Question: Calculate the amounts that will be accumulated

> 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?

> What minimum amount of money earning 2.5% compounded semiannually will sustain withdrawals of $1000 at the end of every month for 12 years?

> 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.

> 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?

> What monthly compounded nominal rate would put you in the same financial position as 5.5% compounded semiannually?

> If a company’s annual sales grew from $165,000 to $485,000 in a period of eight years, what has been the compound annual rate of growth of sales during the period?

> Maxine found an old pay statement from nine years ago. Her hourly wage at the time was $13.50 versus her current wage of $20.80 per hour. At what equivalent (compound) annual rate has her wage grown over the period?

> In 1859, 24 wild rabbits were released at Barwon Park in southern Victoria, Australia. By 1926, it was estimated that the rabbit population had grown to 400 million times this number. What is the effective compounded growth rate in the rabbit population?

> A $10,000 investment grew to $12,000 after 39 months of semiannual compounding. What effective rate of return did the investment earn?

> Use S = P(1 + rt), to calculate P if r = 0.004, S = $3626, and t = 9.

> Which of the following rates would you prefer for a loan: 7.6% compounded quarterly, 7.5% compounded monthly, or 7.7% compounded semiannually?

> An investor’s portfolio increased in value from $35,645 to $54,230 over a six-year period. At the same time, the Consumer Price Index rose by 26.5%. What was the portfolio’s annually compounded real rate of return?

> A company’s sales dropped 10% per year for five years. 1. What annual rate of sales growth for the subsequent five years would return the sales to the original level? 2. To the nearest month, how long would it take for sales to return to the original lev

> To the nearest day, how long will it take a $20,000 investment to grow to $22,000 (including accrued interest) if it earns 7% compounded quarterly? Assume that a quarter-year has 91 days.

> The population of a mining town declined from 17,500 to 14,500 in a five-year period. If the population continues to decrease at the same compound annual rate, how long, to the nearest month, will it take for the population to drop by another 3000?

> When discounted to yield 9.5% compounded quarterly, a $4500 four-year promissory note bearing interest at 11.5% compounded semiannually was priced at $5697.84. How long after the issue date did the discounting take place?

> What is the time remaining until the maturity date of a $50,000 strip bond if it has just been purchased for $20,822.89 to yield 5.38% compounded semiannually until maturity?

> Terry was supposed to pay $800 to Becky on March 1. At a later date, Terry paid Becky an equivalent payment in the amount of $895.67. If they provided for a time value of money of 8% compounded monthly, on what date did Terry make the payment?

> An investor’s portfolio increased in value by 53% over a five-year period while the Consumer Price Index rose from 121.6 to 135.3. What was the annually compounded real rate of return on the portfolio for the five years?

> An investor paid $4271.17 to purchase a $10,000 face value strip bond for her RRSP. At this price the investment will provide a return of 6.47% compounded semiannually. How long (to the nearest day) after the date of purchase will the bond mature? Assume

> Rearrange the formula FV = PV(1 + i)n to isolate i on the left side.

> A new machine that will lead to savings in labour costs of $16,000 per year can be purchased for $72,000. However, it will cost $1500 per year for the first four years and $2500 per year for the next four years to service and maintain it. In addition, it

> If the Consumer Price Index rose from 109.6 to 133.8 over an 8 1 2 -year period, what was the equivalent compound annual inflation rate during the period?

> Rounded to the nearest month, how long will it take money to lose one-third of its purchasing power if the annual inflation rate is 3%?

> To the nearest month, how long will it take an investment to increase in value by 200% if it earns 7.5% compounded semiannually?

> Maritime Investments pays 4.625% compounded semiannually on its three-year GICs. What quarterly compounded rate of interest will produce the same maturity value?

> A trust company pays 5.375% compounded annually on its five-year GICs. What semiannually compounded interest rate would produce the same maturity value?

> Camille can obtain a residential mortgage loan from a bank at 8.75% compounded semiannually or from an independent mortgage broker at 8.6% compounded monthly. Which source should she pick if other terms and conditions of the loan are the same? Present ca

> If a $15,000 investment grew to $21,805 in 4 1 2 years of quarterly compounding, what effective rate of return was the investment earning?

> If an interest rate of 6.9% compounded semiannually is charged on a car loan, what effective rate of interest should be disclosed to the borrower?

> If the nominal rate of interest paid on a savings account is 3% compounded monthly, what is the effective rate of interest paid?

> If an invoice indicates that interest at the rate of 1.2% per month will be charged on overdue amounts, what effective rate of interest will be charged?