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mathematics
fundamentals of business mathematics in canada
Questions and Answers of
Fundamentals of Business Mathematics in Canada
How long did it take a $5000 investment earning 8% compounded quarterly to grow to be worth $17,067.92?
To be equivalent to 5.5% compounded annually, what must be the nominal rate witha. Semiannual compounding?b. Quarterly compounding?c. Monthly compounding?
How many months will it take for an investment of $1000 to grow to be worth $1072.44 at 3% compounded monthly?
Calculate the income yield, capital gain yield, and rate of total return in each of 2014 and 2015 for Suncor Energy shares and RBC Canadian Dividend Fund units. Use the data in Tables 9.3 and
Philippe contributed $4300 to an RRSP eight years and six months ago. The money was invested in a Canadian Equity mutual fund. The investment is now worth $5537.82. Over the entire period, what
A few years ago Avtar invested $6000 in a compound-interest GIC that earned 2.5% compounded semiannually. He recently received the maturity value of $6626.92. What was the term of the GIC?
To be equivalent to 7% compounded quarterly, what must be the nominal rate witha. Annual compounding?b. Semiannual compounding?c. Monthly compounding?
Jessica borrowed $5963 at an interest rate of 9% compounded annually. No payments have been made on the loan, and its current balance is $10,000. How many years ago did Jessica borrow the money?
A bank pays a simple interest rate of 2.1% on 30-to-179-day Gies of at least $100,000. What is the effective annualized rate of returna. On a 40-day GIC?b. On a 160-day GIC?
Calculate the income yield, capital gain yield, and rate of total return in each of 2014 and 2015 for Cineplex Inc. shares and PH&N Bond Fund units. Use the data in Tables 9.3 and 9.4.Tables
Camille can obtain a residential mortgage loan from a bank at 5.5% compounded semiannually or from an independent mortgage broker at 5.4% compounded monthly. Which source should she pick if other
A strip bond that will mature 8 years from now at its $10,000 face value can be purchased today for $8630.18. What rate of return (compounded semiannually) will this bond provide to an investor?
Lisa is offered a loan from a bank at 4.2% compounded monthly. A credit union offers similar terms, but at a rate of 4.4% compounded semiannually. Which loan should she accept? Present calculations
A trust company pays 1.5% compounded semiannually on its three-year GIC. For you to prefer an annually compounded GIC of the same maturity, what value must its nominal interest rate exceed?
Liam invested $1800 at 4.15% compounded quarterly. The investment is now worth $2692.11. How long ago was the original investment made?
A $1000 five-year compound-interest GIC matured at $1041.25. What semiannually compounded rate of interest did it earn?
Rounded to the nearest month, how long will it take a town's population to grow from 32,500 to 40,000 if the annual growth rate is 3%?
A community festival attracted 1354 people this year. If organizers expect attendance to grow at 5% per year, how many years will it take for the festival attendance to grow to 2000 people? Round
The maturity value of a $5000 four-year compound-interest GIC was $5839.72. What quarterly compounded rate of interest did it earn?
Rounded to the nearest month, how long will it take a business to grow from 400 customers per year to 550 customers per year if the business owner expects the customer base to grow by 12.5% per year?
Mr Maxine found an old pay statement from nine years ago. Her hiring wage at the time was $13.50 versus her current wage of $20.80 per hour. At what equivalent (compound) annual rate has her wage
Banks usually quote residential mortgage interest rates on the basis of semiannual compounding. An independent mortgage broker is quoting rates with monthly compounding. What rate would the broker
If the Consumer Price Index rose from 111.5 to 125.8 over an 8 1/2 year period, what was the equivalent compound annual inflation rate during the period?
Three years ago Mikhail invested $7000 in a three-year compound-interest GIC. He has just received its maturity value of $7321.99. What was the monthly compounded rate of interest on the GIC?
Use the Rule of 72 to estimate how long it will take for an investment to double in value if it earns 4.65% compounded annually. Then; solve for the exact doubling time using the algebraic approach
The home the Bensons purchased 13 years ago for $115,000 is now appraised at $385,000. What has been the annual rate of appreciation of the value of their home during the 13-year period?
Jeff purchased Hudson's Bay Company shares on the Toronto Stock Exchange for $27.10. Twelve months later the shares were trading at $23.01. The shares paid dividends totalling $0.20. What was Jeff's
What annually compounded rate of interest will an investor need to earn if an investment of $100,000 is to grow to be worth $1,000,000 over a 25 year period?
Marina deposited $1800 into an investment earning 6.4% compounded quarterly. When her investment is worth $2000, she will withdraw the money and make a down payment on a car. Rounded to the nearest
Section 347 of the Criminal Code of Canada makes it illegal to charge more than 60% annual interest Is a private lender who is charging a rate of 4.2% per month operating within the law? Provide
A bank offers a rate of 1.8% compounded semiannually on its four-year GIC. What monthly compounded rate should the bank offer on four-year GICs to make investors indifferent between the alternatives?
What is the time remaining until the maturity date of a $50,000 strip bond if it has just been purchased for $33,839.92 to yield 2.38% compounded semiannually until maturity?
The price of Telus shares rose 26.68%, 13.61%, 12.15% and 1439% in the years 2011, 2012, 2013, and 2014, respectively. Then the share price fell by 8.95% in 2015.a. What was the overall five-year
Hussain's marketing business grew from only 36 active customers, to a total of 212 customers five years later. What annually compounded rate of growth has Hussain's business experienced over the
A sum of $10,000 invested in the BirchLeaf Growth Fund at the end of 2004 would have declined to $5054.22 by the end of 2015. What compound annual rate of return did the fund realize during this 11
On December 31, 2015, the Templeton Growth Fund fad sheet reported that$10,000 INVESTED IN TEMPLETON GROWTH FUND IN 1954 WOULD BE WORTH $10.43 MILLION TODAY.What compound annual rate of return did
To the nearest month, how long will it take an investment to double in value if it earns 3.75% compounded semiannually?
Camille can obtain a residential mortgage loan from a bank at 4.75% compounded semiannually or from an independent mortgage broker at 4.68% compounded monthly. Which source should she pick if other
The population of Canada grew from 24,820,000 in 1981 to 35,851,800 in 2015. What was the overall compound annual rate of growth in our population during the period?
A $20,000-face-value strip bond was purchased for $10,045.94, providing the investor with a rate of return of 4.2% compounded semiannually. To the nearest day, how long before the maturity date was
Mutual funds with assets in precious metals have displayed high price volatility in recent years. For example, the Sentry Precious Metals Growth Fund had annual returns in successive years from 2010
The Consumer Price Index (based on a value of 100 in 2002) rose from 44.0 in 1980 to 78.4 in 1990. What was the (equivalent) annual rate of inflation in the decade of the 1980s?
A $4000 loan at 4.8% compounded monthly was settled by a single payment of $5000 including accrued interest. Rounded to the nearest day, how long after the initial loan was the $5000 payment made?
ABC Ltd. reports that its sales are growing at the rate of 12% per month. DEF Inc. reports sales increasing by 4% each quarter. What is each company's effective annual rate of sales growth?
The Consumer Price Index (based on a value of 100 in 2002) rose from 78.4 in 1990 to 95.4 in 2000. What was the (equivalent) annual rate of inflation in the decade of the 1990s?
If money is worth 3.6% compounded quarterly, how long (to the nearest day) before a scheduled payment of $6000 will $5000 be an equivalent payment? For the purpose of determining the number of days
Belleville Credit Union has established interest rates on its three-year GICs so that the effective rate of interest is 2.6% on all three compounding options. What are the monthly, semiannually, and
You are offered a loan at a rate of 4.5% compounded monthly. What semiannually compounded nominal rate would a competing bank need to offer in order to provide an equivalent rate?
The Consumer Price Index (based on a value of 100 in 2002) rose from 116.5 in 2010 to 126.6 in 2015. What was the (equivalent) annual rate of inflation in the five years from 2010 to 2015?
Columbia Trust wants its annually, semiannually, and monthly compounded five-year GICs all to have an effective interest rate of 2.75%. What nominal annual rates should it quote for the three
An investor paid $6315.29 to purchase a $10,000 face value strip bond for her RRSP. At this price the investment will provide a return of 3.47% compounded semiannually. How long (to the nearest day)
Victor cannot find the original record of his purchase four years ago of units of the Imperial Global Equity Income Pool Fund. The current statement from the fund shows that the total current value
According to the Canadian Real Estate Association, the average selling price of Canadian homes rose from $67,000 in 1980 to $470,000 in 2016. What has been the overall compound annual appreciation of
Consider the Province of Nova Scotia strip bond in Table 9.1.a. Present calculations to verify, to the nearest dollar, the bond's price on February 26, 2016, based on the quoted yield of 1.75%
Terry was supposed to pay $800 to Becky on March 1. At a later date, Terry paid Becky an equivalent payment in the amount of $895.67. If they provided for a time value of money of 8% compounded
The following table shows the rates of total return in successive years from 2011 to 2015 for the BMO Global Diversified Fund Series T5 and for the benchmark Toronto Stock Exchange S&P/MX
An investor's portfolio increased in value from $100,000 to $193,000 over a seven-year period in which the Consumer Price Index rose from 114.1 to 125.2. What was the compound annual real rate of
Consider the Province of Ontario strip bond in Table 9.1.a. Present calculations to verify, to the nearest dollar, the bond's price on February 26, 2016, based on the quoted yield of 2.66% compounded
A bank offers a rate of 2.3% compounded semiannually on its four-gear GICs. What monthly and annually compounded rates should it quote in order to have the same effective interest race at all three
The following table shows the rates of total return in successive gears from 2011 to 2015 for the Renaissance Global Health Care Fund and for the benchmark Toronto Stock Exchange S&P/TSX
An investment grew in value from $14,380 to $21,570 during a five-year period. During that same period, the Consumer Price Index rose from 116.5 to 125.2. What was the compound annual real rate of
The proceeds from the sale of a $4500 five-year promissory note bearing interest at 5% compounded quarterly were $5277.81. How many months before its maturity date was the note sold if it was
To the nearest day, how long will it take a $20,000 investment to grow to $22,000 (including accrued interest) if it earns 3% compounded quarterly? Assume that a quarter-year has 91 days.
The following table shows the rates of total return in successive years from 2011 to 2015 for the Dynamic Precious Metals Fund and for the benchmark Toronto Stock Exchange S&P/TSX Composite
If the number of workers in the manufacturing sector in Canada declined by 9% from the end of 2008 to the end of 2016, what was the compound annual rate of attrition in the industry during the period?
When discounted to yield 71.98% compounded monthly, a $2600 three-year promissory note bearing interest at 9.25% compounded annually was priced at $3110.41. How many months after the issue date did
A four-year promissory note for $3800 plus interest at 1.5% compounded semiannually was sold 18 months before maturity for $4000. What quarterly compounded nominal rate of return will the buyer
According to Statistics Canada, undergraduate students paid an average of $6191 in tuition fees for the 2015/2016 academic year compared to fees of $4747 for the 2008/2009 year. During the same
Assume that the Royal Bank shares in Table 9.3 will pay a $3.50 per share dividend in 2016. What would the share price have needed to be at the end of 2016 for a total rate of return in 2016 of
An investment earned 3% compounded semiannually for two years and 5% compounded annually for the next three years. What was the equivalent annually compounded rate of return for the entire five-year
The Lipper Fund Awards recognized mutual funds that have excelled in delivering strong performance. The Fidelity Canadian Growth Company Series B (managed by Pyramis Global Advisors) won a Lipper
The Mawer Canadian Equity Fund won a 2015 Lipper Award for one of the best 10-year compound annual returns of any Canadian mutual fund. This fund invested in securities of larger Canadian companies.
An investor's portfolio increased in value by 53% over a five-year period. At the same time, the Consumer Price Index rose from 119.9 to 126.6. What was the portfolio's annually compounded real rate
When discounted to yield 3.5% compounded quarterly, a $4500 four-year promissory note bearing interest at 5.5% compounded semiannually was priced at $5169.10. How long after the issue date did the
The following table shows the rates of total return in successive years from 2011 to 2015 for the NEI Ethical Balanced Fund Series A and for the benchmark Toronto Stock Exchange S&T/TSX Composite
How much interest will you have earned altogether at the end of a two-year period if you deposit $75 at the start of every month for 24 months? Assume your money will earn 6% compounded monthly.
Sylvia and Maclean are exactly the same age. From age 30 to age 60, Sylvia invested $3000 at the end of every six months. Maclean invested $6000 at the end of every six months from age 45 to age 60.
Calculate the future value of an ordinary annuity consisting of monthly payments of $300 for five years. The rate of return was 3% compounded monthly for the first two years, and will be 4.5%
You are selling a residential building lot. Mr. Seebach is offering $195,000 cash. Mrs. Chan is offering $100,000 down and payments of $6250 at the end of each calendar quarter for the next four
What semiannually compounded rate and effective rate of interest are being charged on a $12,000 loan if payments of $1022.89 at the end of every six months will repay the loan in seven years?
To accumulate $200,000 after 20 years, what amount must be invested each year if the investment earns 6% compounded annually and the contributions are made a. At the beginning of each year?b. At
After contributing $2000 at the end of each quarter for 13 3/4 years, Foster has accumulated $151,147.22 in his RRSP. What effective rate of return was earned by the RRSP over the entire period?
Kelli deposited $500 at the end of every month into an investment earning 5% compounded quarterly. What type of annuity is this?
What is the future value after 5 1/2 years of $100 invested at the end of every quarter if the funds earn 5% compounded quarterly?
An annuity consists of payments of $100 at the end of every quarter for 5 years. What is the annuity's present value, using a discount rate of 10% compounded quarterly?
Calculate the amounts that will be accumulated after 20 years ifa. $1000 is invested at the end of every six months at 3.5% compounded semiannually.b. $2000 is invested at the end of every year at
An ordinary general annuity earns a nominal rate of 4% compounded annually. Rounded to the nearest 0.001%, what is the corresponding periodic rate (1,) if the annuity's payments are made semiannually?
Payments at the end of every three months are made on a loan carrying an interest rate of 8% compounded quarterly. What type of annuity is this?
$75 was invested at the end of every month for 2 1/2 years. Calculate the future value if the funds earned 3% compounded monthly.
An ordinary general annuity earns a nominal rate of 6% compounded monthly. Rounded to the nearest 0.001%, what is the corresponding periodic rate (9 if the annuity's payments are made quarterly?
A recent college graduate is going to begin making savings deposits of $100 at the start of every month into an investment earning 3.6% compounded monthly. What type of annuity is this?
Aaron has been contributing $2000 at the end of every half-year for the past four years to a savings plan that earns 6% compounded semiannually. What amount will he have in three years from now if he
What amount is needed to purchase an annuity paying $2500 at the end of every calendar quarter for the next 25 years? Assume the funds used to purchase the annuity will earn 6% compounded quarterly.
Brunswick Trucking has signed a five-year lease with Ford Credit Canada Ltd. on a new truck. Lease payments of $1900 are made at the beginning of each month. To purchase the truck, Brunswick Trucking
An ordinary general annuity earns a nominal rate of 5% compounded semiannually. Rounded to the nearest 0.001%, what is the corresponding periodic rate (9 if the annuity's payments are made monthly?
What is the present value of an annuity due consisting of semiannual payments of $1000 for 25 years, if money can earn a. 3% compounded semiannually? b. 4% compounded semiannually?
Roham deposits $275 at the start of every month into an account that earns 4% compounded quarterly. What type of annuity is this?
What will be the future value after 6 years and 7 months of regular month-end investments of $435 earning 3.6% compounded monthly?
A contract requires end-of-month payments of $175 for the next 81 gears. How much would an investor pay to purchase this contract if she requires a rate of return of 3% compounded monthly?
Connor is exactly 27 years old today. Beginning today, he will deposit $2000 at the start of each year into a savings account that earns 4.75% compounded annually. How much will Connor have in his
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