Question: The owner of a residential building lot

> A portfolio earned annual rates of 20%, −20%, 0%, 20%, and −20% in five successive years. What was the portfolio’s five-year equivalent annually compounded rate of return?

> An investment earned 6% compounded semiannually for two years and 8% compounded annually for the next three years. What was the equivalent annually compounded rate of return for the entire five-year period?

> An investment grew in value from $5630 to $8485 during a five-year period. The annual rate of inflation for the five years was 2.3%. What was the compound annual real rate of return during the five years?

> An investor’s portfolio increased in value by 93% over a seven-year period in which the Consumer Price Index rose from 95.6 to 115.3. What was the compound annual real rate of return on the portfolio during the period?

> An initial $1800 investment was worth $2299.16 after two years and nine months. What quarterly compounded nominal rate of return did the investment earn?

> A $6000, three-year promissory note bearing interest at 11% compounded semiannually was purchased 15 months into its term for $6854.12. What monthly compounded discount rate was used in pricing the note?

> A four-year promissory note for $3800 plus interest at 9.5% compounded semiannually was sold 18 months before maturity for $4481. What quarterly compounded nominal rate of return will the buyer realize on her investment?

> Alihan’s transcript shows the following academic record for four semesters of part-time college studies. Calculate his cumulative GPA at the end of his fourth semester.

> A five-year promissory note for $5700 plus interest at 6.75% compounded semiannually was sold 18 months before maturity for $6620. What monthly compounded nominal rate of return will the buyer realize on the investment?

> Using the data given in Problems 21 and 22, calculate the annual rate of inflation for the 1970–1990 period. (Note: Simply averaging the two answers to Problems 21 and 22 will give only an approximation of the correct result.) Data from Problem 21: The

> According to Statistics Canada, business students in an undergraduate program paid an average of $6838 in tuition fees for the 2018/2019 academic year compared to fees of $1464 for the 1990/1991 year. During the same period, the Consumer Price Index rose

> The Consumer Price Index (based on a value of 100 in 2002) rose from 93.5 in 2000 to 115.1 in 2010. What was the (equivalent) annual rate of inflation in the first decade of the 2000s?

> The Consumer Price Index (based on a value of 100 in 1992) rose from 93.3 in 1990 to 113.5 in 2000. What was the (equivalent) annual rate of inflation in the decade of the 1990s?

> The Consumer Price Index (based on a value of 100 in 1986) rose from 67.2 in 1980 to 119.5 in 1990. What was the (equivalent) annual rate of inflation in the decade of the 1980s?

> The Canadian Consumer Price Index (based on a value of 100 in 1971) rose from 97.2 in 1970 to 210.6 in 1980. What was the (equivalent) annual rate of inflation in the decade of the 1970s?

> If the number of workers in the auto industry in Canada declined by 32% from its peak at the end of 1999 to the beginning of 2011, what was the compound annual rate of attrition in the industry during this period?

> What was the annually compounded nominal rate of growth if the future value of $1000 after 20 years was $4016.94?

> Monty purchased a strip bond for his RRSP. He paid $3800 for a $5000 face value bond with three years remaining until maturity. What semiannually compounded rate of return will he realize over the three years?

> A survey of 254 randomly chosen residences in a city revealed that 4 had four television sets, 22 had three TV sets, 83 had two TV sets, 140 had one TV set, and 5 had no TV set at all. Based on the survey, what would you estimate to be the average number

> What compound annual rate of return is required for an investment to double in: 1. 12 years? 2. 10 years? 3. 8 years? 4. 6 years? For each case, multiply the annual rate of return (in %) by the time period (in years). Compare the four products. Does the

> For an investment to triple in value during a 15-year period, 1. What annually compounded rate of return must it earn? 2. What quarterly compounded rate of return must it earn? 3. What monthly compounded rate of return must it earn?

> For an investment to double in value during a 10-year period, 1. What annually compounded rate of return must it earn? 2. What semiannually compounded rate of return must it earn? 3. What monthly compounded rate of return must it earn?

> The following table contains 1981 and 2018 population figures for five provinces. Calculate each province’s equivalent compound annual rate of population change during the period.

> 1. The population of Canada grew from 24,343,000 in 1981 to 37,268,000 in 2019. What was the overall compound annual rate of growth in our population during the period? 2. According to the Canadian Real Estate Association, the average selling price of Ca

> Three years ago Mikhail invested $7000 in a three-year compound interest GIC. He has just received its maturity value of $7867.34. What was the monthly compounded rate of interest on the GIC?

> The maturity value of a $5000 four-year compound interest GIC was $6147.82. What quarterly compounded rate of interest did it earn?

> Jan and Chelsea purchased their home 15 years ago for $198,000 and it is now appraised at $430,000. What was the (equivalent) annual rate of appreciation in the value of their home during the 15-year period?

> Mr. and Mrs. Markovich note that the condo they purchased 20 years ago for $70,000 is now appraised at $340,000. What was the (equivalent) annual rate of appreciation in the value of their condo during the 20-year period?

> No payments were made on a $3400 loan during its three-year term. What was the annually compounded nominal interest rate on the loan, if the amount owed at the end of the term was $4297.91?

> Svetlana is an independent insurance broker placing various clients with any of several insurance companies. On homeowner insurance policies, each month she receives: - $20 for each renewal of an existing policy; - $35 for each policy placed with a new c

> Ralph Harder has been transferred to Regina for five years. He has found a one-bedroom condo that he can buy for $180,000 or rent for $1000 per month, payable at the beginning of each month. He estimates that the resale value of the condo in five years w

> Two payments of $2000 each are scheduled for six months from now and two years from now. They are to be rescheduled as follows: a payment one year from now and a second payment, half the size of the first payment, three years from now. What must the amou

> Payments of $400 due eight months ago and $650 due three months ago were not made. Now the debtor is proposing to “make good” by two future payments that provide for a 7.5% compounded monthly rate of return to the creditor on the missed payments. The fir

> The scheduled payment stream consists of $5000 due today and $10,000 due in five years. It is proposed to replace this stream by an economically equivalent stream comprised of three equal payments due one, three, and five years from now. Determine the si

> Jorge is unable to make a $4500 payment due today. He proposes to settle the obligation by making three equal payments—one today, another in four months, and a third in nine months. What must each payment be to make the proposed payment stream equivalent

> Payments of $850 due two years ago and $1760 due six months ago have not been made. The proposed alternative is two equal payments, three months and nine months from now, that will put the payee in an equivalent economic position allowing that money can

> Marvin was supposed to make three payments of $2000 each—the first one year ago, the second one year from now, and the third three years from now. He missed the first payment and proposes to pay $3000 today and a second amount in two years. If money can

> Patrice defaulted on payments of $1000 due one year ago and $1500 due six months ago. A small claims court judgment orders her to make three payments—$800 one month from now, $900 four months from now, and a third payment seven months from now. The third

> A two-payment stream consisting of $1750 due today and $2900 due in 18 months is to be replaced by an economically equivalent stream comprised of an undetermined payment due in 9 months and a payment of $3000 due in 19 months. Calculate the unknown repla

> Three years ago, Andrea loaned $2000 to Heather. The principal with interest at 9% compounded semiannually is to be repaid four years from the date of the loan. Eighteen months ago, Heather borrowed another $1000 for 3 1 2 years at 8% compounded semiannu

> A $15,000 loan with interest being charged at 10% compounded quarterly was made 2 1 2 years ago and is due in two years. The debtor is proposing to settle the debt by a payment of $5000 today and a second payment in one year that will place the lender in

> Herb packs fish in 500-g cans on a processing line. He is paid $8.25 per hour plus $0.18 per kilogram for production in excess of 500 kg in a 7.5-hour shift. How much will he earn per day if he packs 250 cans per hour?

> Payments of $8000 due 15 months ago and $6000 due in six months are to be replaced by a payment of $4000 today, a second payment in nine months, and a third payment, three times as large as the second, in 1 1 2 years. What should the last two payments be

> Two payments of $3000 each are due today and five years from today. The creditor has agreed to accept three equal payments due one, three, and five years from today. Assuming that money can earn 7.5% compounded monthly, what payments will the creditor ac

> Payments of $5000 due three years from today and $7000 due five years from today are to be replaced by two payments due 1 1 2 and four years from today. The first payment is to be half the amount of the second payment. What should the payments be if mone

> CompuSystems was supposed to pay a manufacturer $19,000 on a date four months ago and another $14,000 on a date two months from now. Instead, CompuSystems is proposing to pay $10,000 today and the balance in five months, when it will receive payment on a

> A lottery prize gives the winner a choice between (1) $10,000 now and another $10,000 in 5 years, or (2) four $6700 payments—now and in 5, 10, and 15 years. 1. Which alternative should the winner choose if money can earn 3% compounded annually? In curren

> Henri has decided to purchase a $25,000 car. He can either liquidate some of his investments and pay cash, or accept the dealer’s proposal that Henri pay $5000 down and $8000 at the end of each of the next three years. 1. Which choice should Henri make i

> During its January Sale, Furniture City is offering terms of 25% down with no further payments and no interest charges for six months, when the balance is due. Furniture City sells the conditional sale contracts from these credit sales to a finance compa

> Scheduled payments of $3000 due today and $2000 due in 15 months are to be replaced by two payments—$1500 due in 15 months and a second payment of undetermined size due in 24 months. What must the second payment be for the two streams to be economically

> Using the information given in Problem 8, calculate the interest earned in the second year from a $1000 investment in each GIC. Data from Problem 8: Sun Life Financial offers a five-year compound interest GIC earning rates of 2.5%, 3%, 3.5%, 4.25%, and

> Mary sews for a clothing manufacturer. She is paid $7.50 per hour plus a piecework rate that depends on the type of garment in production. The current production run is men’s shirts, for which she is paid $3.00 for each unit exceeding her quota of 20 shi

> Sun Life Financial offers a five-year compound interest GIC earning rates of 2.5%, 3%, 3.5%, 4.25%, and 5% in successive years. Manulife offers a similar GIC paying rates of 2.75%, 3.25%, 3.5%, 4%, and 4.25% in successive years. For a $10,000 investment,

> How, if at all, will the future value of $1000 invested in a three-year variable-rate GIC differ if it earns 2%, 3%, and 4% in successive years instead of 4%, 3%, and 2% in successive years?

> If an investor has the choice between rates of 5.4% compounded quarterly and 5.5% compounded annually for a six-year GIC, which rate should she choose?

> A trust company offers three-year compound interest GICs earning 4.8% compounded monthly or 4.9% compounded semiannually. Which rate should an investor choose?

> Mrs. Sandhu placed $11,500 in a four-year compound interest GIC earning 6.75% compounded monthly. What is the GIC’s maturity value?

> A $5000 loan at 10% compounded annually is to be repaid by two payments three and five years from the date of the loan. The first payment of $3000 will be applied to the balance owed after conversion of interest to principal at the end of the first three

> The contract for a $4000 loan at 9% compounded quarterly requires two payments. The first payment of $2000 is required two years after the date of the loan. (It is applied to the balance owed after conversion of interest to principal.) A second payment i

> An eight-year note for $3800 with interest at 11% compounded semiannually was sold after three years and three months to yield the buyer 14% compounded quarterly. What price did the buyer pay?

> A four-year $8000 promissory note bearing interest at 13.5% compounded monthly was discounted 21 months after issue to yield 12% compounded quarterly. What were the proceeds from the sale of the note?

> Wojtek purchased a $10,000 face value strip bond on a date when it had 14 years left until maturity. The purchase price was based on a market yield of 6.2% compounded semiannually. He sold the bond 4 1 2 years later when the market yield was 5.2% compoun

> Sam is paid $34.50 per hour as a power plant engineer. He is paid 1.5 times the regular rate for all time exceeding 8 hours in a day or 40 hours in a week. Statutory holidays worked are paid at double time (in addition to holiday pay). What are his gross

> A pharmaceutical company had sales of $28,600,000 in the year just completed. Sales are expected to decline by 4% per year for the next three years until new drugs, now under development, receive regulatory approval. Then sales should grow at 8% per year

> The late 1970s and early 1980s were years of historically high rates of inflation in Canada. For the years 1978, 1979, 1980, 1981, and 1982 the rates of inflation were 8.8%, 9.2%, 10.9%, 12.6%, and 10.0%, respectively. 1. Suppose your hourly wage at the

> For a given term of a compound interest GIC, the nominal interest rate with annual compounding is typically 0.125% higher than the rate with semiannual compounding and 0.25% higher than the rate with monthly compounding. Suppose that the rates for five-y

> If the current discount rate on 15-year strip bonds is 4.75% compounded semiannually, how many $1000 face value strips can be purchased with $10,000?

> Mr. Dickson purchased a seven-year, $30,000 compound interest GIC with funds in his RRSP. If the interest rate on the GIC is 2.25% compounded semiannually, what is the GIC’s maturity value?

> Mrs. Janzen wishes to purchase some 13-year-maturity strip bonds with the $12,830 in cash she now has in her RRSP. If these strip bonds are currently priced to yield 5.25% compounded semiannually, how many $1000 denomination bonds can she purchase?

> Consider a $5000 face value Province of Saskatchewan strip bond that matures on March 5, 2029. If the yield does not change as years go by, what will be the bond’s value on: 1. March 5, 2019? 2. March 5, 2021? 3. March 5, 2023?

> Consider a $10,000 face value Government of Canada strip bond from the issue in Table 9.2 that matures on December 1, 2033. Assume the yield does not change as years go by. 1. What will be the bond’s value on June 1, 2022? 2. What will be the bond’s valu

> What price should be paid for a $5000 face value strip bond with 19.5 years remaining to maturity if it is to yield the buyer 6.1% compounded semiannually?

> A $1000 face value strip bond has 22 years remaining until maturity. What is its price if the market rate of return on such bonds is 2.5% compounded semiannually?

> Allison’s regular hourly rate of pay is $17.70. She is paid time and a half for all work on weekends and for any time over 7.5 hours on weekdays. Calculate her gross earnings for a week in which she works 4.5, 0, 7.5, 8.5, 6, 6, and 9 hours on Saturday t

> According to the 2016 census Warman, Saskatchewan, was the fastest growing municipality in Canada, with a population of 11,020 in 2016. If the population grew 9.17% per year from 2011 to 2016, what was the population in 2011?

> Mr. and Mrs. Rasuli would like to retire in 15 years at an annual income level that would be equivalent to $35,000 today. What is their retirement income goal if, in the meantime, the annual rate of inflation is: 1. 2%? 2. 3%? 3. 5%?

> Venezuela’s political crisis during the late 2010s resulted in hyperinflation. By November of 2018, the annual inflation rate stood at 1,300,000%! Prices were doubling every 19 days on average. The government had to issue new currency that chopped five z

> If the inflation rate for the next 10 years is 3.5% per year, what hourly rate of pay in 10 years will be equivalent to $15/hour today?

> How much money was needed 15 years ago to have the purchasing power of $1000 today if the (compound annual) rate of inflation has been: 1. 2%? 2. 4%?

> Eric invested $22,000 in a five-year regular-interest GIC earning 4.5% payable monthly. What is each monthly interest payment?

> How much will you need 20 years from now to have the purchasing power of $100 today if the (compound annual) rate of inflation during the period is: 1. 2%? 2. 3%? 3. 4%?

> Using the information given in Problem 16, how much would have to be initially invested in each GIC to have a maturity value of $20,000? Data from Problem 16: On the same date that the CIBC advertised rates of 2%, 2.5%, 3%, 3.25%, and 7% in successive y

> Using the information given in Problem 16, calculate the interest earned in the fourth year from a $10,000 investment in each GIC. Data from Problem 16: On the same date that the CIBC advertised rates of 2%, 2.5%, 3%, 3.25%, and 7% in successive years o

> On the same date that the CIBC advertised rates of 2%, 2.5%, 3%, 3.25%, and 7% in successive years of its five-year compound interest Escalating Rate GIC, it offered 2.75% compounded annually on its five-year fixed-rate GIC. How much more will a $10,000

> Ross’s compensation is to be changed from an hourly rate of $31.50 for a 40-hour workweek to a salary paid semimonthly. What should he be paid semimonthly in order for his annual earnings to remain the same?

> The BMO Bank of Montreal advertised rates of 1.8%, 2.25%, 2.6%, 3%, and 3.25% for the five successive years of its five-year compound interest RateOptimizer GIC. At the same time, the bank was offering fixed-rate five-year compound interest GICs yielding

> Western Life’s “Move-Up” compound interest GIC earns 4.125%, 4.25%, 4.5%, 4.875%, and 5% in successive years. What will be the maturity value of $7500 invested in this GIC?

> $8000 is invested in a five-year compound interest GIC earning interest rates of 2%, 2.5%, 3%, 3.5%, and 5% in successive years. What amount will the investor receive at maturity?

> A compound interest GIC will earn 5% compounded annually for the first two years and 6% compounded annually for the last three years of its five-year term. What will be the maturity value of $3000 invested in this GIC?

> Calculate the maturity value of $2000 invested in a five-year compound interest GIC earning 2.1% compounded annually.

> Using the information given in Problem 8, calculate the interest earned in the third year from a $10,000 investment in each GIC. Data from Problem 8: Sun Life Financial offers a five-year compound interest GIC earning rates of 2.5%, 3%, 3.5%, 4.25%, and

> Krista invested $18,000 in a three-year regular-interest GIC earning 4.2% payable semiannually. What is each semiannual interest payment?

> If your client’s objective is to have $10,000 in four years, how much should he invest today in a product earning 5.5% compounded annually?

> What amount today is economically equivalent to $8000 paid 18 months from now, if money is worth 5% compounded monthly?

> The maturity value of an investment after 42 months is $9704.61. What was the original investment, if it earned 3.5% compounded semiannually?

> Hasad is paid an annual salary of $54,600 based on a 40-hour workweek. What is his gross pay for a biweekly pay period if he works 43 hours in the first week and 46.5 hours in the second week? Overtime is paid at time and a half.

> What principal amount will have a maturity value of $5437.52 after 27 months if it earns 8.5% compounded quarterly?

> What is the present value of $10,000 discounted at 4.5% compounded annually over 10 years?

> Peggy has never made any payments on a five-year-old loan from her mother at 6% compounded annually. The total interest owed is now $845.56. How much did she borrow from her mother?

> If the total interest earned on an investment at 8.2% compounded semiannually for 8 1 2 years was $1175.98, what was the original investment?