Question: Rounded to the nearest month, how long

> Which interest rate would you prefer to pay on a loan: 9% compounded monthly, 9.1% compounded quarterly, 9.2% compounded semiannually, or 9.3% compounded annually?

> Which interest rate would you prefer to earn on a three-year GIC: 6% compounded monthly, 6.1% compounded quarterly, 6.2% compounded semiannually, or 6.3% compounded annually?

> Which of the following nominal interest rates has the highest effective rate: 12% compounded annually, 11.9% compounded semiannually, 11.8% compounded quarterly, or 11.7% compounded monthly?

> For the effective rate to be 7%, what must be the corresponding nominal interest rate with: 1. Annual compounding? 2. Semiannual compounding? 3. Quarterly compounding? 4. Monthly compounding?

> To have an effective rate of 5%, what must be the corresponding nominal interest rate with: 1. Annual compounding? 2. Semiannual compounding? 3. Quarterly compounding? 4. Monthly compounding?

> What is the effective interest rate corresponding to a nominal annual rate of: 1. 4% compounded monthly? 2. 8% compounded monthly? 3. 12% compounded monthly?

> The balance on Nucorp’s revolving loan began the month at $35,000. On the eighth of the month another $10,000 was borrowed. Nucorp was able to repay $20,000 on the 25th of the 31-day month. What was the average balance on the loan during the month? (Use

> What is the effective interest rate corresponding to a nominal annual rate of: 1. 9% compounded semiannually? 2. 9% compounded quarterly? 3. 9% compounded monthly?

> An oil company wants to drop the effective rate of interest on its credit card by 3%. If it currently charges a periodic rate of 1.7% per month, at what amount should it set the periodic rate?

> A department store chain currently charges 18% compounded monthly on its credit card. To what amount should it set the monthly compounded annual rate if it wants to add 2% to the effective interest rate?

> Belleville Credit Union has established interest rates on its three-year GICs so that the effective rate of interest is 7% on all three compounding options. What are the monthly, semiannually, and annually compounded rates?

> Columbia Trust wants its annually, semiannually, and monthly compounded five-year GICs all to have an effective interest rate of 5.75%. What nominal annual rates should it quote for the three compounding options?

> What is the effective interest rate corresponding to a nominal annual rate of: 1. 7.5% compounded semiannually? 2. 7.5% compounded quarterly? 3. 7.5% compounded monthly?

> ABC Ltd. reports that its sales are growing at the rate of 1.3% per month. DEF Inc. reports sales increasing by 4% each quarter. What is each company’s effective annual rate of sales growth?

> Camille can obtain a residential mortgage loan from a bank at 6.5% compounded semiannually, or from an independent mortgage broker at 6.4% compounded monthly. Which source should she pick if other terms and conditions of the loan are the same? Present ca

> Craig can buy a three-year compound interest GIC paying 4.6% compounded semiannually or 4.5% compounded monthly. Which option should he choose? Present calculations that support your answer.

> Lisa is offered a loan from a bank at 7.2% compounded monthly. A credit union offers similar terms, but at a rate of 7.4% compounded semiannually. Which loan should she accept? Present calculations that support your answer.

> A restaurant owner sets her menu prices at a predetermined percentage of her input costs for food, ingredients, and beverages. The second column of the following table shows the prices as a percentage of these costs for various menu categories. The third

> After 27 months of quarterly compounding, a $3000 debt had grown to $3810. What effective rate of interest was being charged on the debt?

> If a $5000 investment grew to $6450 in 30 months of monthly compounding, what effective rate of return was the investment earning?

> A company reports that its sales have grown 3% per quarter for the last eight fiscal quarters. What annual growth rate has the company been experiencing for the last two years?

> If the nominal rate of interest paid on a savings account is 2% compounded monthly, what is the effective rate of interest?

> If an invoice indicates that interest at the rate of 0.62% per month will be charged on overdue amounts, what effective rate of interest will be charged?

> What is the effective rate of interest on a credit card that calculates interest at the rate of 1.8% per month?

> What is the effective interest rate corresponding to a nominal annual rate of: 1. 6% compounded semiannually? 2. 6% compounded quarterly? 3. 6% compounded monthly?

> Rounded to the nearest month, how long will it take a town’s population to: 1. Grow from 32,500 to 40,000 if the annual growth rate is 3%? 2. Shrink from 40,000 to 32,500 if the annual rate of decline is 3%?

> A few years ago Avtar invested $6000 in a compound interest GIC that earned 4.5% compounded semiannually. He recently received the maturity value of $7168.99. What was the term of the GIC?

> A number of years ago, your client invested $6000 at a rate of return of 9% compounded annually. If the investment is currently worth $10,968.25, for how long has she held the investment?

> Suppose a group of consumers spend 30% of their disposable income on food, 20% on clothing, and 50% on rent. If over the course of a year the price of food rises 10%, the price of clothing drops 5%, and rent rises 15%, what is the average price increase

> What is the remaining time until the maturity date of a $10,000 strip bond if it is purchased for $4011.33 to yield 6.4% compounded semiannually until maturity?

> Marilyn was supposed to pay $1450 to Bernice on March 1. Some time later Marilyn paid Bernice an equivalent payment of $1528.01, allowing for a time value of money of 4.5% compounded monthly. When did Marilyn make the payment?

> The current balance on a loan is $3837.30. If the interest rate on the loan is 10% compounded monthly, how long ago was the $2870 loan made?

> $5000 invested in a GIC earning 3.7% compounded semiannually matured at $5789.73. What was the term of the GIC?

> $7500 was borrowed for a four-year term at 9% compounded quarterly. The terms of the loan allow prepayment of the loan based on discounting the loan’s maturity value at 7% compounded quarterly. How long (to the nearest day) before the maturity date was t

> A $5000 face value strip bond may be purchased today for $1073.36 yielding the purchaser 7.27% compounded semiannually. How much time (to the nearest day) remains until the maturity date? Assume that each half-year has exactly 182 days.

> Wilf paid $557.05 for a $1000 face value strip bond. At this price the investment will yield a return of 5.22% compounded semiannually. How long (to the nearest day) before its maturity date did Wilf purchase the bond? Assume that each half-year has exac

> If money is worth 8% 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 in a partial calendar quarter, assume that a full quarter

> A $4000 loan at 7.5% 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? For the purpose of determining the number of days in a pa

> The proceeds from the sale of a $4500 five-year promissory note bearing interest at 9% compounded quarterly were $6055.62. How many months before its maturity date was the note sold if it was discounted to yield 10.5% compounded monthly?

> One of the methods permitted by Generally Accepted Accounting Principles (GAAP) for reporting the value of a firm’s inventory is weighted average inventory pricing. The Boswell Corporation began its fiscal year with an inventory of 156

> How long did it take $4625 earning 7.875% compounded annually to grow to $8481.61?

> When discounted to yield 10.5% compounded monthly, a $2600 three-year promissory note bearing interest at 12.25% compounded annually was priced at $3283.57. How many months after the issue date did the discounting take place?

> Rounded to the nearest month, how long will it take money to lose 25% of its purchasing power if the annual rate of inflation is: 1. 2%? 2. 4%?

> Rounded to the nearest month, how long will it take money to lose half of its purchasing power if the annual rate of inflation is: 1. 2.5%? 2. 3.5%?

> Your client invests $10,000 today at a rate of return of 7.7% compounded quarterly. Rounded to the nearest month, how long will it take the investment to grow to $22,000?

> Your client wants to invest a $250,000 inheritance and grow it to $325,000. Rounded to the nearest month, how long will this take if the investment earns 7% compounded annually?

> How long before a future payment of $1000 would a payment of just $100 (only 10% of the nominal amount of the future payment) be an economically equivalent alternative? Round your answer to the nearest month. Assume money can earn 4.8% compounded semiann

> Rounded to the nearest month, how long before a scheduled payment of $10,000 would a payment of $5000 be an economically equivalent alternative? Assume money is worth 5% compounded annually.

> Rounded to the nearest quarter year, how long will it take an investment to quadruple if it earns: 1. 8% compounded annually? 2. 9% compounded semiannually?

> One year ago, Sook-Yin allocated the funds in her portfolio among five securities in the proportions listed below. The rate of return on each security for the year is given in the third column of the table. Calculate the rate of return for the entire por

> Rounded to the nearest month, how long will it take an investment to double if it earns: 1. 8.4% compounded annually? 2. 10.5% compounded semiannually?

> An $1100 investment earning 6.3% compounded annually grew to $4483.92. What was the term of the investment?

> Anders discovered an old pay statement from 11 years ago. His monthly salary at the time was $2550 versus his current salary of $4475 per month. At what (equivalent) compound annual rate has his salary grown during the period?

> The Templeton Growth Fund has been around since 1954. If you had invested $10,000 in the fund when it was launched in 1954 it would have been worth $5.09 million 54 years later. What compound annual rate of return did the fund realize over this period?

> When he died in 1790, Benjamin Franklin left $4600 to the city of Boston, with the stipulation that the money and its earnings could not be used for 100 years. The bequest grew to $332,000 by 1890. What (equivalent) compound annual rate of return did the

> 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 $10,440.32. Over the entire period, what annually compounded nominal rate of return has the investm

> The amount owed on a promissory note for $950 after two years and five months is $1165.79. What monthly compounded nominal rate of interest was charged on the debt?

> A strip bond that will mature 7 1 2 years from now at its $13,000 face value can be purchased today for $9042. What rate of return (compounded semiannually) will this strip bond provide to an investor?

> In June of 2006, AIC Limited published full-page advertisements focused on the fact that its AIC Advantage Mutual Fund was Canada’s “Best Performing Canadian Equity Fund” over the 20 years ending May 31, 2006. The equivalent annual rate of return during

> BMO’s Dividend Fund was launched in 1994 and had annual returns in successive years from 2009 to 2018 inclusive of 19.83%, 9.71%, −2.62%, 6.93%, 17.92%, 13.54%, –1.43%, 11.76%, 10.93% and –6.78%, respectively. For 3-year, 5-year, and 10-year periods ende

> The “age” of an account receivable is the length of time that it has been outstanding. At the end of October, a firm has $12,570 in receivables that are 30 days old, $6850 in receivables that are 60 days old, and $1325 in receivables that are 90 days old

> At the end of 2014, the Industrial Alliance (IA) Dividends Fund had the best 10-year compound annual return of any Canadian diversified equity mutual fund. During the 10-year period, this fund invested primarily in the shares of large Canadian companies.

> At the end of 2018, the RBC Canadian Dividend Fund was the largest equity mutual fund in Canada. The aggregate market value of its holdings at the end of 2018 was $18.8 billion. The fund’s annual returns in successive years from 2009 to 2018 inclusive we

> A portfolio earned annual rates of 20%, 15%, −10%, 25%, and −5% in five successive years. What was the portfolio’s five-year equivalent annually compounded rate of return?

> 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