Calculate interest rates accurate to the nearest 0.01%. What semiannually compounded rate is equivalent to 6% compounded: 1. Annually? 2. Quarterly? 3. Monthly?
> A hockey goalie’s goals against average (GAA) is the average number of goals scored against him per (complete) game. In his first 20 games in goal, O.U. Sieve had one shutout, two 1-goal games, three 2-goal games, four 3-goal games, seven 4-goal games, t
> The monthly payments on a five-year loan at 7.5% compounded monthly are $200.38. 1. What was the original amount of the loan? 2. What is the balance after the 30th payment?
> A 20-year loan requires semiannual payments of $1037.33 including interest at 6.8% compounded semiannually. 1. What was the original amount of the loan? 2. What is the loan’s balance 8 1 2 years later (just after the scheduled payment)?
> Gabriela’s monthly payments of $567.89 will pay off her mortgage loan in 7 years and 5 months. The interest rate on her mortgage is 6.6% compounded monthly. What is the current balance on the loan?
> This problem demonstrates the dependence of the present value of an annuity on the number of payments. Using 7% compounded annually as the discount rate, calculate the present value of an ordinary annuity paying $1000 per year for: 1. 5 years. 2. 10 year
> Harold and Patricia Abernathy made a loan to their son, Jason, to help him purchase his first car. To repay the loan, Jason made payments of $2000 at the end of each year for five years. If the interest rate on the loan was 5% compounded annually, what w
> Isaac wishes to purchase a 25-year annuity providing monthly payments of $1000 for the first 15 years and $1500 for the remaining 10 years. An insurance company has quoted him a rate of return of 4.8% compounded monthly for such an annuity. How much will
> If money can earn 6% compounded monthly, how much more money is required to fund an ordinary annuity paying $200 per month for 30 years than to fund the same monthly payment for 20 years?
> Mr. and Mrs. Dafoe are doing some estimates of the amount of funds they will need in their RRSP to purchase an annuity paying $5000 at the end of each month. For each combination of term and monthly compounded interest rate in the following table, calcul
> The rate of return offered by Reliance Insurance Co. on its 20-year annuities is 4.8% compounded monthly. What amount is required to purchase a 20-year annuity with month-end payments of $1000?
> Imperial Life Inc. is quoting a rate of return of 5.2% compounded quarterly on 15-year annuities. How much will you have to pay for a 15-year annuity that pays $5000 (at the end of) every three months?
> The Rising Dough Bakery surveyed 100 customers to determine which of price, service, quality of goods, and promotions was the most important factor resulting in a recommendation to a friend or family member. Each factor was rated using a 4-point scale wh
> What is the present value of end-of-quarter payments of $2500 for seven years? Use a discount rate of 6% compounded quarterly.
> Determine the present value of payments of $100 at the end of each month for 20 years. Use a discount rate (interest rate) of 6% compounded monthly.
> Your client is scheduled to receive $2000 at the end of each year for the next 10 years. If money is currently worth 7% compounded annually, what is the present value of the annuity?
> The original lender wishes to sell a loan contract delivering month-end payments of $350 for another 11 years and 5 months. At what price would an investor be prepared to buy the contract in order to “build in” a rate of return of 8.75% compounded monthl
> This problem demonstrates the dependence of an annuity’s present value on the size of the periodic payment. Calculate the present value of 25 end-of-year payments of: 1. $1000 2. $2000 3. $3000 Use a discount rate of 5% compounded annually. After complet
> Danica has purchased $700 worth of units in a Global Equity Fund every calendar quarter for the past 7 years and 9 months. On average, the fund has earned 9% compounded quarterly. What were Danica’s holdings worth immediately after her last purchase?
> Elga plans to invest $175 every month by purchasing units of a diversified equity mutual fund. If the fund generates an overall rate of return of 6% compounded monthly, what will her holdings be worth after 8 1 4 years?
> Aaron contributed $2000 to his RRSP at the end of every half-year. What was the value of his RRSP after 12 1 2 years if the RRSP grew at 3.5% compounded semiannually?
> $75 was invested at the end of every month for 2 1 2 years. Calculate the future value if the funds earned 8% compounded monthly.
> Teddy plans on contributing $6,000 every year (the maximum allowable contribution in 2019) to his TFSA. What is the future value after 20 years if the funds earn 4.5% compounded annually?
> Lien, the proprietor of a grocery store, prepares her Deluxe Nut Combo Mix by mixing various ingredients she buys in bulk. The second column of the following table shows the amount of each ingredient Lien uses in making a batch of the combo mix. To set t
> Calculate the future value after 25 years in each of the following scenarios: 1. $6000 invested at end of each year earning 9% compounded annually. 2. $3000 invested at end of each half-year earning 9% compounded semiannually. 3. $1500 invested at end of
> This problem demonstrates the dependence of the future value of an annuity on the interest rate. Suppose $1000 is invested at the end of each year for 20 years. Calculate the future value if the investments earn an annually compounded rate of return of:
> Leona contributed $3000 to her RRSP on every birthday from age 21 to age 30 inclusive. She stopped employment to raise a family and made no further contributions. Her husband, John, started to make annual contributions of $3000 to his RRSP on his 31st bi
> Howard has been contributing $1200 every three months to an investment plan that has consistently earned 3% compounded quarterly. He did this for 4½ years until he lost his job unexpectedly and had to stop contributing to the plan during the 9 months he
> Rajeev’s new financial plan calls for end-of-quarter contributions of $2000 to his RRSP. In addition, at each year-end, he intends to contribute another $5000 out of the annual bonus he receives from his employer. What will be the amount in his RRSP afte
> Marika has already accumulated $18,000 in her RRSP. If she contributes $2000 at the end of every six months for the next 10 years, and $300 per month for the subsequent five years, what amount will she have in her plan at the end of the 15 years? Assume
> Herb has made contributions of $2000 to his RRSP at the end of every six months for the past eight years. The plan has earned 9.5% compounded semiannually. He has just moved the funds to another plan that earns 8% compounded quarterly. He will now contri
> Amir started contributing $5500 to a TFSA at the end of every year beginning in 2017. In 2019, the maximum allowable annual contribution was increased to $6000 and Amir planned to continue to contribute the maximum amount at the end of every year for the
> Dakota intends to save for occasional major travel holidays by contributing $275 at the end of each month to an investment plan. At the end of every three years, she will withdraw $10,000 for a major trip abroad. If the plan earns 6% compounded monthly,
> This problem demonstrates the dependence of the future value of an annuity on the number of payments. Suppose $1000 is invested at the end of each year. Assume the investments earn 10% compounded annually. Calculate the future value of the investments af
> An investor accumulated 1800 shares of Microtel Corporation over a period of several months. She bought 1000 shares at $15.63, 500 shares at $19.00, and 300 shares at $21.75. What was her average cost per share? (Note: Investors who purchase shares in th
> How much more will you have in your RRSP 30 years from now if you start to contribute $1000 per year at the end of this year, instead of waiting five years to begin contributing $1000 at each year-end? Assume that the funds earn 8% compounded annually in
> How much more will you have in your RRSP at age 65 if you begin annual $1000 contributions to your plan on your 26th birthday instead of on your 27th birthday? Assume that the RRSP earns 8% compounded annually, and that the last contribution is on your 6
> Dave has saved $20,000 for a down payment on a home and plans to save another $5000 at the end of each year for the next five years. He expects to earn 2.25% compounded annually on his savings. How much will he have in five years’ time?
> Calculate and rank the equivalent values eight years from now of the following cash flow streams: (i) A single payment of $5000 today. (ii) An ordinary annuity starting today with eight annual payments of $910. (iii) An ordinary annuity starting in three
> Pascal has just agreed with his financial planner to begin a voluntary accumulation plan. He will invest $500 at the end of every three months in a balanced mutual fund. How much will the plan be worth after 20 years if the mutual fund earns: 1. 5% compo
> Marcus spends $60 per month on cigarettes. Suppose he quits smoking and invests the same amount at the end of each month for 20 years. If the invested money earns 7.5% compounded monthly, how much will Marcus accumulate after 20 years?
> Your client has systematically invested $1000 at the end of each half-year for the past 17 years. The invested funds have earned 6.4% compounded semiannually. What is the value of your client’s investments today?
> Your client plans to invest $2000 at the end of each year. The rate of return on the investment is 7.5% compounded annually. What will be the value of the investment at the end of the 12 years?
> 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 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?
> 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
