Question: Rounded to the nearest month, how long

> 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?

> 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?

> 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?

> Use the formula PV = FV(1 + i)–n to calculate i if PV = $5167.20, FV = $10,000, and n = 15.

> A bank offers a rate of 5.3% compounded semiannually on its four-year GICs. What monthly and annually compounded rates should it quote in order to have the same effective interest rate at all three nominal rates?

> The home the Bensons purchased 13 years ago for $85,000 is now appraised at $215,000. What has been the annual rate of appreciation of the value of their home during the 13-year period?

> A credit union’s Rate Climber GIC pays rates of 2%, 2.5%, and 3% compounded semiannually in successive years of a three-year term. 1. What will be the maturity value of $12,000 invested in this GIC? 2. How much interest will be earned in the second year?

> Accurate Accounting obtained a private loan of $25,000 for five years. No payments were required, but the loan accrued interest at the rate of 9% compounded monthly for the first 2 1 2 years and then at 8.25% compounded semiannually for the remainder of

> Jacques has just been notified that the combined principal and interest on an amount he borrowed 19 months ago at 8.4% compounded monthly is now $2297.78. How much of this amount is principal and how much is interest?

> At the same time as compound interest Government Bonds were being sold with guaranteed minimum annual rates of 5.25%, 6%, and 6.75% in the first three years of their 10-year term, a trust company offered three-year Bond Beater GICs paying 5.75%, 6.5%, an

> The population for the Region of Waterloo as recorded in the census of 2016 was 583,500. Estimates for population growth in the region are predicting increases of 1.85% per year for the next 15 years. What is the predicted population for the region in 20

> If an investor has the choice between rates of 5.5% compounded semiannually and 5.6% compounded annually for a six-year GIC, which rate should be chosen?

> Four years ago John borrowed $3000 from Arlette. The principal with interest at 10% compounded semiannually is to be repaid six years from the date of the loan. Fifteen months ago, John borrowed another $1500 for 3 1 2 years at 9% compounded quarterly. J

> If the total interest earned on an investment at 2.6% compounded monthly for 3 1 2 years was $618.55, what was the original investment?

> Use the formula FV = PV(1 + i)n to calculate i if PV = $2000, FV = $9321.91, and n = 20.

> Three equal payments were made one, two, and three years after the date on which a $10,000 loan was granted at 10.5% compounded monthly. If the balance immediately after the third payment was $5326.94, what was the amount of each payment?

> To satisfy more stringent restrictions on toxic waste discharge, a pulp mill will have to reduce toxic waste by 10% from the previous year’s level every year for the next five years. What fraction is the target level of the current discharge level?

> A five-year, compound interest GIC purchased for $1000 earns 4% compounded annually. 1. How much interest will the GIC earn in the fifth year? 2. If the rate of inflation during the five-year term is 2.2% per year, what will be the percent increase in th

> Two payments of $5000 are scheduled six months and three years from now. They are to be replaced by a payment of $3000 in two years, a second payment in 42 months, and a third payment, twice as large as the second, in five years. What should the last two

> A $1000 face value strip bond has 19 years remaining until maturity. What is its price if the market rate of return on such bonds is 5.9% compounded semiannually? At this market rate of return, what will be the increase in the value of the strip bond dur

> Payments of $2300 due 18 months ago and $3100 due in three years are to be replaced by an equivalent stream of payments consisting of $2000 today and two equal payments due two and four years from now. If money can earn 9.75% compounded semiannually, wha

> $6500 loan at 11.25% compounded monthly is to be repaid by three equal payments due 3, 6, and 12 months after the date of the loan. Calculate the size of each payment.

> Payments of $1800 and $2400 were made on a $10,000 variable-rate loan 18 and 30 months after the date of the loan. The interest rate was 11.5% compounded semiannually for the first two years and 10.74% compounded monthly thereafter. What amount was owed

> A loan contract called for a payment after two years of $1500 plus interest (on this $1500 only) at 8% compounded quarterly, and a second payment after four years of $2500 plus interest (on this $2500) at 8% compounded quarterly. What would you pay to pu

> On February 1 of three successive years, Roger contributed $3000, $4000, and $3500, respectively, to his RRSP. The funds in his plan earned 9% compounded monthly for the first year, 8.5% compounded quarterly for the second year, and 7.75% compounded semi

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

> For the 10 years ended December 31, 2018, the annually compounded rate of return on the portfolio of stocks represented by the S&P/TSX Composite Index was 7.9%. For the same period, the compound annual rate of inflation (as measured by the increase in th

> A four-year $7000 promissory note bearing interest at 10.5% compounded monthly was discounted 18 months after issue to yield 9.5% compounded quarterly. What were the proceeds from the sale of the note?

> If the inflation rate for the next 10 years is 1.7% per year, what hourly rate of pay in 10 years will be equivalent to $15 per hour today?

> Jarmila borrowed $3000, $3500, and $4000 from her grandmother on December 1 in each of three successive years at college. They agreed that interest would accumulate at the rate of 4% compounded semiannually. Jarmila is to start repaying the loan on June

> Payments of $2400 originally scheduled to be paid today, $1200 due 18 months from today, and $3000 due 33 months from today are to be replaced with a single payment due six months from now. Using 6% compounded quarterly as the rate of return money can ea

> Todd agreed to pay Laurie two payments of $1500: one on May 1 and the second on October 1. Todd now wishes to settle the debt with one equivalent payment on August 1. If the money was borrowed at 4.25% compounded monthly, what single payment on August 1

> For the five-year period ended October 31, 2019, a North American Resource Fund had a compound annual return of 7.99% compared to the average annual five-year returns of –0.337% for funds in the same category. How much more would an initial $1000 investm

> Isaac borrowed $3000 at 10.5% compounded quarterly 3 1 2 years ago. One year ago he made a payment of $1200. What amount will extinguish the loan today?

> For the five-year period ended October 31, 2019, a Canadian Equity Income Fund had compound annual returns of 14.40% while a Canadian Dividend fund had returns of 4.31% compounding annually. How much more would an initial $1000 investment in the Canadian

> Donnelly Excavating has received two offers on a used backhoe that Donnelly is advertising for sale. Offer 1 is for $10,000 down, $15,000 in 6 months, and $15,000 in 18 months. Offer 2 is for $8000 down, plus two $17,500 payments one and two years from n

> Rearrange N = L(1 – d1)(1 – d2)(1 – d3), to isolate d3 on the left side.

> Maynard Appliances is holding a “Fifty-Fifty Sale.” Major appliances may be purchased for nothing down and no interest to pay if the customer pays 50% of the purchase price in six months and the remaining 50% in 12 months. Maynard then sells the conditio

> On the same date that the Alberta Treasury Branches were advertising rates of 2.25%, 3%, 3.75%, 4.5%, and 6.5% in successive years of their five-year compound interest Springboard GIC, they offered 3.5% compounded annually on their five-year fixed-rate c

> What price should be paid for a $10,000 Government of Ontario strip bond with 17 years remaining to maturity if it is to yield the buyer 2.770% compounded semiannually?

> What amount three years ago is equivalent to $4800 on a date 1.5 years from now if money earns 3% compounded semiannually during the intervening time?

> A $100,000, 168-day Government of Canada Treasury bill was purchased on its date of issue to yield 1.97%. 1. What price did the investor pay? 2. Calculate the market value of the T-bill 85 days later if the annual rate of return then required by the mark

> Suppose that the current rates on 60- and 120-day GICs are 5.50% and 5.75%, respectively. An investor is weighing the alternatives of purchasing a 120-day GIC versus purchasing a 60-day GIC and then reinvesting its maturity value in a second 60-day GIC.

> Paul has $20,000 to invest for six months. For this amount, his bank pays 3.3% on a 90-day GIC and 3.5% on a 180-day GIC. If the interest rate on a 90-day GIC is the same three months from now, how much more interest will Paul earn by purchasing the 180-

> An agreement stipulates payments of $4500, $3000, and $5500 in 4, 8, and 12 months, respectively, from today. What is the highest price an investor will offer today to purchase the agreement if he requires a minimum rate of return of 10.5%?

> An Investment Savings account offered by a trust company pays the following rates: What interest will be paid for the month of January if the opening balance was $3678, $2800 was withdrawn on the 14th of the month, and $950 was deposited on the 25th of t