Chapter 8
Lesson 8-1 Find a Place to Live
Check Your Understanding (Example 1)
Check Your Understanding (Example 2)
to determine the monthly rent for an 880-square
Check Your Understanding (Example 3)
Check Your Understanding (Example 4)
Check Your Understanding (Example 5)
Solve both equations for y:
8x + 130y = 1,250
130y = –8x + 1,250
y = 4
−x + 125
about 8. Set the viewing window: Xmin = 0, Xmax
= 225, Xscl = 25, Ymin = 0, Ymax = 10, Yscal = 1.
Applications
$7,166.67 × 0.25 = $1,791.67
$7,166.67 × 0.30 = $2,150.01
3. 0.28x = $1,400
x = $5,000 per month
4b. 23% + 5% = 28%
5. Application fee: 2% of $1,300 $26
6a. $2,200 × 26 = $57,200
6b. 18% + 10% + 5% = 33%
7. Use the elimination method:
3x + 2y = 480
8. Multiply the first equation by 5 and the second
equation by 4 and use the elimination method:
9a. Enter the square feet and monthly rent into L1
y = $1,708.86
Credit application fee: $10
Add these amounts to find the total: 0.015D
709.35 = x
About 709 square feet
$750 + $595 + $350 = $1,695
1,695 × 1.08 = $1,830.60
Lesson 8-2 Read a Floor Plan
Check Your Understanding (Example 1)
Set up a proportion:
Check Your Understanding (Example 2)
rectangle: 2x(x + 3) – 5x = 2x2 + 6x – 5x = 2x2 + 6x.
Check Your Understanding (Example 3)
Check Your Understanding (Example 4)
Check Your Understanding (Example 5)
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
= 4,680 ≈ 5,000 BTUs
4b. 14 × 8 = 112 sq ft
4c. 20 × 8 = 160 sq ft
4f. BTU rating ≈ 60
while = (20)(8)(10)(14)(16)
60
= 5,973.33 ≈ 6,000 BTUs
6d. Add the area of the walls and the ceiling and
divide by 400 to get the number of gallons of
paint, 22
400
x
cycxy++
gallons.
1 foot 9 feet
x = 2.25 or 1
24 inches
0.25 inch
x
=
x = 1 inch
x = 1.75 or 3
14 inches
8a (continued).
(7 × 6) = 195 sq ft.
8c. 195 × $18 = $3,510
9a. 25 × 25 = 625 sq ft
9b. 3,200
Lesson 8-3 Mortgage Application
Process
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)
Total monthly expenses without the car payment
is $7,552 ÷ $14,916 = 0.5063 or 51%
Check Your Understanding (Example 6)
Applications
1. In the movie, Dorothy runs away from home,
and eventually realizes that nothing matches the
4a. Use the monthly payment formula and substitute
4c. Use the monthly payment formula and substitute
$120,000 for p, 0.065 for r, and 25 for t.
12(25)
= $810.25
4d. 25 × 12 = 180
5. $186,000 × 0.0215 = $3,999
6. To calculate the interest, multiply the monthly
payments by 12 and the number of years then
8. Use the monthly payment formula twice and
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
12. Front-end ratio = Monthly housing expenses
Monthly gross income ,
so all amounts must be converted to monthly
13a. Front-end ratio =
$6,780 $710
$1,877 12 6
$117,445
12
++
13c. Back-end ratio =
16. Use the monthly payment formula and substitute
$275,000 for p, 0.08 for r, and 20 for t.
11
+−
⎜⎟
240 × $2,300.21 = $552,050.40
$552,050.40 – $275,000 = $277,050.40
The interest is paid in the first 239 payments:
$277,050.40 ÷ 239 = $1,159.21 or $1,160.
17d. $350,000 – $1,195.77 = $348,804.23 or
$348,800
17e. From the monthly payment in part a above, it
would be $3,618.02.
19.
Square
Footage Assessed Value
extra baths 1 full = $100
fireplace $125
tennis
$375
= $4,572.
20a. The formula will divide the amounts in B2 and
12
20g. $8,944
12 + $1,540
12 = $873.67
20i. $7,711
12 + $1,564
12 = $772.92
Lesson 8-4 Purchase a Home
Check Your Understanding (Example 1)
Check Your Understanding (Example 2)
Check Your Understanding (Example 3)
Divide the interest amount by the monthly payment
Check Your Understanding (Example 4)
Check Your Understanding (Example 5)
Check Your Understanding (Example 6)
Applications
1. For many, home ownership is a sign of financial
stability, security, and an indication that “we’ve
2. Down payment: $250,000 × 0.15 = $37,500
Mortgage: $250,000 – $37,500 = $212,500
3. Down payment: $180,000 × 0.1 = $18,000
4. B9 is the loan amount multiplied by the APR
expressed as a decimal: =B1*B7/100; B10 is the
5. $430,000 × 0.02 = $8,600
6. Since $4,000 would be 2% of the price of her
home, divide, $4,000 by 0.02 to get $200,000.
7. B1 = $400,000
I1 = $400,000 × 6.55
1, 2 0 0 = $2,183.33
1, 2 0 0 = $2,178.91
P
2 = $2,994.08 – $2,178.91 = $815.17
E
2 = $399,189.25 – $815.17 = $398,374.08
8. B1 = $275,000
= $2,305.78
E
1 = $275,000 – $953.70 = $274,046.30
B
2 = E1 = $274,046.30
E
2 = $274,046.30 – $958.39 = $273,087.91
2 274,046.30 2,305.78 1,347.39 958.39 273,087.91
9. Assume the Beginning Balance is column B,
Monthly Payment is column C, Towards Interest
determine interest is, =B2*7/1200. The formula
for the amount towards principal is, =C2–D2.
The formula for the ending balance is, =B2–E2.
Beginning
Balance Monthly
Payment Towards
Interest Towards
Principal Ending
Balance
6 194,154.69 2,322.17 1,132.57 1,189.60 192,965.09
7 192,965.09 2,322.17 1,125.63 1,196.54 191,768.55
8 191,768.55 2,322.17 1,118.65 1,203.52 190,565.03
10. In order to calculate the last year of the
amortization table, you will need to complete the
(12*10)–1). After the initial row for monthly
payment, the formula that will repeat the amount
for all remaining rows is =$C$2. The formula to
determine interest is, =B2*7/1200. The formula
for the amount towards principal is, =C2–D2.
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
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
⎛⎞⎛ ⎞
+
⎜⎟⎜ ⎟
⎝⎠⎝ ⎠
⎛⎞
+−
⎜⎟
12c. I178 = $12,337.73 × 5.75
13a. M =
12(15)
6
11
⎝⎠⎝ ⎠
⎛⎞
+−
⎜⎟
13b. B2 = E1 = $209,177.90
13e. P4 = $1,772.10 + $100 – $1,037.61 = $834.49
14a. $723.72 + $576.67 = $1,300.39
15. B7 = E6 = $429,182.44
Lesson 8-5 Rentals,
Condominiums, and Cooperatives
Check Your Understanding (Example 1)
Check Your Understanding (Example 2)
Check Your Understanding (Example 3)
Answers will vary, but should include: renting:
Check Your Understanding (Example 4)
Check Your Understanding (Example 5)
Check Your Understanding (Example 6)
The current value of the co-op is represented by
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
= $672.03
7b. $672.03 + $310 = $982.03
9. Let x represent the number of years. The
10a. Let x represent the number of years. The
10b. The function is linear because the yearly
10c. The graph of the function is shown below.
graphing calculator and calculate the
exponential regression: y = 2,141.940(1.032)x–1.
12(15)
0.06 0.06
12
⎛⎞⎛ ⎞
⎝⎠
14e. y = 900(1.02)x–1 = 900(1.02)15–1 = $1,187.53
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.
A2 = 1, then put the formula = A2+1 in A3 and
copy to the remaining rows. B2 = 2,100, then put
the formula = B2*1.015 in B3 and copy to the
remaining rows. C2 = B2*12 and copy to the
remaining rows. Sum the values in annual rent
for the first 5 years to get the total paid,
$129,837.13. To determine the total paid and
total paid to principal after 5 years in a
spreadsheet, make the Payment Number
column A, Beginning Balance column B, Monthly
Payment column C, Towards Interest column D,
Towards Principal column E, and Ending
Balance column F. The row number is one more
than the payment number. The first entry for
beginning balance is the original principal
amount. The formula for the remaining rows is
the last month’s previous balance, =F2. The
monthly payment formula is,
=(B2*(5.75/1200)*(1+5.75/1200)^(12*20))/((1+5.
75/1200)^(12*20)–1). After the initial row for
monthly payment, the formula that will repeat the
amount for all remaining rows is =$C$2. The
formula to determine interest is, =B2*5.75/1200.
The formula for the amount towards principal is,
=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:
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
for the first 10 years to get the total paid,
$341,631.30. To determine the total paid and
total paid to principal after 10 years in a
spreadsheet, make the Payment Number
column A, Beginning Balance column B, Monthly
Payment column C, Towards Interest column D,
Towards Principal column E, and Ending
Balance column F. The row number is one more
than the payment number. The first entry for
beginning balance is the original principal
amount. The formula for the remaining rows is
the last month’s previous balance, =F2. The
monthly payment formula is,
=(B2*(6.5/1200)*(1+6.5/1200)^(12*15))/((1+6.5/1
200)^(12*15)–1). After the initial row for monthly
payment, the formula that will repeat the amount
for all remaining rows is =$C$2. The formula to
determine interest is, =B2*6.5/1200. The formula
for the amount towards principal is, =C2–D2.
The formula for the ending balance is, =B2–E2.
Sum the columns up to payment 120 for the
10-year total to get purchase total paid
$313,598.65, total paid toward principal:
$169,935.92.
Assessment
2. 2,000 × 1.01 = 2,200 lb
4. 33,308,000
÷ 9,000 ≈ 3,701 average elephants
1b. 0.25 inch
x
=
0.25 inch
x
=
x = 6.25 or 1
64 inches
1
42 by 1
64
2a. M =
12(30)
360 × $1,665.84 = $599,702.40
$599,702.40 – $268,000 = $331,702.40
12(20)
7.45
11
⎛⎞
+−
M =
12(30)
1,200 1,200
7.45
⎝⎠⎝ ⎠
⎛⎞
5. The area of a regular polygon can be found with
the formula A = 1
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
$246,000 – d. The amount the Bricely family
8. $9,400 × 0.9082 = $8,537.08
10. Front-end ratio = Monthly housing expenses
Monthly gross income ,
s, and monthly
front-end ratio is 63
sq
m
++
=
$137,865
12
= 0.213 or 21%
12. Let x represent the number of years. The
exponential function is the rent multiplied by 1
plus the increase expressed as a decimal raised
to the power x–1; y = 1,975(1.036)x–1.
13a. 30 × 25 = 750 sq ft
14a. $1,700
$928 + $696 + $290 + $1,700 = $3,614
$5,800 – $3,614 = $2,186
expenses.
15a. y = 1.137x + 598.98
16. B1 = $500,000
12(30)
6.95 6.95
$500,000 1
⎛⎞⎛ ⎞
+
17. Let x represent the number of years. The
x = 70
5(70) + 4y = 730
4y = 380
y = 95
$70 per hour for loading/unloading and $95 per
12(20)
5.95
11
⎛⎞
+−
1, 2 0 0 = $1,086.07
19d. $1,569.81 – $1,083.67 = $486.14
19e. $218,069.80 – $488.55 = $217,581.25
20. B1 = $350,000
12(15)
6.25 6.25
$350,000 1
⎛⎞⎛ ⎞
+
I1 = $350,000 × 6.25
1, 2 0 0 = $1,822.92
P1 = $3,000.98 – $1,822.92 = $1,178.06
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.
A2 = 1, then put the formula = A2+1 in A3 and
copy to the remaining rows. B2 = 1,700, then put
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.
A2 = 1, then put the formula = A2+1 in A3 and
copy to the remaining rows. B2 = 2,600, then put
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
⎛⎞⎛ ⎞
+
⎜⎟⎜ ⎟