Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Review Exercises 6
Review Exercise 6, Solution 1:
a. Point A lies in the fourth quadrant
b. Point B lies in the second quadrant
c.
Point C lies on the Xaxis
d.
Point D lies in the fourth quadrant
e.
Point E lies on the Xaxis
f.
Point F lies on the Yaxi
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 6.4
Exercise 6.4, Solution 1:
a.
Equation (1)
y 3x 8 0
Equation (2)
y x 4 0
From equation (1), y 3x + 8 = 0
y = 3x 8
Substitute this into Equation (2)
y x 4 0
(3x 8) x + 4 = 0
2x 4 = 0
2x = 4
x= =2
4
Solving for x,
2
Substituting this in Equatio
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 3.2
Exercise 3.2, Solution 1:
a.
0.70 =
V f 180
180
, Solving for V f , we get,
V f = 306.00
b.
0.90 =
V f 90
90
, Solving for V f , we get,
V f = $9.00
c.
1.50 =
V f 4500
4500
, Solving for V f , we get,
Vf = $11,250.00
d.
0.2575 =
855.10 Vi
,
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 5.3
Identify the last date of the discount period and the credit period for the payment terms with ordinary dating in
Problem 1 and 2
Exercise 5.3, Solution 1:
#
Invoice date
Payment terms
Last date of
discount period
Last date of credit
period
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 8.5
Exercise 8.5, Solution 1:
Maturity value in Option (a) = $50,000(1 + 0.0185 2) = $51,850.00
Maturity value in Option (b) = $50,000(1 + 0.015) 2 = $51,511.25
Therefore she can earn more in Option (a), by $51,850.00  $51,511.25 = $338.75
Exer
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 4.3
Exercise 4.3, Solution 1:
a. CHF200 to British pounds
CHF: = CHF:
1.4865: 1 = 200: x
1.4865 200
=
1
x
x = 134.544231.= 134.54
Therefore, you will receive 134.54 for CHF200.
b. C$3000 to US dollars
C$: US$ = C$: US$
1.1115: 1 = 3000: x
1.111
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 7.4
Exercise 7.4, Solution 1:
Number of units: 84, S= $90, VC=$65, FC=$2100
TR=$7560
TVC=$5460
Using the formula:
CM
CM
TR TVC
100%
TR
7560 5460
100% 27.7778%
7560
NI= (CM Ratio
NI = (0.2778
TR) FC
7560) 2100 = 0
Net income is $0, this means t
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 11.3
Exercise 11.3, Solution 1:
a.
This is an ordinary simple annuity because:
Payments are made at the end of each payment period (semiannually)
Compounding period (semiannually) = payment period (semiannually)
n = 2 payments/year 5 years =
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 7.2
Exercise 7.2, Solution 1:
a.
Assume that she has to produce and sell x pens to breakeven.
FC = $1900.00, S = $3.00, VC = $0.50, capacity = 1000
TR = S
x = 3x
TC = FC + (VC
x) = 1900 + 0.50x
At breakeven, TR = TC
3x = 1900 + 0.50x
2.50x =
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
SelfTests Exercises 11
SelfTest Exercise 11, Solution 1:
This is an ordinary simple deferred annuity as:
Payments are made at the end of each payment period (monthly)
Compounding period (monthly) = payment period (monthly)
The deferred period is 1 year
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 9.1
Exercise 9.1, Solution 1:
Nominal Interest Rate,
Compounding Frequency,
and Time Period
a.
b.
c.
d.
Number of
compounding
periods per year
(m)
Periodic
Interest Rate (i)
Terms in
Years (t)
Number of
Compoundin
g Periods for
the Term (n)
2
2.
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 9.2
Exercise 9.2, Solution 1:
Present
Value
(PV)
Nominal
Interest
Rate (j)
Compounding
Frequency (m)
a.
$1000.00
5.11%
2
b.
$3550.50
4.65%
4
c.
$16,500.0
0
6.30%
12
d.
$9650.75
6.57%
1
Periodic
Interest
Rate (i)
Number of
Compoundin
g Periods (n
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 4.4
Exercise 4.4, Solution 1:
Index Number on selected date =
Index number 2011=
Index number2014=
Value on selected date
10
Value on base date
37,000
100 115 .6
32,000
40,000
100 125.0
32,000
Exercise 4.4, Solution 3:
Index Number on selected d
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 5.5
Exercise 5.5, Solution 1:
a.
C = $50.75
S =?
S=C+M
$
%
$14.25
M/C = 28.08%
P
Therefore, S = C + M = 50.75 + 14.25 = $65
Rate of markup on cost: M/C =
14.25
50.75
= 0.280788.
+E
M
M/S = 21.92%
+C
S
= 28.08%
$50.75
$65.00
Rate of markup on sel
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 9.3
Exercise 9.3, Solution 1:
a.
Present
Value
(PV)
$4984.62
Nominal
Interest
Rate (j)
5.38%
b.
$8597.29
5.82%
4
c.
$12,000.0
0
4.89%
12
d.
$7500.00
7.42%
1
Periodic
Interest
Rate (i)
2.69%
Number of
Compoundin
g Periods (n)
10
Future
Value
(FV)
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Review Exercises 11
Review Exercise 11, Solution 1:
This is an ordinary simple deferred annuity as:
Payments are made at the end of each payment period (quarterly)
Compounding period (quarterly) = payment period (quarterly)
The deferred period is 4 years.
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 5.6
Exercise 5.6, Solution 1:
a.
P
$
$850.00
+E
$300.00
S = $2150
P = $850
E = $300
Therefore, M = P + E = 850 + 300 = $1150.00
M
$1150.00
S=C+M
M/C = 115.00%
M/S = 53.49%
Therefore, C = S M = 2150 1150 = $1000.00
Rate of markup on cost: M/C =
1
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 2.1
Exercise 2.1, Solution 1:
a.
7xy;
4y
y; 3
b.
c.
9xy;
6y
Exercise 2.1, Solution 3:
3.
a.
Constant term is 5; coefficient of the first term is 5; the coefficient of the second term is
b.
Constant term is 1; coefficient of the first term is
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 9.5
Exercise 9.5, Solution 1:
a.
Principal
$7000
b.
$2500
$2850
3 years and 5 months
c.
$3250
$3925
4 years and 6 months
d.
$5000
$5650
3 years
a.
Maturity Value
$7975
t = 2years and 9months
2
Term
2 years and 9 months
Nominal Interest Rate
4.77
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 7.1
Exercise 7.1, Solution 1:
Fixed Cost
(FC)
per month
Variable
cost (VC)
per unit
Selling
Price (S)
per unit
Breakeven
volume (x)
per month
a.
$1000
$3
$13
b
.
c.
$8000
$70
$5890
d
.
$2300
Total Revenue
(TR) per month
at BreakEven
100
Total
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 7.3
Exercise 7.3, Solution 1:
Fixed Costs
(FC)
per period
Variable
costs (VC)
per unit
Selling
Price (S)
per unit
Total Variable
Costs (TVC)
per period
Total
Revenue
(TR) per
period
Total
Costs
(TC) per
period
Net
Income
(NI) per
period
Number
o
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 2.2
Exercise 2.2, Solution 1:
a.
2x 3
2x
5
b.
c.
3x + 25
d.
6(3 + x)
Exercise 2.2, Solution 3:
a.
x + 6 = 10
b.
6x = 72
x
5
c.
2
3
d.
4
x 12
Exercise 2.2, Solution 5:
a.
x + 6 = 10
x + 6 6 = 10 6
x=4
b.
6x = 72
6x
6
72
6
x = 12
c.
x
5
x
5
4
5 4
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercise 2.5
Exercise 2.5, Solution 1:
S=C+M
C+M=S
C+MM=SM
C=SM
Exercise 2.5, Solution 3:
S=C+E+P
C+E+P=S
C+E+PCP=SCP
E=SCP
Exercise 2.5, Solution 5:
P=RB
RB=P
R B P
R
R
B
P
R
Exercise 2.5, Solution 7:
S = P (1 + r t)
P (1 + r t) = S
S
1+rt= P
S
11+rt= P
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Review Exercises 7
Review Exercise 7, Solution 1:
a.
Let x be the number of bouquets to be sold per month to breakeven.
S = $14, FC = $2700, VC = $8.50, =?
TR = S
x = 14x
x = 8.5x
TVC = VC
TC = FC + TVC = 2700 + 8.5x
At breakeven TR = TC
14x = 2700 +
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 5.2
Exercise 5.2, Solution 1:
List price (L)
Single discount rate (d)
Amount of discount (d L)
a
$1875
20%
$375
$1500
b
$230
12%
$27.60
$202.40
c
$800
54%
$432
$368
d
$500
2%
$10
$490
a.
Amount of discount = d
L=
N
b.
d=
c.
= $1875.00
L dL 1875
Southern Alberta Institute of Technology (SAIT) (SAIT Polytechnic)
Business Mathematics
BMAT 1040

Fall 2016
Exercises 6.2
Exercise 6.2, Solution 1:
a.
Let the missing value be b
(3, b) satisfies the equation 2x + 3y = 18
We have 2 3 + 3b = 18
6 + 3b = 18
3b = 18 6 = 12
12
b= 3 =4
Therefore, the missing value is 4 and the ordered pair is (3, 4)
b.
Let the missin