MATH 114
Final (Version A)
Fall 2022
INSTRUCTOR:
Claude Hurtubise
COURSE:
Math114 Business Math
Mathematics and Statistics
Okanagan College
Kelowna Campus
Date: December 08, 2022; Time: 13:00PM; Duration 165 minutes.
This exam has 11 questions for a total of 100 points. Partial marks may be awarded.
SPECIAL INSTRUCTIONS
ˆ Show and explain all your work unless the question directs otherwise. Simplify all answers.
ˆ The use of a BAII plus calculator or a graphing calculator is permitted.
ˆ Answer the questions in the spaces provided on the question sheets. If you run out of room
for an answer, continue on the back of the page.
ˆ All time value of money questions require a timeline.
ˆ If additional space is needed, you may write on the back of the page. Please indicate if you
do so.
ˆ There are 12 short answer parts, 3 medium answer questions, 7 long answer questions in this
exam.
Question: S/A
2
3
4
5
6
7
8
9
10
11
Total
Points:
4
4
6
6
8
8
8
8
10
14
100
24
Score:
STUDENT NAME (print):
STUDENT NUMBER:
SIGNATURE:
This exam consists of 14 pages including this cover page. Check to ensure that it is complete.
MATH 114 (Fall 2022)
Final A (continued)
Short Answer: Total of 24 marks
Clearly indicate you answer either by underlining or circling.
24
1. (1) Solve x : 2 = 3 : 7 for x.
(2) Simplify
500
(1 +
0.08 25
)
2
0.08
2
−1
.
(3) There are 60 miles in 100Km. How many miles are there in 425Km?
(4) What is 135% of $17?
Page 2 of 14
MATH 114 (Fall 2022)
Final A (continued)
(5) Simplify 2 × (23 − 3) − 20 ÷ (2 + 23 )
(6) If T C represents total costs, and T C = 15x + 850. At what price would the firm
be better off shutting down production rather than produce?
(7) How many days are there between May 16, 2009 and December 10, 2021?
(8) $5000 is invested for 7 months at 4% simple interest. How much interest is earned
Page 3 of 14
MATH 114 (Fall 2022)
Final A (continued)
(9) The net price on a laptop is $1,444.75. The list price is $1,899.99. What is the
discount rate?
(10) Solve for a and b. Leave solutions in the form (a, b).
3a − b = 7
2a + b = 8
(11) How many payments will it take an initial investment of $25,000 grows to $35,000
at a rate of return of 3.95% per year compounded quarterly? (Round up)
(12) What monthly compounded interest rate is equivalent to 6% compounded semiannually?
Page 4 of 14
MATH 114 (Fall 2022)
Final A (continued)
Medium Answer: Total of 20 marks
All questions from this section must be done algebraically.
4
2. Consider the timeline below.
Today
1 mo
299 mo
25 yrs
2000
2000
2000
5% monthly
(1) Classify the annuity. (There should be two names.)
(2) How much would you pay for this annuity?
4
3. The alumni of UNBC donated a total of $37,500 for the institution’s scholarship fund.
If the fund earns 5.5% compounded semiannually, what is the size of the annual bursary
UNBC can award in perpetuity, starting immediately? (Hint: Factor out payment)
Page 5 of 14
MATH 114 (Fall 2022)
6
Final A (continued)
4. Suppose year end contributions to an RRSP start at $2,000 and increase by 3.5% per
year thereafter, for the next 25 years. If money earns 5.25% compounded annually,
compute the following.
(1) Draw a time diagram for this annuity with as much detail as you can.
(2) Wow much will have in your account at the end of 25 years?
(3) What is the value of the 16th payment? (Hint: Think of this as finding the FV.)
Page 6 of 14
MATH 114 (Fall 2022)
6
Final A (continued)
5. John bought a loan that would have paid him $9,750 in two years. Six months in, he
had to sell the loan at a discounted rate. The loan was paying 5.25% quarterly.
(1) What did John pay for the loan?
(2) If the buyer earns 6% quarterly for the remainder of the term, what price did the
buyer purchase the loan for from John?
(3) What is the effective interest rate (compounded quarterly) that John earned for the
time he held the loan?
Page 7 of 14
MATH 114 (Fall 2022)
Final A (continued)
Long Answer: Total of 62 marks
Show your work either using the BAII calculator or algebraically. Timelines
are required for this section; with dates properly displayed.
8
6. You took out three loans: $3500 on June 21, 2020, a loan for $6,000 on October 10, 2020
and a final loan for $10,000 on January 4, 2021. What total debt do I owe on October
31, 2022? Assume that I was charged 5% simple interest on all of the short term debts.
Use October 31, 2008 as a focal date. Include a time-line.
Page 8 of 14
MATH 114 (Fall 2022)
Final A (continued)
7. You own a whisky shop and purchase a bottle for a list price of $425 less discounts of
10%, 20% and 40%.
2
(a) What single discount is equivalent to the discount you received?
2
(b) You mark up the bottle 30% of cost for overhead and 35% of the selling price to
account for profit. What is the selling price of the bottle?
2
(c) Compute both the rate of markup over cost and the gross profit margin.
2
(d) The bottle was marked down so that it sells at 5% above cost. What was the rate
of markdown?
Page 9 of 14
MATH 114 (Fall 2022)
Final A (continued)
8. Black Swan Cooperage coopers bourbon barrels. It requires 10 hours of labour at $35 per
hour and $70 worth of material (on average) to cooper one barrel. It sells the barrels to
distilleries for $700 each. Annual fixed costs at Black Swan Cooperage total $7,200,000.
3
(a) Write down the profit function for Black Swan Cooperage.
2
(b) What is the break-even volume of barrels per month? (Round up)
2
(c) How many barrels must Black Swan Cooperage sell per month for a monthly net
income (profit) of $250,000? (Round up)
1
(d) When should Black Swan Cooperage shut down its operations
Page 10 of 14
MATH 114 (Fall 2022)
8
Final A (continued)
9. You have decided to sell your stake in a business to your business partner. To this end,
a contract was signed that required your partner to pay you sums of $5,000 and $10,000
in 3 and 5 years respectively. Your partner has asked to re-negotiate the contract and
has proposed to make a payment of $8,000 in 4 years and to complete his obligation with
a second payment at 5 years. If interest is 5% compounded monthly, what should you
accept as the second payment using year-5 as the focal date? Include a time-line.
SET
N
I/Y
P/Y
C/Y
Present Value
Payment
Future Value
SET
N
I/Y
P/Y
C/Y
Present Value
Payment
Future Value
Therefore, the second payment at year-5 is:
Page 11 of 14
MATH 114 (Fall 2022)
Final A (continued)
10 10. Christina contributed $1,000 to an RRSP at the beginning of each calendar quarter for
the past 25 years. The plan earned 8% compounded monthly for the first 10 years and
11% compounded quarterly for the last 15 years. Christina now intends to withdraw
equal amounts at the beginning of each month for the next 15 years. If the funds earn
8.25 % compounded semiannually, what maximum monthly amount can be withdrawn?
Include a time-line.
Compute
SET
N
I/Y
P/Y
C/Y
Present Value
Payment
Future Value
Compute
SET
N
I/Y
P/Y
C/Y
Present Value
Payment
Future Value
Compute
SET
N
I/Y
P/Y
C/Y
Present Value
Payment
Future Value
Page 12 of 14
MATH 114 (Fall 2022)
Final A (continued)
14 11. Nathan takes a $450,000 mortgage in order to purchase a Big White condo. The mortgage will be repaid by monthly payments for the next 25 years at 3.25% compounded
semi-annually, starting at the end of the month.
(a) Compute the required periodic equivalent rate needed to do the problem by hand.
(b) Compute the payments required to pay off the loan.
SET
N
I/Y P/Y C/Y Present Value Payment
Page 13 of 14
Future Value
MATH 114 (Fall 2022)
Final A (continued)
(c) Use the table above to construct a partial amortization schedule for Nathan’s mortgage giving details of the first payment, the 50th payment and the last two payments,
and include the payment lines.
Payment Number Payment
0
Interest Portion Principal Portion Principal Balance
1
.
.
.
50
.
.
.
.
n-1 =
n=
(d) Show how the last interest portion is calculated using the periodic interest.
(e) What is the total interest paid on the mortgage?
Page 14 of 14