Question: If a $5000 investment grew to $6450

> Assume that your client invests $1000 at the end of each of the next three years. The investments earn 4% compounded annually. What is the future value at the end of the three years?

> What will be the future value after 6 years and 7 months of regular month-end investments of $435 earning 8.5% compounded monthly?

> When a company calculates its earnings per common share for its financial statements, it uses the weighted average number of common shares outstanding during the year. Enertec Corp. began its fiscal year (January 1 to December 31) with 5 million common s

> This problem demonstrates the dependence of an annuity’s future value on the size of the periodic payment. Suppose a fixed amount will be invested at the end of each year and that the invested funds will earn 4% compounded annually. What will be the futu

> What semiannually compounded rate is equivalent to 4% compounded monthly?

> Calculate interest rates accurate to the nearest 0.01%. What monthly compounded interest rate is equivalent to 6% compounded: 1. Annually? 2. Semiannually? 3. Quarterly?

> Calculate interest rates accurate to the nearest 0.01%. What quarterly compounded rate is equivalent to 6% compounded: 1. Annually? 2. Semiannually? 3. Monthly?

> Calculate interest rates accurate to the nearest 0.01%. What semiannually compounded rate is equivalent to 6% compounded: 1. Annually? 2. Quarterly? 3. Monthly?

> Calculate interest rates accurate to the nearest 0.01%. What annually compounded interest rate is equivalent to 6% compounded: 1. Semiannually? 2. Quarterly? 3. Monthly?

> Calculate interest rates accurate to the nearest 0.01%. To be equivalent to 10% compounded monthly, what must be the nominal rate with: 1. Annual compounding? 2. Semiannual compounding? 3. Quarterly compounding?

> Calculate interest rates accurate to the nearest 0.01%. To be equivalent to 10% compounded quarterly, what must be the nominal rate with: 1. Annual compounding? 2. Semiannual compounding? 3. Monthly compounding?

> Ted and Laurie need to borrow money to pay their annual golf membership dues or they will have to pay interest on the late dues at 9% compounded weekly. If they borrow money to pay the dues with a one-year payback period, at what quarterly compounded rat

> After completing your 2018 income tax return, you discover that you owe income tax. You can either pay the late payment penalty at 6% compounded daily for one year or borrow the money you need to pay your taxes. Below what semiannually compounded rate wi

> Marcel must temporarily invest extra money in his retail business every fall to purchase additional inventory for the Christmas season. On September 1, he already had a total of $57,000 invested in his business. Subsequently, he invested or withdrew cash

> The timber rights to a tract of forest can be purchased for $250,000. The harvesting agreement would allow 25% of the timber to be cut in each of the first, second, fourth, and fifth years. The purchaser of the timber rights would be required to replant,

> In your search for the best rate on a new-car loan, you note that various lenders quote rates with differing compounding frequencies. Your car dealer offers financing at 7.5% compounded monthly. For you to be indifferent as to which lending rate to choos

> A life insurance company pays investors 5% compounded annually on its five-year GICs. For you to be indifferent as to which compounding option you choose, what would the nominal rates have to be on GICs with: 1. Semiannual compounding? 2. Quarterly compo

> Calculate interest rates accurate to the nearest 0.01%. To be equivalent to 10% compounded semiannually, what must be the nominal rate with: 1. Annual compounding? 2. Quarterly compounding? 3. Monthly compounding?

> A bank offers a rate of 2.0% 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?

> A credit union pays 5.25% compounded annually on five-year compound interest GICs. It wants to set the rates on its semiannually and monthly compounded GICs of the same maturity so that investors will earn the same total interest. What should the rates b

> 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 have to give to match 3.45% compounded semiannually avail

> You are offered a loan at a rate of 9% compounded monthly. Below what nominal rate of interest would you choose semiannual compounding instead?

> A trust company pays 2.5% 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?

> For a three-year GIC investment, what nominal rate compounded monthly would put you in the same financial position as 5.5% compounded semiannually?

> What quarterly compounded rate is equivalent to 10.5% compounded monthly?

> A seasonal manufacturing operation began the calendar year with 14 employees. During the year, employees were hired or laid off on various dates as shown in the following table. What was the average number of employees on the payroll during the calendar

> What semiannually compounded rate is equivalent to 8.5% compounded quarterly?

> What monthly compounded rate is equivalent to 6% compounded quarterly?

> What quarterly compounded rate is equivalent to 7.5% compounded semiannually?

> Calculate interest rates accurate to the nearest 0.01%. To be equivalent to 10% compounded annually, what must be the nominal rate with: 1. Semiannual compounding? 2. Quarterly compounding? 3. Monthly compounding?

> 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?

> 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?

> Rounded to the nearest month, how long will it take an investment to triple if it earns: 1. 9% compounded annually? 2. 8% compounded quarterly?

> 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?