Mid Term Practice
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Which line of the table shows the correct values for i and n?
Compound Interest Rate per Annum (%) / Compounding Frequency / Term / Interest Rate per Compounding Period, i (%) / Number of Compounding Periods, n5.4 / annually / 3 years / 0.54 / 3
3.0 / semi-annually / 18 months / 0.015 / 3
2.4 / monthly / 2 years / 0.001 / 24
3.65 / daily / 2 years / 0.001 / 730
A. / Line 1
B. / Line 2
C. / Line 3
D. / Line 4
____ 2. Determine the interest earned on a 4-year investment with an interest rate of 2.85%, compounded semi-annually, if the future value is $5039.33.
A. / $139.33B. / $439.33
C. / $539.33
D. / $5039.33
____ 3. Determine the regular annual payment required to have $5000 at the end of 12 years if the investment earns 3% interest, compounded annually.
A. / $320.08B. / $333.82
C. / $348.61
D. / $352.31
____ 4. Claude has been approved for a $12 400 loan to pay for a new boat. The terms of the loan state that it must be repaid in 4 years at a simple interest rate of 9.6%. How much interest must Claude pay on this loan?
A. / $17 892.21B. / $4761.60
C. / $5492.21
D. / $17 161.60
____ 5. Soloman bought a used car for $12 000 during a sale. The sale was that as long as the debt was paid off in three years, no interest would be charged. Otherwise, a penalty equal to an interest rate of 10.5%, compounded monthly, would be charged, starting from when he first borrowed the money. If Soloman were to make regular monthly payments, how much would each payment need to be so that he pays off the debt in time?
A. / $390.03B. / $456.13
C. / $533.71
D. / $333.33
____ 6. Nigel is purchasing a house for $225 000 that appreciates at a rate of about 1.5% per year. He will finance this purchase with a 20-year mortgage at an interest rate of 4.5%, compounded semi-annually, with monthly payments, where he is required to make a 15% down payment. If Nigel sells the house in 10 years at market value, what is his total cost over the 10 years?
A. / $114.12B. / $144 677.98
C. / $178 427.98
D. / $33 864.12
____ 7. Jace needs special equipment for his job as a landscaper. He has two options. He can buy the equipment which costs $9600. Jace will finance this purchase through the vendor by making regular monthly payments over 4 years at an interest rate of 6.2%, compounded monthly. At the end of the 4 years, the equipment will be worthless. He can also lease the equipment at a cost of $180 per month. Both options require a down payment of $750. What is the total cost of the cheaper option?
A. / $9390.00B. / $10 765.44
C. / $10 015.44
D. / $7890.00
____ 8. Consider the following two sets:
• A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
• B = {–9, –6, –3, 0, 3, 6, 9, 12}
Which Venn diagram correctly represents these two sets?
A. /B. /
C. /
D. /
____ 9. What is a biconditional statement?
A. / a conditional statement that is only true in two casesB. / a statement that uses the form “if p, then q”
C. / a conditional statement whose converse is also true
D. / a conditional statement whose inverse is also true
____ 10. Which truth tables apply to the conditional statement below and its converse?
“If the milk is not refrigerated, then it will spoil.”
A. C.
p / q / p Þ q / p / q / p Þ qT / T / T / T / T / T
q / p / q Þ p / q / p / q Þ p
T / T / T / T / F / F
B. D.
p / q / p Þ q / p / q / p Þ qF / F / T / T / F / F
q / p / q Þ p / q / p / q Þ p
F / F / T / T / F / F
A. / A.
B. / B.
C. / C.
D. / D.
Short Answer
1. Bella has created the following investment portfolio:
• Every month, for the past 7.5 years, she has put $100 from her paycheque into a savings account, earning 1.75%, compounded monthly.
• She has a $6000 GIC, with a 10-year term, that she purchased 10 years ago and earned 6.2%, compounded annually.
What is the current value of her portfolio?
2. Vladimir is buying a house that costs $375 000. He has negotiated a mortgage with the bank that requires a down payment of 12% of the cost of the house. He will pay off the mortgage with regular monthly payments over 25 years at an interest rate of 2.8%, compounded semi-annually. How much interest will he pay?
3. A loan of $73 550 at an interest rate of 4.5%, compounded monthly, is to be paid off in 8 years with regular monthly payments. How much will each monthly payment be?
4. Yorgan is buying his friend’s used car for $5000. He cannot afford it now but he has two different options to finance the cost.
Option A: Get a loan from his friend that must be paid back in 1 year with a $1000 fee.
Option B: Use his credit card which charges 16.7%, compounded daily. He plans to make the minimum monthly payment of $100 on the debt for 1 year, then pay off the debt in full.
What annual interest rate does the fee in Option A equate to if you assume the interest compounds monthly?
5. Fredo purchased a new computer that costs $1200. He wants to pay off the debt in 6 months and has two options:
• Use his line of credit, compounded monthly, which is 2.4% above the Bank of Canada rate, which is 1%.
• Finance the purchase through the vendor at a rate of 3.6%, compounded monthly.
What is the total cost of the cheaper option?
6. If you draw a card at random from a standard deck of cards, you will draw a card that is either red (R) or black (B). The card will also either be a number card (N) or a face card (F). Determine n(F È N).
7. A music school offers lessons on 12 different instruments.
piano / bagpipe / guitarrecorder / accordion / clarinet
violin / flute / xylophone
trumpet / steel drum / banjo
Determine the number of instruments with both keys (K) and strings (S).
8. A music school offers lessons on 12 different instruments.
piano / bagpipe / guitarrecorder / accordion / clarinet
violin / flute / xylophone
trumpet / steel drum / banjo
Determine the number of instruments that are played with sticks or have a mouthpiece (PÈM).
9. A music school offers lessons on 12 different instruments.
piano / bagpipe / guitarrecorder / accordion / clarinet
violin / flute / xylophone
trumpet / steel drum / banjo
Determine the number of instruments with strings (S), and with strings and a bow (S Ç B).
10. Write the converse of the conditional statement below. Verify the converse or disprove it with a counterexample.
“If an animal has eight legs, then the animal is a scorpion.”
Problem
1. a) Olivia plans to retire in 45 years, when she is 65, and hopes to have $900 000 saved. For each investment option below, how much does she need to invest at the end of each period to reach her goal? Show your work.
i) 4.35% compounded monthly
ii) 6.15% compounded annually
b) Compare the rate of return for options i) and ii). Which option should she choose?
2. Jayma wants to buy a new bicycle at the end of the season in 4 months. The bicycle she wants costs $450, but will be on sale for 10% off. How much should Jayma deposit at the end of each month into an account that earns 3.2%, compounded monthly, to save enough for the bicycle? Explain. Show your work.
3. Danielle is buying a house that costs $275 000. She will finance the purchase with a 25 year mortgage with an interest rate of 2.9%, compounded semi-annually. She must make a down payment of 15% of the purchase price.
a) How much will each payment be? Show your work.
b) How much interest will Danielle end up paying by the time she has paid off the loan? Show your work.
c) How much will she pay altogether for the house? Show your work.
4. Arjun is opening a summer business as a handyman. He has 50 clients. He wants to earn $8000 over the summer. Equipment and supplies for all the projects costs $4500 which he will finance with a bank loan at 5.0%, compounded monthly, which he will pay off with regular monthly payments of $650.
a) How much will it cost Arjun to run his business? Show your work.
b) On average, how much should Arjun charge each client if he wants to make his desired profit of $8000? Show your work.
5. Liam asked 90 people if they preferred tea or coffee.
• 8 people liked both.
• 55 people liked coffee.
• 32 people liked tea.
Determine how many people did not like coffee or tea. Draw a Venn diagram to show your solution.
6. A restaurant survey asked 300 people if they preferred Indian or Chinese food.
• 146 people liked both.
• 213 people liked Indian food.
• 219 people liked Chinese food.
Determine how many people did not like Indian or Chinese food. Draw a Venn diagram to show your solution.
7. Write the statement below in “if p, then q” form. If the statement is biconditional, rewrite it in biconditional form. If the statement is not biconditional, provide a counterexample.
“A streetcar is a vehicle that runs on rails.”
8. If the converse of a conditional statement is true, what do you know about the inverse? Explain.
9. Consider this conditional statement:
“If a is negative in the quadratic function y = ax2 + bx + c, then the parabola opens downward.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
10. Consider this conditional statement:
“If = a, then a < b.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
Mid Term Practice
Answer Section
MULTIPLE CHOICE
1. ANS: B PTS: 1 DIF: Grade 12 REF: Lesson 1.3
OBJ: 1.1 Explain the advantages and disadvantages of compound interest and simple interest. | 1.2 Identify situations that involve compound interest. | 1.3 Graph and compare, in a given situation, the total interest paid or earned for different compounding periods. | 1.8 Solve a contextual problem that involves compound interest.
TOP: Compound interest: future value KEY: compound interest | compounding period
2. ANS: C PTS: 1 DIF: Grade 12 REF: Lesson 1.4
OBJ: 1.2 Identify situations that involve compound interest. | 1.8 Solve a contextual problem that involves compound interest. TOP: Compound interest: present value
KEY: compound interest | future value | present value
3. ANS: D PTS: 1 DIF: Grade 12 REF: Lesson 1.5
OBJ: 3.2 Determine, using technology, the total value of an investment when there are regular contributions to the principal. | 3.5 Determine, using technology, possible investment strategies to achieve a financial goal. | 3.8 Solve an investment problem.
TOP: Investments involving regular payments
KEY: compound interest | future value
4. ANS: B PTS: 1 DIF: Grade 12 REF: Lesson 2.1
OBJ: 1.1 Explain the advantages and disadvantages of compound interest and simple interest. | 1.2 Identify situations that involve compound interest. | 1.3 Graph and compare, in a given situation, the total interest paid or earned for different compounding periods. | 1.4 Determine, given the principal, interest rate and number of compounding periods, the total interest of a loan. | 1.5 Graph and describe the effects of changing the value of one of the variables in a situation that involves compound interest. | 1.6 Determine, using technology, the total cost of a loan under a variety of conditions; e.g., different amortization periods, interest rates, compounding periods and terms. | 1.8 Solve a contextual problem that involves compound interest.
TOP: Analyzing loans KEY: loans
5. ANS: D PTS: 1 DIF: Grade 12 REF: Lesson 2.3
OBJ: 1.2 Identify situations that involve compound interest. | 1.3 Graph and compare, in a given situation, the total interest paid or earned for different compounding periods. | 1.4 Determine, given the principal, interest rate and number of compounding periods, the total interest of a loan. | 1.5 Graph and describe the effects of changing the value of one of the variables in a situation that involves compound interest. | 1.7 Compare and explain, using technology, different credit options that involve compound interest, including bank and store credit cards and special promotions. | 1.8 Solve a contextual problem that involves compound interest.
TOP: Solving problems involving credit KEY: loans
6. ANS: D PTS: 1 DIF: Grade 12 REF: Lesson 2.4
OBJ: 2.1 Identify and describe examples of assets that appreciate or depreciate. | 2.2 Compare, using examples, renting, leasing and buying. | 2.3 Justify, for a specific set of circumstances, if renting, buying or leasing would be advantageous. | 2.4 Solve a problem involving renting, leasing or buying that requires the manipulation of a formula. | 2.5 Solve, using technology, a contextual problem that involves cost-and-benefit analysis. TOP: Buy, rent, or lease?