Question: Four years from now, Tim and Justine

> A property development company obtained a $2.5-million loan to construct a commercial building. The interest rate on the loan is 10% compounded semiannually. The lender granted a period of deferral, meaning that the first quarterly payment of $100,000 is

> Helen and Morley borrowed $20,000 from Helen’s father to make a down payment on a house. The interest rate on the loan is 8% compounded annually, but no payments are required for two years. The first monthly payment of $300 is due on the second anniversa

> Novell Electronics recently bought a patent that will allow it to bring a new product to market in 2 1 2 years. Sales forecasts indicate that the product will increase the quarterly profits by $28,000. If the patent cost $150,000, how long after the date

> Twelve years ago, Mr. Lawton rolled a $17,000 retiring allowance into an RRSP that subsequently earned 10% compounded semiannually. Three years ago he transferred the funds to an RRIF. Since then, he has been withdrawing $1000 at the end of each quarter.

> Nancy borrowed $8000 from her grandfather to buy a car when she started college. The interest rate being charged is 4.5% compounded monthly. Nancy is to make the first $200 monthly payment on the loan three years after the date of the loan. How long afte

> For $200,000, Jamal purchased an annuity that delivers end-of-quarter payments of $3341.74. If the undistributed funds earn 4.5% compounded quarterly, what is the term of the annuity?

> $10,000 was invested in a fund earning 7.5% compounded monthly. How many monthly withdrawals of $300 can be made if the first occurs 3 1 2 years after the date of the initial investment? Count the final smaller withdrawal.

> Sawchuk’s Home and Garden Centre in Toronto files monthly HST returns. The purchases on which it paid the HST and the sales on which it collected the HST for the last four months were as follows: Based on an HST rate of 13%, calculate t

> A 60-year-old woman can purchase either of the following annuities from a life insurance company: a 30-year term annuity that will pay $367 at the end of each month or a life annuity that will pay $405 at the end of every month until the death of the ann

> A 65-year-old male can purchase either of the following annuities from a life insurance company: a 25-year term annuity that will pay $307 at the end of each month or a life annuity that will pay $408 at the end of every month until the death of the annu

> Rashid wants to use $500,000 from his RRSP to purchase an annuity that pays him $2000 at the end of each month for the first 10 years and $3000 per month thereafter. Global Insurance Co. will sell Rashid an annuity of this sort with a rate of return of 4

> Finest Furniture sells a television set priced at $1395 for $50 down and payments of $50 per month, including interest at 13.5% compounded monthly. How long after the date of purchase will the final payment be made?

> Bonnie and Clyde want to take a six-month leave of absence from their jobs to travel extensively in South America. Rounded to the next higher month, how many months will it take them to save $40,000 for the leave if they make month-end contributions of $

> What duration of annuity paying $5000 at the end of every quarter can be purchased with $200,000 if the invested funds earn 5.5% compounded semiannually?

> How much longer will it take monthly payments of $1000 to pay off a $100,000 loan if the monthly compounded rate of interest on the loan is 10.5% instead of 9.75%?

> How much longer will it take to pay off a $100,000 loan with monthly payments of $1000 than with monthly payments of $1100? The interest rate on the loan is 10.5% compounded monthly.

> Suppose that you contribute $400 per month to your RRSP. Rounding up to the nearest month, how much longer will it take for the RRSP’s value to reach $500,000 if it earns 7.5% compounded annually than if it earns 7.5% compounded monthly?

> The future value of an annuity consisting of end-of-year investments of $1658.87 earning 5.2% compounded annually is $100,000. How many annual investments were made?

> The total assessed value of property in Brockton has risen by $97 million from last year’s figure of $1.563 billion. The property tax rate last year for city services was $0.94181 per $100 of assessed value. If the city’s budget has increased by $750,000

> How much longer will it take month-end RRSP contributions of $500 to accumulate $500,000 than month-end contributions of $550? Assume that the RRSP earns 7.5% compounded monthly. Round the time required in each case to the next higher month.

> 1. How long will it take monthly payments of $400 to repay a $50,000 loan if the interest rate on the loan is 8% compounded semiannually? 2. How much will the time to repay the loan be reduced if the payments are $40 per month larger?

> If $300,000 is used to purchase an annuity earning 7.5% compounded monthly and paying $2500 at the end of each month, what will be the term of the annuity?

> Farah has $600,000 in her RRSP and wishes to retire. She is thinking of using the funds to purchase an annuity that earns 5% compounded annually and pays her $3500 at the end of each month. If she buys the annuity, for how long will she receive payments?

> How long will $500,000, in an investment account that earns 3.25% compounded monthly, sustain month-end withdrawals of $3000?

> Silas is about to begin regular month-end contributions of $500 to a bond fund. The fund’s long-term rate of return is expected to be 6% compounded semiannually. Rounded to the next higher month, how long will it take Silas to accumulate $300,000?

> Rounded to the next higher month, how long will it take end-of-month deposits of $500 to accumulate $100,000 in an investment account that earns 5.25% compounded monthly?

> How long will it take an RESP to grow to $200,000 if the plan owner contributes $250 at the end of each month and the plan earns: 1. 8% compounded monthly? 2. 8% compounded quarterly? 3. 8% compounded semiannually? 4. 8% compounded annually?

> How long will it take for monthly payments of $740 to repay a $100,000 loan if the interest rate on the loan is: 1. 7.5% compounded annually? 2. 7.5% compounded semiannually? 3. 7.5% compounded quarterly? 4. 7.5% compounded monthly?

> How long will it take for monthly payments of $800 to repay a $100,000 loan if the interest rate on the loan is: 1. 6% compounded monthly? 2. 7% compounded monthly? 3. 8% compounded monthly? 4. 9% compounded monthly?

> The school board in a municipality will require an extra $2,430,000 for its operating budget next year. The current mill rate for the school tax component of property taxes is 7.1253. 1. If the total of the assessed values of properties in the municipali

> Semiannual payments of $3874.48 are made on a $50,000 loan at 6.5% compounded semiannually. How long will it take to pay off the loan?

> Kyle wants to save $15,000 so he can take a trip to Australia when he graduates from college three years from now. How much must he contribute to a savings plan at the end of every month if the plan earns 4% compounded monthly?

> Norman financed the $2800 purchase price of his new washer and dryer with monthly payments at 6.4% compounded monthly made over two years. What will be the amount of each payment?

> What monthly payment is required to pay off a $50,000 loan in seven years if the interest rate on the loan is 7.5% compounded: 1. Annually? 2. Semiannually? 3. Quarterly? 4. Monthly?

> Marissa intends to make contributions to a TFSA such that the account will accumulate $150,000 after 20 years. What end-of-quarter contributions must be made if the TFSA earns 6% compounded: 1. Annually? 2. Semiannually? 3. Quarterly? 4. Monthly?

> Assume that the investments within an RRSP will earn 5% compounded annually. What monthly contribution must be made to the RRSP for it to grow to $750,000 in: 1. 15 years? 2. 20 years? 3. 25 years? 4. 30 years? In each case, also calculate the total earn

> 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

> 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

> 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 t

> 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.