Question: Rajeev’s new financial plan calls for

> A baseball player’s slugging percentage is the average number of hits a batter gets in all the “at bats” they have in their games played. This statistic differs from their batting average in that it is weighted based on the number of bases run for a sing

> Influence of Annuity Variables Go to the Student Edition on Connect. Under the Student Resources, you will find a link to the “Influence of Annuity Variables” chart. This interactive chart enables you to observe and compare the effects of changes in the

> An ordinary annuity consists of quarterly payments of $100 for 5 1 2 years. What is the annuity’s present value, discounting at 10% compounded quarterly?

> The British Columbia Teachers’ Pension Plan allows a teacher to begin collecting a retirement pension before age 60, but the pension is reduced by 3% for each year the retiring teacher’s age is under 60. For example, a teacher retiring at age 56 would re

> An individual qualifying for Canada Pension Plan benefits may elect to start collecting the CPP monthly retirement benefit at any time between the ages of 60 and 70. If the retirement benefit starts after age 65, the pension payments are increased (from

> For its No Interest for One Year sale, Flemming’s Furniture advertises that customers pay only a 10% down payment. The balance may be paid by 12 equal monthly payments with no interest charges. Flemming’s has an operating loan on which it pays interest a

> A lottery offers the winner the choice between a $150,000 cash prize or month-end payments of $1000 for 12 1 2 years, increasing to $1500 per month for the next 12 1 2 years. Which alternative would you choose if money can earn 8.25% compounded monthly o

> A mortgage broker offers to sell you a mortgage loan contract that will pay $800 at the end of each month for the next 3 1 2 years, at which time the principal balance of $45,572 is due and receivable. What is the highest price you should pay for the con

> What is the maximum price you should pay for a contract guaranteeing month-end payments of $500 for the next 12 years if you require a rate of return of at least 8% compounded monthly for the first five years and at least 9% compounded monthly for the ne

> Pierre and Pat wish to structure the payments from a 20-year annuity so that the end-of-quarter payments increase by $500 every five years. Maritime Insurance Co. will pay 5% compounded quarterly on funds received to purchase such an annuity. How much mu

> A Government of Canada bond will pay $50 at the end of every six months for the next 15 years, and an additional $1000 lump payment at the end of the 15 years. What is the appropriate price to pay if you require a rate of return of 6.5% compounded semian

> Serge’s graduated commission scale pays him 3% on his first $30,000 in sales, 4% on the next $20,000, and 6% on all additional sales in a month. What is his average commission rate on sales for a month totaling: 1. $60,000? 2. $100,000?

> You have received two offers on the used car you wish to sell. Mr. Lindberg is offering $9500 cash, and Mrs. Martel’s offer is five semiannual payments of $2000, including one on the purchase date. Which offer has the greater economic value using a disco

> You can purchase a residential building lot for $90,000 cash, or for $20,000 down and quarterly payments of $5000 for four years. The first payment would be due three months after the purchase date. If the money you would use for a cash purchase can earn

> This problem demonstrates the dependence of the present value of an annuity on the discount rate. For an ordinary annuity consisting of 20 annual payments of $1000, calculate the present value using an annually compounded discount rate of: 1. 5% 2. 10% 3

> Your client has the following choices for an insurance benefit: She can receive $2000 at the end of each year for the next five years or one lump sum today. If the current interest rate is 4.5% compounded annually, what lump payment today is equivalent t

> The Montreal Canadiens have just announced the signing of Finnish hockey sensation Gunnar Skoroften to a 10-year contract at $3 million per year. The media are reporting the deal as being worth $30 million to the young Finn. Rounded to the dollar, what c

> The Ottawa Senators fired their coach two years into his five-year contract, which paid him $90,000 at the end of each month. If the team owners buy out the remaining term of the coach’s contract for its economic value at the time of firing, what will be

> Osgood Appliance Centre is advertising refrigerators for six monthly payments of $199, including a payment on the date of purchase. What cash price should Osgood accept if it would otherwise sell the conditional sale agreement to a finance company to yie

> A conditional sale contract between Classic Furniture and the purchaser of a dining room set requires month-end payments of $250 for 15 months. Classic Furniture sold the contract to Household Finance Co. at a discount to yield 19.5% compounded monthly.

> Manuel purchased a boat for $2000 down with the balance to be paid by 36 monthly payments of $224.58 including interest at 10% compounded monthly. 1. What was the purchase price of the boat? 2. What is the balance owed just after the ninth payment?

> Kent sold his car to Carolyn for $2000 down and monthly payments of $295.88 for 3 1 2 years, including interest at 7.5% compounded monthly. What was the selling price of the car?

> 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

> 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 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