Chapter 8
Lesson 8-1 Find a Place to Live
Check Your Understanding (Example 1)
Add the percents she spends on taxes, a student
Check Your Understanding (Example 2)
to determine the monthly rent for an 880-square
foot apartment.
Approximately $1,200 is a good estimate.
Check Your Understanding (Example 3)
Larry should plan on paying the following:
Application fee $100
Last month’s rent $r
r + 0.6r + r = 125 + 4.6r.
Check Your Understanding (Example 4)
Multiply the number of hours by the appropriate
rate and add to get the moving costs: 60P + 70L.
Check Your Understanding (Example 5)
Solve both equations for y:
8x + 130y = 1,250
130y = –8x + 1,250
y = 4
65
−x + 125
13
about 8. Set the viewing window: Xmin = 0, Xmax
Applications
1. Perhaps this is the earliest version of the phrase
2a. $86,000 ÷ 12 = $7,166.67
$7,166.67 × 0.25 = $1,791.67
$7,166.67 × 0.30 = $2,150.01
The range is $1,792–$2,150.
2b. $7,000 × 0.25 = $1,750
2c. ($1,500 × 52) ÷ 12 = $6,500
3. 0.28x = $1,400
x = $5,000 per month
$5,000 × 12 = $60,000 annual salary
4a. $18.50 × 37 = $684.50
4b. 23% + 5% = 28%
Yes, but it is not recommended because he will
only have about $600 for all other expenses.
5. Application fee: 2% of $1,300 $26
Credit application fee: $10
First month’s rent: $1,300
Add these amounts to find the total: $26 + $10
+ $1,300 + $1,300 + $1,872 + $1,300 = $5,808.
6a. $2,200 × 26 = $57,200
6b. 18% + 10% + 5% = 33%
100% – 33% = 67%
$4,766.67 × 0.67 = $3,193.67
7. Use the elimination method:
3x + 2y = 480
5x + 2y = 680
–2x = –200
x = 100
y = 90
8. Multiply the first equation by 5 and the second
5x + 80y = 780
9a. Enter the square feet and monthly rent into L1
9b. y = 1.74x + 299.46
9c. y = 1.74(810) + 299.46
y = $1,708.86
10a. Enter the monthly rent and square feet into L1
10b. y = 0.56(1,710) – 149.07
y = 808.53 or approximately 809 feet
11. Application fee: 1.5% of D 0.015D
Credit application fee: $10
Add these amounts to find the total: 0.015D
+ $10 + D + D + 1.08D + D = $10 + 4.095D.
12. y = 0.775x + 950.25
709.35 = x
About 709 square feet
13a. y = 1.165(1,500) + 615.23
y = $2,362.73
13b. $8,000 × 0.28 = $2,240; no, the
14. Mileage: 150 × $5 = $750
$750 + $595 + $350 = $1,695
15. Mileage: D × M = MD
Lesson 8-2 Read a Floor Plan
Check Your Understanding (Example 1)
Set up a proportion:
Check Your Understanding (Example 2)
Check Your Understanding (Example 3)
Use the formula for the area of a regular polygon,
substitute and solve.
A = 1
2ap
1
Check Your Understanding (Example 4)
Set up a proportion similar to the one used in
Example 4, cross multiply, and solve for x.
Check Your Understanding (Example 5)
V = lwh, where l and w are equal since the room is
square. Let x represent the length and width,
Check Your Understanding (Example 6)
Use the formula from Example 6 substituting 18 for
i instead of 10.
that goes on inside a house.
2a. 13 × 15 = 195 square feet
x = 3.25 or 1
34 inches
0.25 inch
1 foot 15 feet
x
=
x = 3.75 or 3
34 inches
= 4,680 ≈ 5,000 BTUs
3a. Area of a rectangle is length times width or LW.
3b. Since there are 9 square feet in a square yard,
divide the area by 9 and then multiply by the
4c. 20 × 8 = 160 sq ft
4d. 2(112 + 160) = 544 sq ft
4e. To paint the room twice, you will need to cover
4f. BTU rating ≈ 60
while = (20)(8)(10)(14)(16)
60
5a. 7 × 9 = 63 × $7.90 = $497.70
5b. A = 1
2ap = 1
2(10.9)(72) = 392.4 sq ft
5c. 392.4 × 3 = $1,177.2 or $1,200
6a. Small wall: xc, large wall: yc
6b. Since there are 2 walls of each size, the total
6d. Add the area of the walls and the ceiling and
divide by 400 to get the number of gallons of
x
7. Total cost is the area times the cost per square
unit: 0.5(a)(6s)c = 3asc.
x
1 foot 9 feet
=
x = 2.25 or 1
24 inches
0.25 inch
1 foot 3 feet
x
=
x
x = 1 inch
0.25 inch
x
x
8a (continued).
(7 × 6) = 195 sq ft.
8c. 195 × $18 = $3,510
5,000 = 0.64 = 64%
9c. 625 × 0.64 = 400 sq ft
10. The area of the rectangle is xy. The percent of
the area of the pond, 10,000
Lesson 8-3 Mortgage Application
Process
Check Your Understanding (Example 1)
The interest paid on the house would be the total
Check Your Understanding (Example 2)
Property tax is calculated by multiplying the
Check Your Understanding (Example 4)
The front end ratio uses monthly amounts, so
Check Your Understanding (Example 5)
Total monthly expenses without the car payment
is 239
x
.
Applications
1. In the movie, Dorothy runs away from home,
feeling for granted, or not even realize it.
2. 30 × 12 = 360
4a. Use the monthly payment formula and substitute
$120,000 for p, 0.062 for r, and 15 for t.
12(15)
4c. Use the monthly payment formula and substitute
$120,000 for p, 0.065 for r, and 25 for t.
12(25)
0.065 0.065
⎛⎞⎛ ⎞
4f. $1,025.64 – $810.25 = $215.39
4g. 25 – 15 = 10
5. $186,000 × 0.0215 = $3,999
6. To calculate the interest, multiply the monthly
7a. $230,000 ÷ $1,000 = 230
230 × $17.50 = $4,025
8. Use the monthly payment formula twice and
substitute $135,000 for p, 0.0625 for r, and 20
then 30 for t.
12(20)
0.0625
⎛⎞
= $831.22 or $831
Financial Algebra Solutions Manual Chapter 8 Page 122
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9. $9,000 × 0.9722 = $8,749.80
10. Divide the assessed value by 100 to get the
11. First convert all payments to monthly amounts
values before substitution into the formula.
Monthly adjusted gross income is
ratio is 12 12
$4,500
12
a
+.
13a. Front-end ratio =
$117,445
12
13b. Yes; because the front-end ratio is less than
13c. Back-end ratio =
$6,780 $710
$1,877 $430 $5,100 $1,000
12 6
+++++
13d. No; because 93% > 36%. Based on the total of
12
15. Add the value of the stolen items and subtract
16. Use the monthly payment formula and substitute
$275,000 for p, 0.08 for r, and 20 for t.
11
+−
⎜⎟
17a. Use the monthly payment formula and substitute
$350,000 for p, 0.071 for r, and 12 for t.
17b. 144 – 1 = 143
17c. $170,994.88 ÷ 143 = $1,195.77
17e. From the monthly payment in part a above, it
18. Divide the interest by the total number of
payments minus 1 for the balloon payment:
t.
19.
Square
dormer 15 × 26 = 390 390 × $1 = $390
land 0.5 × $1,000 = $500
extra baths 1 full = $100
fireplace $125
tennis
court
$375
gas heat $700
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= $4,572.
20a. The formula will divide the amounts in B2 and
20b. Using the future value of a periodic deposit
20c. $5,900
12 + $1,234
12 = $594.50
12
20e. $8,766
20g. $8,944
12 + $1,540
12 = $873.67
()
12 0.5
0.01
$873.67 1 1
•
⎛⎞
⎛⎞
+−
⎜⎟
⎜⎟
20i. $7,711
0.01
$772.92 1 1
12
⎛⎞
⎛⎞
+
−
⎜⎟
⎜⎟
Lesson 8-4 Purchase a Home
Check Your Understanding (Example 1)
The annual interest is $400,000 × 0.06 = $24,000.
Check Your Understanding (Example 2)
purchase price by dividing the mortgage amount by
0.85 = $400,000
$400,000 × 0.02 = $8,000
Check Your Understanding (Example 3)
Divide the interest amount by the monthly payment
to calculate the percent paid toward interest:
Check Your Understanding (Example 4)
Divide the principal for 12 months by the original
principal amount to calculate the percent of the
Check Your Understanding (Example 5)
Subtract the interest with the extra payment from
Check Your Understanding (Example 6)
The change in monthly payment is $2,526.94 –
Applications
1. For many, home ownership is a sign of financial
stability, security, and an indication that “we’ve
7. B1 = $400,000
12(20)
6.55 6.55
$400,000 1
⎛⎞⎛ ⎞
+
P1 = $2,994.08 – $2,183.33 = $810.75
E
1 = $400,000 – $810.75 = $399,189.25
P
2 = $2,994.08 – $2,178.91 = $815.17
E
2 = $399,189.25 – $815.17 = $398,374.08
9. Assume the Beginning Balance is column B,
Monthly Payment is column C, Towards Interest
is column D, Towards Principal is column E, and
Ending Balance is column F and the row number
is one more than the payment number. The first
entry for beginning balance is the original
principal amount. The formula for the remaining
Beginning
Balance Monthly
Payment Towards
Interest Towards
Principal Ending
Balance
5 195,337.39 2,322.17 1,139.47 1,182.70 194,154.69
6 194,154.69 2,322.17 1,132.57 1,189.60 192,965.09
7 192,965.09 2,322.17 1,125.63 1,196.54 191,768.55
8 191,768.55 2,322.17 1,118.65 1,203.52 190,565.03
10. In order to calculate the last year of the
amortization table, you will need to complete the
entire amortization table using formulas.
Assume the Beginning Balance is column B,
Monthly Payment is column C, Towards Interest
is column D, Towards Principal is column E, and
Ending Balance is column F and the row number
determine interest is, =B2*7/1200. The formula
169 57,114.22 4,902.50 261.77 4,640.73 52,473.49
170 52,473.49 4,902.50 240.50 4,662.00 47,811.49
171 47,811.49 4,902.50 219.14 4,683.36 43,128.13
172 43,128.13 4,902.50 197.67 4,704.83 38,423.30
11. B1 = $300,000
12(15)
77
$300,000 1
1,200 1,200
⎛⎞⎛ ⎞
+
⎜⎟⎜ ⎟
⎝⎠⎝ ⎠
I1 = $300,000 × 7
1, 2 0 0 = $1,750
E
1 = $300,000 – $1,346.48 = $298,653.52
12a. M =
12(15)
12(15)
5.75 5.75
$500,000 1
1,200 1,200
5.75
11
1,200
⎛⎞⎛ ⎞
+
⎜⎟⎜ ⎟
⎝⎠⎝ ⎠
⎛⎞
+−
⎜⎟
⎝⎠
12c. I178 = $12,337.73 × 5.75
1, 2 0 0 = $59.12
12d. P179 = $4,152.05 – $39.51 = $4,112.54
13a. M =
12(15)
6
11
⎛⎞
+−
⎜⎟
13b. B2 = E1 = $209,177.90
13c. E2 = $209,177.90 – $826.21 = $208,351.69
13e. P4 = $1,772.10 + $100 – $1,037.61 = $834.49
14a. $723.72 + $576.67 = $1,300.39
14b. $204,344.02 – $576.67 = $203,767.35
15. B7 = E6 = $429,182.44
12(14.5)
55
$429,182.44 1
1, 2 0 0 1, 2 0 0
⎛⎞⎛ ⎞
+
⎜⎟⎜ ⎟
⎝⎠⎝ ⎠
I1 = $429,182.44 × 5
1, 2 0 0 = $1,788.26
P1 = $3,472.72 – $1,788.26 = $1,684.46
Lesson 8-5 Rentals,
Condominiums, and Cooperatives
Check Your Understanding (Example 1)
Check Your Understanding (Example 2)
Divide the number of shares owned by Sage by the
Check Your Understanding (Example 3)
Answers will vary, but should include: renting:
Check Your Understanding (Example 4)
In this case the function is linear because the
Check Your Understanding (Example 5)
1.051 represents the whole portion of the rent and
Check Your Understanding (Example 6)
The current value of the co-op is represented by
c – 23,000. The amount Paul owes the bank is
Applications
1. Many young people can’t wait to leave their
parents’ home and gain independence in a
2. 12 × 0.2 × 1,397 = $3,352.80
3. Divide the maintenance fee by 3 to get the
x
4. 500
x = 1.125
7a. M =
12(30)
12 12
0.071
11
12
⎝⎠⎝ ⎠
⎛⎞
+−
⎜⎟
⎝⎠
9. Let x represent the number of years. The
10b. The function is linear because the yearly
increase is a flat rate amount, y = 200x +
$2,700.
10c. The graph of the function is shown below.
10d. The steepness of the exponential graph shows
how each increase is greater than the constant
11. The current value of the co-op is represented by
12. 1.062 represents the whole portion of the rent
13a. The scatterplot is shown below.
graphing calculator and calculate the
exponential regression: y = 2,141.940(1.032)x–1.
= $670.87
14c. Both will be $670.87 because this is a fixed rate
15. Let x represent the number of years. The
exponential function is the rent multiplied by 1
16. Sample answer: To determine the total rent paid
after 5 years in a spreadsheet label column A
year, column B rent, and column C annual rent.
=C2–D2. The formula for the ending balance is,
=B2–E2. Sum the columns up to payment 60 for
the 5-year total to get purchase total paid:
$105,312.53, and paid toward principal:
17. Sample answer: To determine the total rent paid
after 10 years in a spreadsheet label column A
the formula = B2*1.02 in B3 and copy to the
remaining rows. C2 = B2*12 and copy to the
remaining rows. Sum the values in annual rent
Assessment
Really? Really! Revisited
2. 2,000 × 1.01 = 2,200 lb
Applications
1a. 18 × 25 = 450 sq ft
1b. 0.25 inch
x
=
0.25 inch
x
=
x = 6.25 or 1
64 inches
1c. BTU rating ≈ 60
while = (25)(8)(10)(18)(18)
60
2a. M =
12(30)
1,200 1,200
6.34
11
⎜⎟⎜ ⎟
⎝⎠⎝ ⎠
⎛⎞
+−
2b. 30 × 12 = 360
4. 27% + 11% = 38% or 0.38
5. The area of a regular polygon can be found with
6. y = 1,330(1.06)1–1 = $1,330 × 12 = $15,960
$15,960 + $16,917.60 + $17,932.68
7a. The current value of the co-op is represented by
is less than what the Bricely family owes, the
inequality is $246,000 – d < b.
7b. Subtract the current value of the co-op,
8. $9,400 × 0.9082 = $8,537.08
9. Divide the assessed value by $1,000 and
multiply by the tax rate, 1, 0 0 0
10. Front-end ratio = Monthly housing expenses
Monthly gross income
=
$137,865
= 0.213 or 21%
11c. Back-end ratio =
11d. Yes, the back-end ratio is less than 36%.
12. Let x represent the number of years. The
13a. 30 × 25 = 750 sq ft
14a. $1,700
$5,800 = 0.293 or 29%; Yes
14b. $2,900 × 2 = $5,800
Taxes: $5,800 × 0.16 = $928
15b. $9,800 × 0.28 = $2,744
16. B1 = $500,000
12(30)
6.95 6.95
⎛⎞⎛ ⎞
17. Let x represent the number of years. The
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18. Multiply the top equation by 4 and the bottom
–9x = –630
x = 70
$70 per hour for loading/unloading and $95 per
19a. M =
12(20)
5.95
11
1, 2 0 0
⎛⎞
+−
⎜⎟
⎝⎠
= $1,569.81
11
+−
⎜⎟
I1 = $350,000 × 6.25
1, 2 0 0 = $1,822.92
1 350,000 3,000.98 1,822.92 348,821.94 274,046.30
21. Sample answer: To determine the total rent paid
after 8 years in a spreadsheet label column A
year, column B rent, and column C annual rent.
column A, Beginning Balance column B, Monthly
Payment column C, Towards Interest column D,
Towards Principal column E, and Ending
Balance column F. The row number is one more
than the payment number. The first entry for
beginning balance is the original principal
amount. The formula for the remaining rows is
the last month’s previous balance, =F2. The
22. Sample answer: To determine the total rent paid
after 7 years in a spreadsheet label column A
year, column B rent, and column C annual rent.
column A, Beginning Balance column B, Monthly
Payment column C, Towards Interest column D,
Towards Principal column E, and Ending
Balance column F. The row number is one more
than the payment number. The first entry for
beginning balance is the original principal
amount. The formula for the remaining rows is
the last month’s previous balance, =F2. The
23. B1 = $366,659.40
12(29.5)
4.8 4.8
$366,659.40 1
1,200 1,200
⎛⎞⎛ ⎞
+
⎜⎟⎜ ⎟
⎝⎠⎝ ⎠
24a. $210,000 – $403.13 – 100 = $209,496.87