Add the principal and the interest:
P + D + +0.02( )
PD
Financial Algebra Solutions Manual Chapter 3 Page 47
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PD
⎝⎠
14g. Add the principal and the interest: P + D – W +
⎛
+
⎛⎞
⎜⎟
⎝⎠
PD
15. Add the opening balance and the deposit to find
0.0225(3 )
12
m
12
Lesson 3-5 Compound Interest
Formula
Check Your Understanding (Example 1)
4
⎛
⎞
0.0387 for r.
B4 = $1,200
0.03
112
⎛
+
⎜
⎝⎠
⎞
⎟
= $1,236.50
Extend Your Understanding (Example 2)
⎝⎠
compounded quarterly: B = P
0.0325
14
⎛⎞
+
⎜⎟

Check Your Understanding (Example 3)
⎝⎠
Extend Your Understanding (Example 3)
Substitute $2,000 for P, 0.035 for r, 365 for n, and k
365•
0.035
k
⎛⎞
⎜⎟
⎝⎠
Check Your Understanding (Example 4)
365
0.041
⎛
⎜
⎝⎠
⎞
⎟
Extend Your Understanding (Example 4)
1.
2. B = $4,000
Applications
Bank interest on its own will not make you rich;
2•10
0.05
12
⎛⎞
+
⎜⎟
⎝⎠
= $6,554.47
3. B = $2,000
12•2
0.0475
112
⎛⎞
+
⎜⎟
⎝⎠
= $2,198.91
365•3
5c. APY =
365
0.043
1365
⎛⎞
+
⎜⎟
⎝⎠
– 1 = 0.0439 = 4.39%
1,484.51 = $7.27
9. B = $3,000
$1,491.78 – $
365•24•2
0.048
1365 • 24
⎛⎞
+
⎜⎟
⎝⎠
= $3,302.28
10a. $20,000
365•14
0.0475
1365
+
⎜⎟
⎝⎠
⎛⎞
= $38,888.13
ulie will not double their money in
14 years.
$38,888.13 < $40,000
Mike and J
10b. $20,000
365•15
0.0475
1365
⎛⎞
+
⎜⎟
= $40,779.73
11a. Lindsay: B = $80
12•1
0.05
112
⎛
+
⎜
⎝⎠
⎞
⎟
= $84.09
Michele: B = $60
52•1
0.08
152
⎛
+
⎜
⎝⎠
⎞
⎟
= $64.99
Michele: B = $60
152
+
⎜⎟
⎝⎠
= $156.59
$156.59 > $145.59, so Michele’s balance is
12g. B = $5,000
1• 6
0.04
11
⎛
+
⎜
⎝⎠
⎞
⎟
= $6,326.60
$6,326.60 – $5,000 = $1,326.60
12i. The annual compounded interest earned
$1,326.60 – $1,200 = $126.60 more than the
simple interest.
12j. No; they are the same for one year. For anything
longer, compounded interest grows faster than
simple interest.
13. Rodney: B = P
1•1
11
r
⎛⎞
+
⎜⎟
⎝⎠
= P(1 + r)
1•1
Financial Algebra Solutions Manual Chapter 3 Page 49
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P(1 + r) > P(0.5 + r), so Rodney’s balance will
always be greater.
14. APY =
0.0655
1365
⎛
+
⎜
⎝⎠
⎞
⎟
– 1 = 0.0677 = 6.77%
⎜
⎝⎠
⎟
$10,525,296 – $10,000,000 = $525,296
15c. $525,296 – $512,000 = $13,296
16a. I = prt = ($955,000,000)(0.0533)(1)
= $50,901,500
16b. B = $955,000,000
365•1
0.0533
1365
⎛⎞
+
100
16c. $52,278,530.93 – $50,901,500 = $1,377,030.93
16d. compounded daily: $1,007,278,531 ÷ $61,000
Lesson 3-6 Continuous
Compounding
Check Your Understanding (Example 1)
The value of g(x) will decrease as x increases
Check Your Understanding (Example 2)
x f(x)
100
1,000 1
= 0.001
10,000 1
= 0.0001
100,000
The values in the table are approaching 0.
Check Your Understanding (Example 3)
x f(x)
10 1
10
= 1
100 1
100
= 1
10
Check Your Understanding (Example 4)
⎝⎠
1,000
1,000
0.05
11,000
⎛⎞
+
⎜⎟
⎝⎠
= 1.05127
10,000
10,000
0.05
110,000
⎛⎞
+
⎜⎟
= 1.05127
1,000,000
0.05
⎛⎞
Applications
1. People have a difficult time conceiving of infinity.
The concept of infinite time, space, and number
triggers the imagination and often boggles the
mind.
2b. B = $2,000
1• 3
0.04
11
⎛
+
⎜
⎞
⎟
= $2,249.73
5c. $767.74 – $751.53 = $16.21
State Bank pays $16.21 more in interest.
5d. Sample answers: How close is the bank to her
home? Will she still be living in the same place
in two years? Does she have other banking
How customer-friendly is the service?
6a. B = pert = $1,000e(0.16)(5) = $2,225.54
Lesson 3-7 Future Value of
Investments
Check Your Understanding (Example 1)
Find the amount in the account after 21 years:
Applications
1. Answers will vary but should include some
mention of the fact that the longer an amount is
in a savings account the more it will accrue in
interest. Therefore, the earlier the start of the
7a. B =
0.05
= $13,537.79
7b. B =
0.05
4
0.05
+
7c. Enter the equation in Y1. The minimum on the
+
+
7d. Use the CALC feature on your calculator. Then
select “value”. Enter 12 as the x-value because
+
0.08
$80 1 1
⎛⎞
⎛⎞
+
−
⎜⎟
⎜⎟
money.
12(20)
0.05
$100 1 1
⎛⎞
⎛⎞
+
−
⎜⎟
⎜⎟
9e. B =
12
⎜⎟
⎝⎠
⎝⎠
= $47,121.63
B =
0.05
12
0.08
12
+
9i. Enter Sydney’s equation in Y1. Enter Benny’s
equation in Y2. The minimum on the
Financial Algebra Solutions Manual Chapter 3 Page 53
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9j. Sydney’s balance starts out higher than Benny’s
but by the 160th month (a little over 13 years),
and A5 for t in the formula for the future value of
a periodic investment:
A8 =
A6•A5
A4
A
31 1
A6
A4
⎛⎞
⎛⎞
+−
⎜⎟
⎜⎟
⎜⎟
⎝⎠
⎝⎠
. Write the equation
11b. When the balance equals 2 × $4,000 = $8,000
the initial deposit will double.
t = 20: $4,000
1• 2 0
0.02
11
⎛
+
⎜
⎝⎠
⎞
⎟
= $5,943.79
double.
11d. t × percent = 70 × 1 = 70, which is close to 72.
Lesson 3-8 Present Value of
Investments
Check Your Understanding (Example 1)
Check different values of t. Find the value of t so
Check Your Understanding (Example 2)
Everything remains the same except n = 52.
Check Your Understanding (Example 3)
Substitute x for B, y for t, and 2 for n in the present
value of a periodic investment formula.
+
11
2
+−
⎜⎟
Check Your Understanding (Example 4)
+
2a. P = 1( 3 )
0.04
⎛⎞
+
= $889.00
+
14
+
⎜⎟
2d. P = 12(8)
0.0275
112
⎛
+
⎜⎟
⎞
= $40,136.04
3a. P = 1( 8 )
⎝⎠
= $5,825.49 per year
3b. P = 2(4)
⎝⎠
= $3,043.89 per 6 months
3c. P = 4(10)
0.0375
$100,000 4
0.0375
11
4
⎛⎞
⎜⎟
⎝
⎛⎞
⎠
+
−
⎜⎟
⎝⎠
= $2,072.04 per quarter
0.04
⎛⎞
4.
P = 1( 7 )
$50,000 1
⎜⎟
⎝⎠
= $6,292.16
7.
P = 12(3)
⎝⎠
= $260.36
$50,000
⎝⎠
10. Graph the equation: y = 12
$75,000
x
, where x
is the number of years and y is the principal
on the y-axis is 0, the maximum is 100,000, and
Assessment
Really? Really! Revisited
2. The patterns are not identical. Changes in one
category are not the same in direction or
magnitude.
Applications
1b. Write the check number: 1223, the date: 12/11,
1c. Write the date: 12/12, the transaction
– $480.21 = $3,677.09. Write the check number:
1225, the date: 12/17, the transaction
description: Target, and the payment amount:
deposit amount: $120.00. Add: $2,070.91 +
$120.00 = $2,190.91.
1h. Write the date: 12/24, the transaction
description: ATM Withdraw, and the payment
amount: $300.00. Subtract: $2,190.91 – $300.00
1i. Write the check number: 1229, the date: 12/28,
the transaction description: Len’s Auto Body
1j. Write the check number: 1230, the date: 12/29,
the transaction description: AMTRAK, and the
2a. The statement shows that the ending balance is
2b. The deposit of $120.00 is not on the bank
4. Because $1,722 – $400 = $1,322 is less than
5. $7,000 + $224.16 – $1,000 – $250 = $5,974.16
6a. I = prt = ($910)(0.052)(3.5) = $165.52
7a. $74,112.09 + $77,239.01 = $151,351.10
7b. All of Matt’s money is insured. The FDIC insures
8a. I = prt = ($5,600)(0.045) 1
2
⎛⎞
⎜⎟
⎝⎠
= $126
2
⎝⎠
8d. $5,726 + $128.84 = $5,854.84
8d. $5,854.84 – $5,600 = $254.84
9d. I = prt = ($5,200.00)(0.0399) ⎛
⎜
⎝⎠
1
365
⎞
⎟
= $0.57
9i.
I = prt = ($5,900.57)(0.0399) ⎛
⎜
⎝⎠
1
365
⎞
⎟
= $0.65
9j. $5,900.57 + $0.65 = $5,901.22
9k. $5,901.22
9m. $5,901.22 – $500.00 = $5,401.22
⎜⎟
B = $10,000
0.0433
12
⎛⎞
+
⎜
= $11,371.37
12a. B = $2,250
1365
+
⎜
⎝⎟
⎠
= $2,372.46
12b. $2,372.46 – $2,250 = $122.46
13. B = pert = $25,000e(0.047)(2.5) = $28,117.04 18b.
10
2
3(10) 9(10)
+
14a. You want to by a car when you graduate, so you
are looking for a future value. You will make
14c. You want to know how much you should deposit
The values in the table are not approaching a
7(10,000)
16. B =
0.026
⎝⎠
= $12,731.79
17. P = 12(5)
0.03
11
⎜⎟
⎝
⎛⎞
+−
⎠
= $464.06 19. Graph the equation: y = 12
$50,000
x
⎝⎠
, where x
is the number of years and y is the principal
amount. The minimum on the x-axis is 0, the
similar to the one below.
18a.
x f(x)
−
100 9(100) 1
3(100) 5
− = 3.047
1,000 9(1,000) 1
−