Question: What minimum amount of money earning 2.

> A company’s preferred shares pay a $1.25 dividend every three months in perpetuity. What is the fair market value of the shares just after payment of a dividend if the rate of return required by the market on shares of similar risk is: 1. 5% compounded q

> If money can earn 6% compounded annually, what percentage more money is required to fund an ordinary perpetuity paying $1000 at the end of every year, than to fund an ordinary annuity paying $1000 per year for 25 years?

> What price will a finance company pay to a merchant for a conditional sale contract that requires 12 monthly payments of $249, with the first payment due six months from now? The finance company requires a return of 16.5% compounded monthly.

> $30,000 loan bearing interest at 9% compounded monthly was repaid, after a period of deferral, by monthly payments of $425.10 for 10 years. What was the time interval between the date of the loan and the first payment?

> Fred asked two life insurance companies to give quotes on a 20-year deferred annuity (after a 5-year deferral period) that can be purchased for $100,000. Northwest Mutual quoted payments of $875 payable at the end of each month. Liberty Standard stated t

> What percentage more money is required to fund an ordinary perpetuity than to fund a 30-year ordinary annuity, if the funds can earn 5.8% compounded semiannually? The perpetuity and the annuity each pay $1000 semiannually.

> Erin has invested in both an equity mutual fund and a bond mutual fund. Her financial adviser told her that her overall portfolio rose in value by 1.1% last year. Erin noted in the newspaper that the equity fund lost 3.3% last year while the bond fund ro

> Wildcat Drilling Contractors Inc. is considering the acquisition of a new deep-drilling rig at a cost of $14 million. With this added drilling capability, the company’s net operating profits would increase by $2 million in the first year and grow by 10%

> Dr. Pollard donated $100,000 to the Canadian National Institute for the Blind. The money is to be used to make semiannual payments in perpetuity (after a period of deferral) to finance the recording of books-on-CD for the blind. The first perpetuity paym

> How much more money is required to fund an ordinary perpetuity than a 25-year ordinary annuity, if the funds can earn 7% compounded quarterly, and both pay $500 monthly?

> The common shares of Bancorp Ltd. are forecast to pay annual dividends of $3 at the end of each of the next five years, followed by dividends of $2 per year in perpetuity. What is the fair market value of the shares if the market requires a 10% annually

> What minimum amount will have to be dedicated today to a fund earning 5.6% compounded quarterly, if the first quarterly payment of $2000 in perpetuity is to occur: 1. Three months from now? 2. Five years from now?

> What is the current economic value of an inheritance that will pay $2500 to the beneficiary at the beginning of every three months for 20 years starting when the beneficiary reaches 21 years of age, 5 1 4 years from now? Assume that money can earn 6% com

> What amount of money invested now will provide payments of $500 at the end of every month for five years following a four-year period of deferral? The money will earn 7.2% compounded monthly.

> Suppose that $5000 is contributed at the beginning of each year to an RRSP that earns 5% compounded annually. 1. How many contributions will it take to accumulate the first $500,000? 2. How many more contributions will it take for the RRSP to reach $1,00

> A seven-year capital lease of an executive jet requires semiannual payments of $200,000 at the beginning of each six-month period. The company can borrow funds for 5 to 10 years at 7.4% compounded semiannually. 1. What long-term lease liability will the

> A life insurance company quoted an annual premium of $387.50 (payable at the beginning of the year) for a $250,000 term insurance policy on a 35-year-old male nonsmoker. Alternatively, the insured can pay $33.71 at the beginning of each month by preautho

> Calculate the amount that will be accumulated after 20 years if: 1. $1000 is invested at the beginning of every six months at 8.5% compounded semiannually. 2. $2000 is invested at the beginning of every year at 8.5% compounded annually.

> A city’s commercial construction by-laws require five parking spaces for every 100 square metres of retail rental space in a shopping centre. Four percent of the parking spaces must be large spaces for the physically handicapped. Of the remainder, there

> An RRSP is now worth $316,000 after contributions of $3500 at the beginning of every six months for 17 years. What effective rate of return has the plan earned?

> Regular investments made at the beginning of each quarter earn 6% compounded quarterly. How many more $1000 investments than $1100 investments will it take to accumulate $100,000?

> A life insurance company is calculating the monthly premium that it will offer clients as an alternative to paying the full annual premium. With both alternatives, premiums are payable at the beginning of the period of coverage. If the monthly payment by

> What maximum annual withdrawals will a $300,000 fund earning 7.75% compounded annually sustain for 25 years if the withdrawals are made: 1. At the beginning of each year? 2. At the end of each year?

> New Look Fitness Centre offers a one-year membership for $500 in advance, or a three-month membership for $160 in advance. What effective rate of interest is an individual paying if she buys four consecutive three-month memberships instead of a one-year

> Capital Leasing leases commercial kitchen equipment to restaurants, hotels, hospitals, and other institutions. Capital Leasing calculates the payments on its four-year leases so that it recovers the purchase price of the equipment plus a return on invest

> Suppose you contribute $2500 to an RRSP at the beginning of every six months for 25 years, and then use the accumulated funds to purchase an annuity paying $2500 at the beginning of each month. How long after the start of the annuity will the last paymen

> Suppose that $5000 is contributed at the beginning of each year for 25 years to an RRSP that earns 10% compounded annually. By what percentage would annual contributions have to be increased in order to have the same future value after 25 years if the pl

> What amount is required to purchase an annuity that pays $4000 at the end of each quarter for the first five years and then pays $2500 at the beginning of each month for the subsequent 15 years? Assume that the annuity payments are based on a rate of ret

> Mick contributed $5000 at the beginning of each year for 25 years to his RRSP. Assume that the RRSP earned 8% compounded annually. What percentage of the RRSP’s value after 25 years comes from contributions made in the first five years?

> A Web site had 2 7 more hits last month than in the same month of the preceding year. If there were 2655 hits last month, how many were there one year earlier?

> A rental agreement requires the payment of $1000 at the beginning of each month. 1. What single payment at the beginning of the rental year should the landlord accept instead of 12 monthly payments if money is worth 8% compounded monthly? 2. Show that th

> Mr. and Mrs. Zolob contributed $50 on the first of each month to an RESP they set up for their grandson Jeff. By the time he entered Mohawk College, 14 years and 5 months of contributions had accumulated. The grandparents’ contributions stopped, and Jeff

> Ms. Bowers wants to be able to purchase a 20-year annuity at age 62 that will pay her $3500 at the beginning of each month. She makes her first quarterly contribution to an RRSP on her 35th birthday and continues them up to but not including her 62nd bir

> Calculate the future value of an investment plan requiring contributions of $800 at the beginning of each calendar quarter for seven years. Assume that the rate of return will be 8% compounded quarterly for the first 30 months and 7% compounded semiannua

> What minimum amount of money earning 7% compounded semiannually will sustain withdrawals of $1000 at the beginning of every month for 12 years?

> What will be the amount in an RRSP after 30 years if contributions of $4000 are made at the beginning of each year for the first 10 years, and contributions of $6000 are made at the beginning of each year for the subsequent 20 years? Assume that the RRSP

> What is the initial economic value of an annuity due if it consists of 19 semiannual payments of $1500? Money is worth 5% compounded semiannually for the first five years, and 6% compounded semiannually thereafter.

> Fred is about to have his 27th birthday. He has set a goal of retiring at age 58 with $1,000,000 in his RRSP. For planning purposes, he is assuming that his RRSP will earn 8% compounded annually. 1. What contributions on each birthday from age 27 to 57 i

> Sovereign Life Insurance Company of Canada offers $250,000 of term life insurance to a 45-year-old male for an annual premium of $716 (in advance) or for monthly premium payments (in advance) of $62.50 by preauthorized electronic debit. What effective ra

> If a furniture store offers to sell a washer-dryer combination priced at $1395 on a conditional sale contract requiring 12 monthly payments of $125 (including a payment on the date of sale), what effective rate of interest is being charged?

> Use N = L(1 – d1)(1 – d2)(1 – d3), to calculate L if N = $1468.80, d1 = 0.20, d2 = 0.15, and d3 = 0.10.

> As of the date of Colony Farm’s most recent financial statements, 3 1 2 years remained in the term of a lease reported as a long-term liability of $27,400. If the beginning-of-month lease payments are $750, what monthly compounded nominal discount rate w

> How many more RRSP contributions of $300 at the beginning of every month are required to reach $200,000 if the funds earn 7.5% compounded monthly than if they earn 8.5% compounded monthly?

> Apex Fabricating wants to accumulate $800,000 for an expansion expected to begin in four years. If today Apex makes the first of equal quarterly payments into a fund earning 6.75% compounded monthly, what should the size of these payments be?

> Excel Leasing calculates the payments on long-term equipment leases so that it earns a rate of return of 15% compounded quarterly on its investment in the equipment. What beginning-of-month payments will Excel charge on a four-year lease of a photocopier

> The membership dues at Shoreline Golf and Country Club are $2820 payable at the beginning of the year, or four payments of $736.56 payable at the beginning of each quarter. What effective rate of interest is the club charging members who pay their dues q

> Brunswick Trucking has signed a five-year lease with Ford Credit Canada Ltd. on a new truck. Lease payments of $1900 are made at the beginning of each month. To purchase the truck, Brunswick Trucking would have had to borrow funds at 6.25% compounded mon

> Calculate the future value of an ordinary annuity consisting of monthly payments of $300 for five years. The rate of return was 9% compounded monthly for the first two years, and will be 7.5% compounded monthly for the last three years.

> A 15-year loan requires month-end payments of $587.33 including interest at 8.4% compounded monthly. 1. What was the original amount of the loan? 2. What is the balance on the loan after half of the payments have been made?

> Dr. Wilson is buying a 50% ownership in a veterinary practice by end-of-month payments of $714.60, including interest at 7% compounded semiannually for 15 years. Rounded to the nearest dollar, 1. What valuation was placed on the partnership at the beginn

> Use NI = (CM)X – FC, to obtain X if NI = –$542.50, CM = $13.50, and FC = $18,970.

> A victim of a car accident won a judgment for wages lost over a two-year period that ended nine months before the date of the judgment. In addition, the court awarded interest at 3% compounded monthly on the lost wages from the date they would otherwise

> You can purchase a residential building lot for $60,000 cash, or for $10,000 down and month-end payments of $1000 for five years. If money is worth 7.5% compounded monthly, which option should you choose?

> What price will a finance company pay for a conditional sale contract requiring 15 monthly payments of $180.50, if the company requires a rate of return of 21% compounded semiannually? The first payment is due one month from now.

> An advertisement for Ford trucks offered “2.9% financing (for 48 months) or $2000 cash back.” A truck buyer financed $20,000 at the low interest rate instead of paying $18,000 cash (after the $2000 rebate). What was the effective rate of interest on the

> By the time he turns 60, Justin (just turned age 31) wants the amount in his RRSP to have the purchasing power of $250,000 in current dollars. What annual contributions on his 32nd through 60th birthdays inclusive are required to meet this goal if the RR

> Georgina is about to retire with $188,000 in her RRSP. She will make no further contributions to the plan, but will allow it to accumulate earnings for another five years. Then she will purchase an annuity providing payments of $6000 at the end of each q

> $30,000 is placed in a fund earning 7% compounded quarterly. How many quarterly withdrawals of $2000 can be made if the first withdrawal occurs three years from today? Count the final withdrawal, which will be less than $2000.

> Noreen’s RRSP is currently worth $125,000. She plans to contribute for 10 more years and then let the plan continue to grow through internal earnings for an additional five years. If the RRSP earns 8% compounded annually, how much must she contribute at

> A 70-year-old man can purchase either of the following two annuities for the same price from a life insurance company. A 20-year-term annuity will pay $394 at the end of each month. A life annuity will pay $440 at the end of each month until the death of

> 1. How long will it take monthly payments of $600 to repay a $65,000 loan if the interest rate on the loan is 9.5% compounded semiannually? 2. How much will the time to repay the loan be reduced if the payments are $50 more per month?

> NI = (CM)X – FC, contains three two-letter symbols. Use it to calculate CM if NI = $15,000, X = 5000, and FC = $60,000.

> Mr. Braun wants the value of his RRSP 25 years from now to have the purchasing power of $400,000 in current dollars. 1. Assuming an inflation rate of 2.5% per year, what nominal dollar amount should Mr. Braun have in his RRSP after 25 years? 2. What cont

> Suppose Evan contributes $2000 to his RRSP at the end of every quarter for the next 15 years, and then contributes $1000 at each month’s end for the subsequent 10 years. How much will he have in his RRSP at the end of the 25 years? Assume that the RRSP e

> Louiselle purchased a motor home for $9000 down, with the balance to be paid by 60 monthly payments of $1176.40 including interest at 6% compounded monthly. 1. What was the purchase price of the motor home? 2. If the principal balance may be prepaid at a

> What is the appropriate price to pay for a contract guaranteeing payments of $1500 at the end of each quarter for the next 12 years? You require a rate of return of 6% compounded quarterly for the first five years, and 7% compounded quarterly for the nex

> A mortgage broker offers to sell you a mortgage loan contract delivering month-end payments of $900 for the next 2 3 4 years. At that point, the principal balance of $37,886 is due and payable. What should you pay for the contract, if you require a retur

> What percentage more funds will you have in your RRSP 20 years from now if you make fixed contributions of $3000 at the end of every six months for the next 20 years, instead of waiting 10 years and making semiannual contributions that are twice as large

> Charlene has made contributions of $3000 to her RRSP at the end of every half-year for the past seven years. The plan has earned 9% compounded semiannually. She has just moved the funds to another plan earning 7.5% compounded quarterly, and will now cont

> Norma is planning a trip to India when she retires nine years from now and has calculated that she will need $30,000 in her savings to support her travels. If she contributes $800 to her savings at the end of every three months for the first four years o

> Calculate the future value of investments of $800 at the end of each calendar quarter for seven years. The rate of return will be 10% compounded quarterly for the first 30 months and 9% compounded semiannually for the remainder of the annuity’s term.

> A court-ordered award for family support calls for payments of $800 per month for five years, followed by payments of $1000 per month for 10 more years. If money is worth 6% compounded monthly, what is the economic value of the award one month before the

> Use S = P(1 + rt), to calculate t if r = 0.0025, S = $5100, and P = $5000.

> A Province of Ontario bond has 14 1 2 years remaining until it matures. The bond pays $231.25 interest at the end of every six months. At maturity, the bond repays its $5000 face value in addition to the final interest payment. What is the fair market v

> Dr. Krawchuk made deposits of $2000 to his RRSP at the end of each calendar quarter for six years. He then left general practice for specialist training and did not make further contributions for 2 1 2 years. What amount was in his RRSP at the end of thi

> How much larger will the value of an RRSP be at the end of 20 years if the contributor makes month-end contributions of $500, instead of year-end contributions of $6000? In both cases the RRSP earns 7.5% compounded semiannually.

> Calculate the amounts that will be accumulated after 20 years if: 1. $1000 is invested at the end of every six months at 5.5% compounded semiannually. 2. $2000 is invested at the end of every year at 5.5% compounded annually.

> An annuity purchased for $175,000 pays $4000 at the end of every quarter. How long will the payments continue if the funds earn 4% compounded semiannually?

> If $100,000 will purchase a 20-year annuity paying $739 at each month’s end, what monthly compounded nominal rate and effective rate of interest are earned by the funds?

> The interest rate on a $100,000 loan is 6% compounded monthly. How much longer will it take to pay off the loan with monthly payments of $1000 than with monthly payments of $1050?

> What semiannually compounded rate and effective rate of interest are being charged on a $12,000 loan if semiannual payments of $1204.55 will repay the loan in seven years?

> After contributing $2000 at the end of each quarter for 13 3 4 years, Foster has accumulated $205,064 in his RRSP. What effective rate of return was earned by the RRSP over the entire period?

> If $400,000 accumulated in an RRSP is used to purchase an annuity earning 7.2% compounded monthly and paying $4500 at the end of each month, what will be the term of the annuity?

> Use N = L(1 – d), to calculate d if N = $410.85 and L = $498.00.

> For $100,000, Royal Life Insurance Co. will sell a 20-year annuity paying $802.76 at the end of each month. What monthly compounded nominal rate and effective rate of return does the annuitant earn on the invested funds?

> The interest rate on a $100,000 loan is 7.5% compounded quarterly. 1. What quarterly payments will reduce the balance to $75,000 after five years? 2. If the same payments continue, what will be the balance 10 years after the date that the loan was receiv

> What monthly payment for 15 years will pay off a $50,000 loan at 8.25% compounded monthly?

> Mr. Sandstrom’s will directed that $20,000 be placed in each of two investment trusts for his grandchildren, Lena and Axel. On each grandchild’s 18th birthday, he or she is to receive the first of a series of equal quarterly payments running for 15 years

> Weston Holdings Ltd. loaned $3.5 million to a subsidiary to build a plant in Winnipeg. No payments are required for two years, to allow the operations of the plant to become well established. The first monthly payment of $40,000 is due two years after th

> A series of $500 contributions were made at three-month intervals to a fund earning 3.5% compounded quarterly. The accumulated amount continued to earn 3.5% compounded quarterly for three years after the last contribution, ending the period at $10,770.82

> The McGowans are arranging a $90,000 mortgage loan from their bank. The interest rate on the loan will be 7.9% compounded semiannually. 1. What will the monthly payments be if the loan has a 20-year term? 2. If the McGowans choose to pay $800 per month,

> What payments must be made at the end of each quarter to an RRSP earning 7.5% compounded annually so that its value 8 1 2 years from now will be $15,000?

> $2000 will be contributed to an RRSP at the end of every six months for 20 years. What effective rate of return must the funds in the plan earn if it is to be worth $250,000 at the end of the 20 years?

> How much sooner will a $65,000 loan at 7.2% compounded monthly be paid off if the monthly payments are $625 instead of $600? What will be the approximate saving in (nominal) interest costs over the life of the loan?

> Use N = L(1 – d), to calculate L if N = $891 and d = 0.10.

> The interest rate on a $30,000 loan is 7.5% compounded monthly. 1. What monthly payments are required to pay off the loan in eight years? 2. What monthly payments would be required to reduce the balance to $10,000 after five years?

> Howardson Electric obtained a $90,000 loan at 6.75% compounded monthly. What size of semiannual payments will repay the loan in 10 years?

> A finance company paid a furniture retailer $1934 for a conditional sale contract requiring 12 end-of-month payments of $175. What effective rate of return does the finance company earn on the purchase?

> Calculate the amount that must be invested at the end of every six months at 3.75% compounded semiannually in order to accumulate $500,000 after 20 years.

> You are offered a loan at a rate of 10.5% compounded monthly. Below what figure must a semiannually compounded nominal rate be to make it more attractive?