Assignment 2
This assignment covers material from Units 5–7 in the Mathematics 244
Study Guide. It is due after you have completed Unit 7 of the Study Guide.
Total Marks
1.
130
The chart below shows the number of cheques cashed in Alberta
clearing centres during the years 1992–1996.
Cheques Cashed in Alberta Clearing Centres 1992–1996
(Millions of Cheques)
Year
Calgary
Edmonton
Other
Total
1992
1993
1994
1995
1996
62
77
102
115
137
44
59
71
86
105
10
12
14
16
18
116
148
187
217
260
Source: Hypothetical
a.
Business Mathematics
Construct a line chart to compare each centre’s activity over the
five-year period. (9 marks)
1
b. Construct a pie chart for the activity that took place in 1996.
(6 marks)
2
Mathematics 244 / Assignment 2
2.
Solve for x and y, graphically. (6 marks)
4x
x
Business Mathematics
2y
5y
0
11
3
3.
A company produces and sells 15,300 sound cards per year. They sell
each of the cards for $104 wholesale; the cards cost $69.75 each to
produce. The company’s fixed costs per year to produce sound cards is
$320,000.
a.
What is the break-even point on sound cards in terms of dollar
value and units sold? (6 marks)
b. If demand increases and the selling price of the sound cards
increases by 10%, what is the new break-even point? (6 marks)
4
Mathematics 244 / Assignment 2
4.
Assume that the number of work stoppages that occurred in the
automotive industry from 1985 to 1996 were as follows:
18, 8, 14, 12, 20, 20, 10, 18, 14, 20, 16, 15.
a.
Given this hypothetical information, calculate:
i.
the arithmetic mean. (2 marks)
ii. the median. (2 marks)
iii. the mode. (1 mark)
iv. the range. (1 mark)
b. Calculate the standard deviation. (5 marks)
Business Mathematics
5
5.
The following frequency distribution table shows the orders received by
Department A of ABC Mail Order House on December 15 of last year.
ABC Mail Order House Orders
Department A, December 15
Value of Orders
$15 to $25
$25 to $35
$35 to $45
$45 to $55
$55 to $65
$65 to $75
$75 to $85
# of
Orders
5
10
20
30
20
10
5
Source: Hypothetical
a.
Calculate the arithmetic mean. (5 marks)
b. Calculate the standard deviation. (6 marks)
6
Mathematics 244 / Assignment 2
Business Mathematics
6.
Sam borrowed $460 at a simple interest rate of 9.5% for 66 days. How
much must he repay? (3 marks)
7.
A note for $2,400 was repaid after 120 days in the amount of $2,471.01.
What was the simple interest rate on the note? (3 marks)
7
8
8.
How many years are needed for $55 to yield $8.8 in interest at the
simple interest rate of 8%? (3 marks)
9.
Moira received $1,200 in cash as the proceeds from a demand loan from
a bank. After 120 days she paid $1,248. What simple interest rate did the
bank charge? (3 marks)
Mathematics 244 / Assignment 2
10. Margaret received $671.50 in cash as the proceeds from a loan. She paid
the lender back $680. The rate was 10% simple interest. Find the length
of the loan in months. (5 marks)
11. Two payments of $2,000 each are to be received 6 and 12 months from
now. If money is worth 10% simple interest, what is the total equivalent
value of the payments today? (4 marks)
Business Mathematics
9
12. Payments of $2,600, due 50 days ago, and $3,100, due in 40 days, are to
be replaced by $3,000 today and another payment in 30 days. What must
the second payment be if the payee is to end up in an equivalent
financial position? Money now earns 8.25% simple interest. Use 30 days
from now as the focal date. (10 marks)
10
Mathematics 244 / Assignment 2
13. Roland owes three debts:
$500 due in one year;
$1,500 due in two years, plus simple interest at 6%;
$2,000 due in three years, plus simple interest at 5%.
He wants to discharge these debts by paying $1,000 now and two equal
but unknown payments in one and two years, respectively. Find the
size of the equal payments if money is, at present, worth 10% simple
interest. Use a focal date of two years. (10 marks)
Business Mathematics
11
14. Sylvia borrows $10,500 on August 25 and promises to make three equal
payments, one on October 15, one on December 10, and one on
February 28. If money is worth 9.75% simple interest, what is the size of
the equal payments? Use August 25 as the focal date. (12 marks)
12
Mathematics 244 / Assignment 2
15. On the June 12 interest payment date, the outstanding balance on Delta
Nurseries’ revolving loan was $65,000. The floating interest rate on the
loan stood at 9.25% simple interest on June 12, but rose to 9.5% simple
interest on July 3, and to 10% simple interest on July 29. If Delta made
principal payments of $10,000 on June 30 and July 31, what were the
interest charges to its bank account on July 12 and August 12? Present a
repayment schedule supporting the calculations. (12 marks)
Business Mathematics
13
16. A $5,000 demand loan was advanced on June 3. Fixed monthly payments
of $1,000 were required on the first day of each month, beginning July 1.
Prepare the full repayment schedule for the loan. Assume that the interest
rate remained at 12.5% simple interest for the life of the loan. (10 marks)
14
Mathematics 244 / Assignment 2