The RBC Royal Bank offers an “add-on option” on fixed-rate mortgages. The option allows the customer to borrow additional funds partway through the term of the mortgage. The interest rate charged on the combined mortgage debt is the weighted average of the old rate on the former balance and the current competitive rate on new mortgage financing. Suppose Herschel and Julie had a mortgage balance of $37,500 at 8%, when they borrowed another $20,000 at 7%. What interest rate are they charged by the RBC Royal Bank on the new consolidated balance?
> The interest rate on a $100,000 loan is 7.5% compounded monthly. What must be the monthly payment for the loan to be repaid in: 1. 5 years? 2. 10 years? 3. 15 years? 4. 20 years? In each case, also calculate the total interest paid. (Note that a doubling
> Mr. Parmar wants to retire in 20 years and purchase a 25-year annuity that will make equal payments at the end of every quarter. The first payment should have the purchasing power of $6000 in today’s dollars. If he already has $54,000 in his RRSP, what c
> Cynthia currently has $31,000 in her RRSP. She plans to contribute $5000 at the end of each year for the next 17 years, and then use the accumulated funds to purchase a 20-year annuity making month-end payments. 1. If her RRSP earns 8.75% compounded annu
> Jack Groman’s financial plan is designed to accumulate sufficient funds in his RRSP over the next 28 years to purchase an annuity paying $6000 at the end of each month for 25 years. He will be able to contribute $7000 to his RRSP at the end of each year
> The assessed value on a property increased from $285,000 last year to $298,000 in the current year. Last year’s property tax rate was $1.56324 per $100 of assessed value. 1. What will be the change in the property tax from last year if the new tax rate i
> During a one-week promotion, Al’s Appliance Warehouse is planning to offer terms of “nothing down and nothing to pay for four months” on major appliances priced above $500. Four months after the date of the sale, the first of eight equal monthly payments
> A 20-year annuity is purchased for $400,000. What payment will it deliver at the end of each quarter, if the undistributed funds earn: 1. 4% compounded quarterly? 2. 5% compounded quarterly? 3. 6% compounded quarterly? 4. 7% compounded quarterly? In each
> A firm obtained a $3 million low-interest loan from a government agency to build a factory in an economically depressed region. The loan is to be repaid in semiannual payments over 15 years, and the first payment is due three years from today, when the f
> Leslie received a settlement when her employer declared her job redundant. Under special provisions of the Income Tax Act, she was eligible to place $22,000 of the settlement in an RRSP. Fifteen years from now, she intends to transfer the money from the
> As of Brice’s 54th birthday, he has accumulated $154,000 in his RRSP. What size of end-of-month payments in a 20-year annuity will these funds purchase at age 65 if he makes no further contributions? Assume that his RRSP and the investment in the annuity
> Harold, who just turned 27, wants to accumulate an amount in his RRSP at age 60 that will have the purchasing power of $300,000 in current dollars. What annual contributions on his 28th through 60th birthdays are required to meet this goal if the RRSP ea
> Dr. Collins wants the value of her RRSP 30 years from now to have the purchasing power of $500,000 in current dollars. 1. Assuming an inflation rate of 2% per year, what nominal dollar amount should Dr. Collins have in her RRSP after 30 years? 2. Assumin
> Beth and Nelson want to accumulate a combined total of $600,000 in their RRSPs by the time Beth reaches age 60, which will be 30 years from now. They plan to make equal contributions at the end of every six months for the next 25 years, and then no furth
> Four years from now, Tim and Justine plan to take a year’s leave of absence from their jobs and travel through Asia, Europe, and Africa. They want to accumulate enough savings during the next four years so they can withdraw $3000 at each month-end for th
> Ken and Barbara have two children, aged three and six. At the end of every six months for the next 12 1 2 years, they wish to contribute equal amounts to an RESP. Six months after the last RESP contribution, the first of 12 semiannual withdrawals of $500
> Johnston Distributing Inc. files quarterly GST returns. The purchases on which it paid the GST and the sales on which it collected the GST for the last four quarters were as follows: Calculate the GST remittance or refund due for each quarter.
> Elizabeth has been able to transfer a $25,000 retiring allowance into an RRSP. She plans to let the RRSP accumulate earnings at the rate of 5% compounded annually for 10 years, and then purchase a 15-year annuity making payments at the end of each quarte
> On the date of his granddaughter’s birth, Mr. Parry deposited $5000 in a trust fund earning 6.2% compounded annually. After the granddaughter’s 19th birthday, the trust account will make end-of-month payments to her for four years to assist with the cost
> In order to accumulate $500,000 after 25 years, calculate the amounts that must be invested at the end of each year, if the invested funds earn: 1. 6% compounded annually. 2. 7% compounded annually. 3. 8% compounded annually. 4. 9% compounded annually. I
> As of Betty’s 56th birthday, she has accumulated $195,000 in her RRSP. She has ceased contributions but will allow the RRSP to grow at an expected 5.4% compounded monthly until she reaches age 65. Then she will use the funds in the RRSP to purchase a 20-
> The interest rate on a $200,000 loan is 8% compounded quarterly. 1. What payments at the end of every quarter will reduce the balance to $150,000 after 3 1 2 years? 2. If the same payments continue, what will be the balance seven years after the date tha
> Mr. Bean wants to borrow $7500 for three years. The interest rate is 5.5% compounded monthly. 1. What quarterly payments are required on the loan? 2. What will be the balance owed on the loan at the start of the third year?
> n order to purchase another truck, Beatty Transport recently obtained a $50,000 loan for five years at 7.8% compounded semiannually. 1. What are the monthly payments on the loan? 2. What will be the loan’s balance at the end of the second year? 3. How mu
> Ardith is scheduled to make a lump payment of $25,000, 11 months from now, to complete a real estate transaction. What end-of-month payments for the next 11 months should the vendor be willing to accept instead of the lump payment if he can invest the fu
> RBC Royal Bank approved a four-year $20,000 Royal Buy-Back Car Loan to Zaman at 7.5% compounded monthly. The monthly payments are to reduce the balance on the loan to the Royal Bank’s guaranteed buy-back value of $7250. Calculate the monthly payment.
> Henry can buy a farm for $700,000 with terms of $100,000 down and the balance payable over 20 years by quarterly payments including interest at 8% compounded annually. What will be the size of the payments? How much interest will Henry pay over the life
> The distribution of scores obtained by 30 students on a quiz marked out of 10 is listed below. Score: 10 9 8 7 6 5 4 3 2 1 Number of students: 2 6 9 7 3 2 0 1 0 0 What was the average score on the test?
> Brenda and Tom want to save $30,000 over the next four years for a down payment on a house. What amount must they regularly save from their month-end paycheques if their savings can earn 5.5% compounded semiannually?
> Karen obtained a $20,000 loan at 4% compounded semiannually. What monthly payment will repay the loan in 7 1 2 years? How much interest will Karen pay over the life of the loan?
> Claudette plans to retire this year. Currently she has $560,000 in accumulated capital. She wants to invest this capital to provide equal payments at the end of each year for 20 years, at which time the capital will be fully depleted. If her capital earn
> Calculate the amount that must be invested at the end of each year at 9% compounded annually in order to accumulate $500,000 after: 1. 25 years. 2. 30 years. In each case, also determine what portion of the $500,000 represents earnings on the annual inve
> An ordinary annuity consists of semiannual payments of $2750 for a 3 1 2 -year term. Using a nominal rate of 4% compounded monthly, calculate the annuity’s: 1. Present value. 2. Future value.
> An annuity consists of end-of-month payments of $150 continuing for 6 1 2 years. Based on a nominal rate of 10% compounded quarterly, calculate the annuity’s: 1. Present value. 2. Future value.
> An ordinary annuity consists of quarterly payments of $400 for 11 years. Based on a nominal rate of 6.5% compounded annually, calculate the annuity’s: 1. Present value. 2. Future value
> This problem demonstrates the dependence of an annuity’s present value on the compounding frequency. What minimum initial amount will sustain a 25-year annuity paying $1000 at the end of each year if the initial amount can be invested to earn: 1. 6% comp
> This problem demonstrates the dependence of an annuity’s future value on the compounding frequency. Suppose $1000 is invested at the end of each year for 25 years. Calculate the future value if the invested funds earn: 1. 6% compounded annually. 2. 6% co
> The nominal interest rate associated with an ordinary general annuity is 8% compounded monthly. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for: 1. Annual payments? 2. Semiannual pa
> Margot’s grades and course credits in her first semester at college are listed below. Calculate Margot’s grade point average for the semester.
> Repeat Problem 4 with the change that Arrowsmith Lumber’s cost of capital is 7%. Data from Problem 4: 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 f
> What will be the amount in an RRSP after 25 years if contributions of $3000 are made at each year-end for the first seven years and month-end contributions of $500 are made for the subsequent 18 years? Assume that the plan earns 8% compounded quarterly f
> Joshua wants to structure a 20-year annuity so that its end-of-quarter payments are $2000 for the first 10 years and $2500 for the next 10 years. Pacific Life Insurance Co. offers to sell this annuity with a 4.8% compounded monthly rate of return to the
> The nominal interest rate associated with an ordinary general annuity is 4% compounded quarterly. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for: 1. Annual payments? 2. Semiannual
> Micheline wishes to purchase a 25-year annuity providing payments of $1000 per month for the first 15 years and $1500 per month for the remaining 10 years. Sovereign Insurance Co. has quoted her a rate of return of 5% compounded annually for such an annu
> The Toronto Raptors announce the signing of one of their players to a “seven-year deal worth $43.2 million.” The player will earn $400,000 at the end of each month for the first three years, and $600,000 at the end of each month for the subsequent four y
> Gloria has just made her ninth annual $2000 contribution to her RRSP. She now plans to make semiannual contributions of $2000. The first contribution will be made six months from now. How much will she have in her RRSP 15 years from now if the plan has e
> Monty expects to contribute $300 to his TFSA at the end of every month for the next 5 years. For the subsequent 10 years, he plans to contribute $2000 at the end of each calendar quarter. How much will be in his TFSA at the end of the 15 years if the fun
> Year-end contributions of $1000 will be made to a TFSA for 25 years. What will be the future value of the account if it earns 7 1 2 % compounded monthly for the first 10 years and 8% compounded semiannually thereafter?
> A savings plan requires end-of-month contributions of $100 for 25 years. What will be the future value of the plan if it earns 7% compounded quarterly for the first half of the annuity’s term, and 8% compounded semiannually for the last half of the term?
> Mr. Eusanio contributed $1500 to his RRSP on March 1 and on September 1 of each year for 25 years. The funds earned 6% compounded monthly for the first 10 years and 7% compounded annually for the next 15 years. What was the value of his RRSP after his co
> How much larger will the value of a TFSA be at the end of 25 years if the contributor makes month-end contributions of $300 instead of year-end contributions of $3600? In both cases the TFSA earns 8.5% compounded semiannually.
> Rebecca is trying to decide if she should make regular month-end $100 deposits to her TFSA or deposit $300 at the end of every three months instead. How much larger is the option with the higher future value after 20 years if both investments earn 4.25%
> LeVero’s monthly payments of $567.89 will pay off his mortgage loan in 4 years and 7 months. The interest rate on his mortgage is 6.6% compounded semiannually. What is the current balance on the loan?
> The nominal interest rate associated with an ordinary general annuity is 7% compounded semiannually. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for: 1. Annual payments? 2. Quarterl
> Kent sold his car to Carolyn for $2000 down and monthly payments of $259.50 for 3 1 2 years, including interest at 7.5% compounded annually. What was the selling price of the car?
> An Agreement for Sale contract on a house requires payments of $4000 at the end of every six months. The contract has seven years to run. The payee wants to sell her interest in the contract. What will an investor pay in order to realize an annually comp
> What amount will be required to purchase a 20-year annuity paying $2500 at the end of each month if the annuity provides a return of 4.75% compounded annually?
> How much larger will the value of an RRSP be at the end of 25 years if the RRSP earns 9% compounded monthly instead of 9% compounded annually? In both cases a contribution of $1000 is made at the end of every three months.
> What is the future value eight years from now of each of the following cash flow streams if money can earn 4% compounded semiannually? 1. A single payment of $5000 today. 2. An ordinary annuity starting today with eight annual payments of $900. 3. An ord
> Mr. and Mrs. Krenz are contributing to an RESP they have set up for their children. What amount will they have in the RESP after eight years of contributing $500 at the end of every calendar quarter if the plan earns 6% compounded monthly? How much of th
> Brianne spent the summer touring Canadian cities. She spent 4 nights in a hotel in Montreal at $158 a night, 2 nights in a Toronto hotel at $199 a night, 1 night in Niagara Falls for $239, 5 nights in Calgary at $130 a night, and 2 nights in Kamloops for
> Lacey purchased a car with $1200 down and end-of-month payments of $352 for 4 years. What is the purchase price of the car if she has financed it at 7.55% compounded semiannually?
> An annuity consists of semiannual payments of $950 for a term of 8 1 2 years. Using a nominal rate of 9% compounded quarterly, calculate the ordinary annuity’s: 1. Present value. 2. Future value
> Payments of $3500 will be made at the end of every year for 17 years. Using a nominal rate of 5.25% compounded monthly, calculate the annuity’s: 1. Present value. 2. Future value.
> Payments of $1500 will be made at the end of every quarter for 13 1 2 years. Using a nominal rate of 7.5% compounded semiannually, calculate the annuity’s: 1. Present value. 2. Future value.
> The nominal interest rate associated with an ordinary general annuity is 3% compounded annually. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for: 1. Semiannual payments? 2. Quarterl
> Semiannual payments of $1240 will pay off the balance owed on a loan in 9 1 2 years. If the interest rate on the loan is 5.9% compounded semiannually, what is the current balance on the loan?
> A new loan at 9% compounded quarterly requires quarterly payments of $727.88 for seven years. Rounded to the nearest dollar, what amount was borrowed?
> A contract requires end-of-month payments of $175 for another 8 1 4 years. What would an investor pay to purchase this contract if she requires a rate of return of 3% compounded monthly?
> How much will it cost to purchase an ordinary annuity delivering semiannual payments of $2000 for 12 1 2 years if the money used to purchase the annuity can earn 7.5% compounded semiannually?
> Determine the present value of end-of-month payments of $75 continuing for 2 1 2 years. Use 8% compounded monthly as the discount rate.
> 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?
