Quiz 9: Compound Interest: Further Topics and Applications

A six-year, $20,000 GIC has a maturity value of $29,625. Calculate the semi-annually compounded nominal interest rate. A) 6.77% B) 6.66% C) 4.23% D) 6.94% E) 5.44%

A $50,000 GIC will earn $70,000 of interest over its 10-year term. What is the monthly compounded nominal rate of interest? A) 7.32% B) 9.15% C) 3.37% D) 8.79% E) 3.42%

At what quarterly compounded nominal interest rate will money double in 75 months? A) 11.25% B) 15.06% C) 3.77% D) 28.11% E) 11.73%

Albert Greco paid $1,974 for a $10,000 strip bond 16 years before it reached maturity. What semi-annually compounded nominal rate will Albert earn on his investment? A) 11.78% B) 3.17% C) 5.22% D) 10.67% E) 10.40%

Seven years before it matures the value of a $1,000 strip bond is $672. What is the semi-annually compounded nominal interest rate? A) 5.76% B) 5.84% C) 3.10% D) 24.40% E) 2.88%

At what annually compounded interest rate will an investment of $71,294.69 double in 90 months? A) 6.97% B) 7.23% C) 9.68% D) 9.28% E) 10.55%

The Wilsons bought their home 16 years ago for $128,000. Its value now is $141,000. At what annual rate has the value of their home appreciated since they bought it? A) 6.06% B) 7.28% C) 2.41% D) 1.19% E) 0.61%

Twenty years ago the population of a village in Newfoundland was 964. Now it is 612. At what average annual rate has the population of the village declined over the last 20 years? A) 3.02% B) 7.97% C) 2.25% D) 5.11 % E) 1.77%

Maury invested $5,000 in a selection of high-tech stocks. After six years of careful trading, his investments were worth $79,700. At what quarterly compounded nominal rate did his investments grow? A) 37.45% B) 24.90% C) 12.23% D) 58.64% E) 48.91%

A 30-year, $1,000 strip bond was traded for $167, four years after it was issued. What was the semi-annually compounded nominal rate at that time? A) 7.13% B) 7.00% C) 25.07% D) 12.52% E) 7.27%

What amount invested at 10% compounded semiannually will be worth $6380.00 after 38 months? A) $8690.00 B) $6331.04 C) $4684.05 D) $999.14 E) $3488.73

At 14% compounded annually, an investment of $50,000 will grow to $1,000,000 in 22.86 years. How much longer will it take at 11% compounded annually? A) 8.33 years B) 3.45 years C) 5.85 years D) 13.78 years E) 28.71 years

At 11.4% compounded quarterly, how long will it take for money to double? A) 2 years, 1 month B) 5 years, 4 months C) 5 years, 11 months D) 6 years, 2 months E) 7 years, 6 months

A demand loan for $8,000 with interest at 16% compounded quarterly was repaid after two years and eight months. What was the amount of interest paid? A) $4138.26 B) $4155.67 C) $5265.03 D) $5236.19 E) $2763.81

What is the term of a compound-interest Guaranteed Investment Certificate if $8,500 invested at 6.1% compounded annually will earn interest totaling $4,365.50? A) 11.25 years B) 10.59 years C) 8.50 years D) 7.75 years E) 7.00 years

A $50,000 strip bond was discounted to $21,680. The market rate was 7.4% compounded semi-annually. How much time was left before the bond reached maturity? A) 11.5 years B) 21.9 years C) 11.7 years D) 5.04 years E) 23 years

Rounded to the nearest month, how long will it take for $25,000 to grow to $35,000 at 9% compounded quarterly? A) 3 years, 8 months B) 5 years, 1 month C) 4 years, 4 months D) 5 years, 6 months E) 3 years, 1 month

Sollozo just made a single payment to repay a loan he had with the Corleone Finance Company. He paid a total of $86,500 which included interest of $56,500 at 48% compounded monthly. How long ago was the money borrowed? A) 19 months B) 63 months C) 27 months D) 34 months E) 47 months

If the population of Green City is growing at a rate of 5% per year, how long will it take to grow from 2,300 to 10,000? A) 17 years B) 20 years C) 23 years D) 25 years E) 30 years

If the population of Dodge City is decreasing at a rate of 19% per year, how long will it take to decrease from 7,700 to 2,000? A) 7.75 years B) 6.4 years C) 9.6 years D) 5.8 years E) 4.9 years

An investment of $7,500 at 8% compounded monthly is now worth $13,280. How long ago was the investment made? A) 12 years, 9 months B) 11 years, 2 months C) 9 years, 9 months D) 8 years, 6 months E) 7 years, 2 months

An investment of $10,000 on January 1, 1970 grew to $300,000 on January 1, 2010. What average annually compounded rate of return was earned? A) 300% B) 10.025% C) 8.778% D) 8.875% E) 9.185%

A $25,000 strip bond is purchased for $8235 to yield 8% compounded semiannually. What is the remaining time until maturity? A) 30.53 years B) 12.50 years C) 14.16 years D) 22.28 years E) 56.63 years

A $6300 face-value investment earning interest at 10% compounded annually for a six-year term was sold for $7550. How many years before its maturity date was the note sold if it was discounted to yield 12% compounded monthly? A) 2.73 B) 3.27 C) 4.50 D) 12.38 E) 39.28

An investment had the following 4 year returns: -8%, 15%, 10% and -5%. Determine the average annual rate of return. A) 2.54% B) 3.61% C) 3.85% D) 4.03% E) 4.92%

A five-year investment earned the following annual rates of return: 4.2%, 6.8%, 9.8% 12.1% and -11.6%. Determine the average annual rate of return. A) 2.45% B) 2.63% C) 3.05% D) 3.68% E) 3.90%

Enrolment at the local university increased 20% over a four-year period. Determine the average annual rate of enrolment during this time. A) 3.85% B) 4.66% C) 5.85% D) 6.44% E) 8.04%

Smoking among young adults has decreased by 34% over the past 16 years. Determine the average annual rate of decline. A) -3.42% B) -2.56% C) -2.09% D) -1.98% E) -1.60%

At the start of 1991, undergraduate students paid $190 per college course. By the end of 2010, the price per course had increased to $565. Determine the annual rate of increase. A) 4.8% B) 5.1% C) 5.6% D) 6.6% E) 7.2%

An investment earned 5.8% compounded monthly for 6 years, and then 3.8% compounded quarterly for another 4. Determine the annual rate of interest per year compounded annually. A) 4.01 B) 4.11 C) 5.01 D) 5.11 E) 5.21

An investment earned 8% compounded quarterly for 10 years, and then 5.15% compounded semi-annually for another 15. Determine the annual rate of interest per year compounded monthly. A) 7.38% B) 7.16% C) 6.84% D) 6.42% E) 5.85%

An investment earned 6.3% compounded annually for two years, 5.4% compounded semi-annually over another 2 years, and 4.5% compounded quarterly over the last 6 years. Determine the average annual rate of return over this 10 year period based on monthly compounding. A) 4.75% B) 4.98% C) 5.01% D) 5.05% E) 5.15%

A 30-year, Government of Canada $10,000 strip bond was discounted at 4.9% compounded semi-annually and traded for $4,722. How many years earlier had the bond been issued? A) 14.5 years B) 15.0 years C) 15.5 years D) 29.0 years E) 30.0 years

Martha is planning her retirement in 10 years' time. She contributes a lump sum deposit of $10,000 now in a plan earning 5.4% compounded semi-annually. Two years later, she will deposit $20,000 in another investment earning 4.8% compounded monthly. In the final 5 years, she plans on contributing $1,000 per month. Based on quarterly compounding, determine what the rate of interest will be on the final investment if she wishes to end up with $112,000. A) 5.16% B) 4.85% C) 4.12% D) 3.61% E) 2.48%

Norman is planning for his retirement. He initially deposits $25,000 in a retirement plan earning 4.4% compounded quarterly over 25 years. Three years later he begins another investment where he contributes $800 per quarter over 22 years. Based on monthly compounding, determine what the rate of interest will be on the final investment if he wishes to end up with $210,000. A) 5.37% B) 5.48% C) 5.59% D) 5.72% E) 5.85%

15 years ago, Alyssa made an initial deposit of $5,000 along with quarterly contributions in an investment earning 6.1% compounded monthly. 10 years ago, she deposited another lump sum of $25,000 in another investment. If her cumulative investments were $100,000 at the end of the 15 years, determine the rate of interest earned on the second investment based on annual compounding. A) 4.05% B) 4.15% C) 4.30% D) 4.55% E) 5.05%

Anita contributes a lump sum of $50,000 and $350 per month in an investment earning 5.5% compounded monthly over a 10-year period. At the end of the 10th year, Anita plans to transfer her investment into another account where she can withdraw $4,000 per quarter for 10 years and still have $10,000 remaining. Based on quarterly compounding, determine what the rate of interest that will achieve this goal. A) 2.39% B) 2.89% C) 3.39% D) 4.39% E) 4.89%

Jerome is planning on contributing $5,000 at the end of each semi-annual period for 8 years in an investment providing 8.4% compounded quarterly. At the end of this time, Jerome plans to reinvest this amount in another investment that will provide him with the opportunity to withdraw $1,500 per month over 5 years and have $10,000 remaining. Based on monthly compounding, determine what the rate of interest that will achieve this goal. A) 3.77% B) 4.07% C) 4.37% D) 4.77% E) 5.07%

Manuel begins investing $700 per month for 4 years in an account earning 3.8% compounded annually. At the end of this time, he makes a $20,000 lump sum deposit on top of the accumulated investment into another account. At the end of 5 years, this amount has accumulated to $84,000. Based on monthly compounding, determine what the rate of interest that will achieve this goal. A) 8.01% B) 8.28% C) 8.13% D) 8.33% E) 8.97%

Pat and Jaimie are twins. They will both invest $2,500 on their 20^th birthday. Pat's money will accumulate at 14% compounded annually for 35 years until their 55^th birthday. Being less of a risk taker Jamie will select an investment that will provide a return of only 8.5% compounded annually. If when they reach age 055, Jamie decides to leave the money growing at 8.5% how many more years will it take for Jamie's investment to reach the value that Pat's will be at age 55? A) 9.3 years B) 21.2 years C) 14.3 years D) 27.4 years E) 18.4 years

Pat and Jaimie are twins. Pat will invest $2,500 on their 20^th birthday and the money will accumulate at 12% compounded annually until their 60^th birthday. Jamie will wait 10 more years, until they are 30 years old, and will then invest the same amount, $2,500. What annually compounded interest rate will Jamie need to achieve for the investment to catch up to Pat's when they are 60 years old? A) 18.93% B) 14.14% C) 14.89% D) 15.00% E) 16.31%

Calculate the effective annual rate for 14.4% compounded monthly. A) 15.4% B) 12.8% C) 16.4% D) 13.8% E) 17.1%

Calculate the effective annual rate for 9.4% compounded quarterly. A) 13.14% B) 12.88% C) 10.58% D) 9.74% E) 9.98%

Calculate the effective annual rate for 19.2% compounded semi-annually. A) 21.72% B) 20.12% C) 23.44% D) 22.72% E) 19.94%

Calculate the effective annual rate for 18% compounded annually. A) 19.8% B) 16.8% C) 18.0% D) 19.0% E) 20.6%

Many department stores charge 2.4% per month on overdue accounts. What is the effective annual rate in this situation? A) 26.8% B) 32.9% C) 25.6% D) 31.8% E) 28.8%

What monthly compounded nominal rate has an effective rate of 14.29% A) 11.93% B) 13.43% C) 15.26% D) 13.92% E) 13.20%

At what monthly compounded nominal rate of interest will money triple in eight years? A) 13.81% B) 9.59% C) 14.72% D) 1.23% E) 115.10%

For a five-year GIC investment, what monthly compounded nominal rate would put you in the same financial position as 8% compounded semiannually? A) 8.02% B) 8.16% C) 7.84% D) 8.21% E) 7.87%

Determine the equivalent nominal rate of interest compounded monthly, as 8.4% compounded quarterly. A) 8.34% B) 8.67% C) 9.04% D) 9.16% E) 9.34%

Determine the equivalent nominal rate of interest compounded semi-annually, as 4.2% compounded monthly. A) 4.20% B) 4.24% C) 4.28% D) 4.36% E) 4.44%

Determine the rate at which money will quadruple in 20 years if interest is compounded monthly. A) 6.05% B) 6.35% C) 6.65% D) 6.95% E) 7.05%

An invoice indicates that interest at the rate of 1.75% per month will be charged on overdue amounts. What effective rate of interest is being charged? A) 19.21% B) 23.14% C) 24.75% D) 26.67% E) 21.00%

Find the monthly compounded nominal interest rate that is equivalent to an effective rate of 21%. A) 1.75% B) 23.144% C) 1.929% D) 19.214% E) 1.601%

Calculate the effective annual rate, if $100 grew to $165 in 11.5 years with quarterly compounding. A) 10.94% B) 4.38% C) 7.87% D) 7.22% E) 4.45%

On overdue accounts the telephone company charges 1.25% per month. What is the effective annual rate? A) 17.92% B) 17.55% C) 16.33% D) 16.08% E) 15.00%

Over six years Craig earned interest of $8,400 on an investment of $20,000. What effective rate of return did he earn? A) 15.56% B) 6.02% C) 7.00% D) 11.53% E) 14.71%

Over nine years Craig earned interest of $29,700 on an investment of $16,000. What effective rate of return did he earn? A) 7.11% B) 9.44% C) 10.92% D) 12.37% E) 13.56%

A $20,000 face value strip bond is sold for $8,524 to yield 8.4% compounded semi-annually. Calculate the maturity date to the nearest day. A) 11 years and 110 days B) 10 years and 110 years C) 10 years and 133 days D) 9 years and 110 days E) 9 years and 133 days

$100,000 face value strip bonds were sold at 24% of face value to yield 7.14% compounded monthly. Calculate the maturity date to the nearest day. A) 21 years and 15 days B) 20 years and 250 days C) 20 years and 17 days D) 19 years and 64 days E) 19 years and 1 day

Determine how long will take to triple money given an interest rate of 4.39% compounded monthly. Calculate to the nearest day. A) 25 years and 26 days B) 24 years and 46 days C) 23 years and 60 days D) 22 years and 90 days E) 20 years and 60 days

A contract stipulated a payment of $8,500 plus 6.4% interest compounded monthly in 30 months. Prior to the due date, the contract was sold for $9,700 based on 3.8% interest compounded quarterly. How many months before maturity did the contract change hands? A) 9 months and 22 days B) 8 months and 22 days C) 7 months and 22 days D) 6 months and 22 days E) 5 months and 22 days

The proceeds of a $9,000 8-year promissory note earning 5% compounded semi-annually were $10,474. How many years before maturity date was the note sold if the discounted rate was 7.2% compounded annually. A) 3.5 years B) 4.5 years C) 5.5 years D) 6.5 years E) 7.5 years

Rounded to the nearest month, calculate how long it will take money to lose half its purchasing power to a 3.25% inflation rate. A) 20 years and 10 months B) 21 years and 8 months C) 21 years and 10 months D) 22 years and 4 months E) 22 years and 8 months.

Bobby invested $1,000 for five years. For the first two years he earned 9% compounded monthly. For the next two years he earned 11% compounded quarterly. For the final year he earned 14% compounded semi-annually. What was his effective rate of return over the five years? A) 14.49% B) 11.22% C) 10.80% D) 13.38% E) 13.99%

Carlita invested $10,000 for 25 years. For the first 15 years she earned 15% compounded semi-annually. For the last 10 years she earned 9.6% compounded monthly. What was her effective rate of return over the 25 years? A) 13.32% B) 10.03% C) 15.56% D) 12.30% E) 14.51%

Lansky Finance Company was charging 1.87% per month on overdue accounts but negative publicity and public pressure made them decide to reduce the rate. What monthly finance charge would result in an annual effective rate of 19.99%? A) 1.80% B) 1.67% C) 1.53% D) 1.42% E) 1.37%

Rounded to the nearest month, calculate how long it will take for $1,000 to decline to $643.68 due to a 5.2% inflation rate. A) 9 years and 6 months B) 9 years and 3 months C) 8 years and 9 months D) 8 years and 6 months E) 8 years and 3 months

Determine the annual nominal rate of a credit card charging 2.3% effective rate based on monthly compounding. A) 24.62% B) 25.52% C) 26.42% D) 27.32% E) 28.22%

Determine the annual effective rate of a credit card offering 1.3% monthly. A) 16.77% B) 16.47% C) 16.07% D) 15.77% E) 15.47%

A credit card company wishes to reduce its effective interest rate by 4%. It currently charges a periodic rate of 1.75% per month. Determine by what amount the company should it set its new monthly periodic rate. A) 1.17% B) 1.27% C) 1.37% D) 1.47% E) 1.57%

What amount compounded quarterly is equivalent to 7.2% compounded monthly? A) 7.64% B) 7.54% C) 7.44% D) 7.34% E) 7.24%

What effective rate of interest is equivalent to a nominal rate of 19.214% compounded monthly? A) 1.210% B) 21.000% C) 14.530% D) 22.000% E) 17.704%

What amount compounded monthly is equivalent to 6.75% compounded semi-annually? A) 5.66% B) 6.16% C) 6.36% D) 6.66% E) 7.06 %

What is the monthly compounded nominal rate that is equivalent to 7.8% compounded semi-annually? A) 6.40% B) 7.68% C) 8.12% D) 3.90% E) 5.88%

What is the semi-annually compounded nominal rate that is equivalent to 10.5% compounded monthly? A) 11.02% B) 8.75% C) 5.37% D) 10.73% E) 11.44%

What is the semi-annually compounded nominal rate that is equivalent to 16% compounded quarterly? A) 9.91% B) 17.44% C) 15.02% D) 16.32% E) 16.98%

What is the quarterly compounded nominal rate that is equivalent to 18% compounded monthly? A) 18.53% B) 17.84% C) 16.89% D) 18.64% E) 18.27%

What is the monthly compounded nominal rate that is equivalent to 19.56% compounded annually? A) 18.00% B) 15.00% C) 21.41% D) 19.06% E) 18.32%

A bank pays a simple interest rate of 8% per annum on 40-day GICs. What is the annualized rate of return? A) 8.00% B) 8.29% C) 8.77% D) 9.13% E) 8.53%

Patty Lo purchased a house that she planned to use as a rental property for $300,000. During the past year, she rented the house for $1750 per month. Property taxes were $3900 for the year, and other expenses were $450 for a new garage door opener and $650 for lawn care. The current appraised value of the property is $315,000. What is Patty Lo's income yield? A) 7% B) 5.7% C) 5.6% D) 5.3% E) 6.6%

Patty Lo purchased a house that she planned to use as a rental property for $300,000. During the past year, she rented the house for $1750 per month. Property taxes were $3900 for the year, and other expenses were $450 for a new garage door opener and $650 for lawn care. The current appraised value of the property is $315,000. What is Patty Lo's capital gain yield? A) 4.8% B) 4.7% C) 5.3% D) 5.6% E) 5%

Patty Lo purchased a house that she planned to use as a rental property for $300,000. During the past year, she rented the house for $1750 per month. Property taxes were $3900 for the year, and other expenses were $450 for a new garage door opener and $650 for lawn care. The current appraised value of the property is $315,000. What is Patty Lo's rate of total return? A) 10.3% B) 11.8% C) 10.9% D) 11.6% E) 11.0%

Patty Lo purchased a house that she planned to use as a rental property for $300,000. During the past year, she rented the house for $1750 per month. Property taxes were $3900 for the year, and other expenses were $450 for a new garage door opener and $650 for lawn care. The current appraised value of the property is $315,000. What is Patty Lo's total return? A) $15,000 B) $31,000 C) $16,000 D) $21,000 E) $17,100

Last year, Kristina purchased a new condominium in downtown Toronto for $450,000 and used the property for rental income. During the past year, she rented the condo for $2200 per month. Property taxes were $4500 for the year, and there were no other expenses. The current appraised value of the property is the same as the purchase price. What is Kristina's income yield? A) 5.9% B) 6.3% C) 4.9% D) 5.25% E) 4.75%

Last year, Kristina purchased a new condominium in downtown Toronto for $450,000 and used the property for rental income. During the past year, she rented the condo for $2200 per month. Property taxes were $4500 for the year, and there were no other expenses. The current appraised value of the property is the same as the purchase price. What is Kristina's rate of total return? A) 5.9% B) 6.3% C) 4.75% D) 4.9% E) 5.5%

A mutual fund paid 3.5%, 4%, 3.5%, 6%, and 5% over the past five years. If you had invested $1,000 at the beginning of the five-year period, what was your investment worth at the end of the five-year period? A) $1220.00 B) $1617.34 C) $1771.38 D) $1239.96 E) $1180.92

A mutual fund paid 5.5%, 9%, -8%, 3.5%, and 5% over the past five years. If you had invested $2,000 at the beginning of the five-year period, what was your investment worth at the end of the five-year period? A) $2300.00 B) $2699.37 C) $2570.83 D) $2608.09 E) $2299.46

A stock valued at $150 increased by 25% and then decreased by 25%. What was the value of the stock after the decrease? A) $140.63 B) $150.00 C) $187.50 D) $112.50 E) $125.00

A stock valued at $75 decreased by 20% and then increased by 20%. What was the value of the stock after the increase? A) $75 B) $72 C) $60 D) $90 E) $80

The insurance premium on a building is 0.05% of the face value. The face value is 75% of the building's market value. The insurance premium is $1650. What is the face value of the policy? A) $2,475,000 B) $33,000 C) $3,300,000 D) $4,400,000 E) $44,000

For an investment to double in 5 years, the interest rate has to be 14.11% compounded quarterly.

The population of Canada grew from 24,820,000 at the start 1981 to 33,740,000 at the end of 2009. The annual rate of growth over 29 years was 1.06%

The average Canadian home was $70,000 in the early 80s. In 30 years, the average increased to $390,000. The average increase is 5.89%

9.1% compounded annually is a better investment than 8.8% compounded monthly.

5.4% compounded monthly is a better investment than 5.18% compounded semi-annually

An effective rate of 6.6% (based on quarterly compounding) has a higher nominal rate than an effective rate of 6.5% (based on monthly compounding).

A $10,000 payment on March 15^th was not paid. Instead $10,158.63 was paid earning 6.4% interest compounded monthly. The payment was made on June 13.

10.20% compounded monthly is equal to 10.69% compounded annually.

A portfolio earned annual rates of 18%, 25%, -5%, -5%, and 12% in five successive years. The portfolio's equivalent annual compounded rate of return is 20%.

A $45,000 payment on August 11^th was not paid. Instead $46,306.41 was paid earning 8.8% interest compounded quarterly. The payment was made on Dec 20.

A $9,000 payment on March 1 was not paid. Instead $9,140.65 was paid earning 6.3% interest compounded semi-annually. The payment was made on July 1.

An original loan of $6,500 has accumulated to $10,093.14 based on 9.2% interest compounded annually. The loan is five years old.

An effective rate of 11.4% has a nominal rate of 10.84% based on monthly compounding.

An effective rate of 14.9% has a nominal rate of 14.38% based on semi-annual compounding.

No payments were made on a $3,400 loan during its three-year term. What was the annually compounded nominal interest rate on the loan if the amount owed at the end of the term was $4,297.91?

What was the annually compounded nominal rate of growth if the future value of $1,000 after 20 years was $2321.06?

An initial $1,800 investment was worth $2120.31 after two years and nine months. What quarterly compounded nominal rate of return did the investment earn?

A strip bond that will mature 7½ years from now at its $13,000 face value can be purchased today for $9,042. What rate of return (compounded semiannually) will this strip bond provide to an investor?

Mr. and Mrs. Markovich note that the home they purchased 20 years ago for $70,000 is now appraised at $340,000. What was the (equivalent) annual rate of appreciation in the value of their home during the 20-year period?

A $1,000 five-year compound-interest GIC matured at $1,234.01. What semiannually compounded rate of interest did it earn?

The amount owed on a promissory note for $950 after two years and five months is $1082.11. What monthly compounded nominal rate of interest was charged on the debt?

The maturity value of a $5,000 four-year compound- interest GIC was $5,839.72. What quarterly compounded rate of interest did it earn?

Three years ago Mikhail invested $7,000 in a three-year compound interest GIC. He has just received its maturity value of $7,867.34. What was the monthly compounded rate of interest on the GIC?

Philippe contributed $4,300 to an RRSP eight years and six months ago. The money was invested in a Canadian Equity mutual fund. The investment is now worth $5537.82. Over the entire period, what monthly compounded nominal rate of return has the investment delivered?

When he died in 1790, Benjamin Franklin left $4,600 to the city of Boston, with the stipulation that the money and its earnings could not be used for 100 years. The bequest grew to $332,000 by 1890. What equivalent compound annual rate of return did the bequest earn during the 100 year period?

An $1,100 investment earning 6.3% compounded annually grew to $4,483.92. What was the term of the investment?

How long did it take $4,625 earning 4.875% compounded annually to grow to $6768.42?

How long before a future payment of $1,000 would a payment of just $100 be an economically equivalent alternative? Round your answer to the nearest month. Assume money can earn 4.8% compounded semiannually.

$5,000 invested in a GIC earning 3.7% compounded semiannually earned interest of $789.73.What was the term of the GIC?

The current balance on a loan is $3319.59. If the interest rate on the loan is 5% compounded monthly, how long ago was the $2,870 loan made?

Marilyn was supposed to pay $1,450 to Bernice on March 1. Some time later Marilyn paid Bernice an equivalent payment of $1,528.01, allowing for a time value of money of 4.5% compounded monthly. When did Marilyn make the payment?

What is the remaining time until the maturity date of a $10,000 strip bond if it is purchased for $4,011.33 to yield 6.4% compounded semiannually until maturity?

A few years ago Avtar invested $6,000 in a compound-interest GIC that earned 4.5% compounded semiannually. He recently received the maturity value of $7,168.99. What was the term of the GIC?

In early 2013, the Templeton Growth Fund ran advertisements containing the message: $10,000 INVESTED IN TEMPLETON GROWTH FUND IN 1954 WOULD BE WORTH OVER $9.09 MILLION TODAY. What compound annual rate of return did the fund realize over this period (December 31, 1954 to December 31, 2012)?

Anders discovered an old pay statement from 11 years ago. His monthly salary at the time was $2,550 versus his current salary of $4,475 per month. At what (equivalent) compound annual rate has his salary grown during the period?

The population of Canada grew from 24,343,000 in 1981 to 34,880,500 in 2012. What was the overall compound annual rate of growth in our population during the period?

The Consumer Price Index (based on a value of 100 in 1992) rose from 93.3 in 1990 to 113.5 in 2000. What was the (equivalent) annual rate of inflation in the decade of the 1990s?

A four-year promissory note for $3,800 plus interest at 4.5% compounded semiannually was sold 18 months before maturity for $4093. What quarterly compounded (annual) rate of return will the buyer realize on her investment?

An investor's portfolio increased in value from $100,000 to $193,000 over a seven-year period in which the Consumer Price Index rose from 95.6 to 115.3. What was the compound annual real rate of return on the portfolio during the period?

A portfolio earned 20%, -20%, 0%, 20%, and -20% in five successive years. What was the portfolio's five-year equivalent annually compounded rate of return?

A portfolio earned 20%, 15%, -10%, 25%, and -5% in five successive years. What was the portfolio's five-year equivalent annually compounded rate of return?

Rounded to the nearest month, how long will it take a town's population to grow from 32,500 to 40,000 if the annual growth rate is 3%?

When discounted to yield 7.98% compounded monthly, a $2,600 three-year promissory note bearing interest at 9.25% compounded annually was priced at $3110.41. How long after the issue date did the discounting take place?

A $4,000 loan at 4.8% compounded monthly was settled by a single payment of $5,000 including accrued interest. Rounded to the nearest day, how long after the initial loan was the $5,000 payment made? For the purpose of determining the number of days in a partial month, assume that a full month has 30 days.

Wilf paid $557.05 for a $1,000 face value strip bond. At this price the investment will yield a return of 5.22% compounded semiannually. How long (to the nearest day) before its maturity date did Wilf purchase the bond? Assume that each half-year has exactly 182 days.

A $5,000 face value strip bond may be purchased today for $1073.36 yielding the purchaser 7.27% compounded semiannually. How much time (to the nearest day) remains until the maturity date? Assume that each half-year has exactly 182 days.

A $10,000 face value strip bond was purchased for $4188.77. At this price, the bond provided a return of 5.938% compounded semiannually until the maturity date. To the nearest day, how long before the maturity date was the bond purchased? Assume that each half year is exactly 182 days long.

A $5000 strip bond was purchased for $3054.29, providing the investor with a return of 3.9% compounded semiannually until the maturity date. To the nearest day, how long before the maturity date was the bond purchased?

$7,500 was borrowed for a four-year term at 9% compounded quarterly. The terms of the loan allow prepayment of the loan based on discounting the loan's maturity value at 7% compounded quarterly. How long (to the nearest day) before the maturity date was the loan prepaid if the payout amount was $9,380.24? For the purpose of determining the number of days in a partial calendar quarter, assume that a full quarter has 91 days.

The proceeds from the sale of a $4,500 five-year promissory note bearing interest at 5% compounded quarterly were $5277.81. How long before its maturity date was the note sold if it was discounted to yield 6.3% compounded monthly?

Which of the flowing nominal interest rates has the highest effective rate: 12% compounded annually, 11.9% compounded semiannually, 11.8% compounded quarterly, or 11.7% compounded monthly?

Which interest rate would you prefer to earn on a three-year GIC: 6% compounded monthly, 6.1% compounded quarterly, 6.2% compounded semiannually, or 6.3% compounded annually?

Which interest rate would you prefer to pay on a loan: 9% compounded monthly, 9.1% compounded quarterly, 9.2% compounded semiannually, or 9.3% compounded annually?

Is the effective rate of interest ever numerically smaller than the nominal interest rate?

Is the effective rate of interest ever equal to the nominal interest rate?

A semiannually compounded nominal rate and a monthly compounded nominal rate have the same effective rate. Which has the larger nominal rate? Explain.

From a lender's point of view, would you rather disclose to borrowers the nominal interest rate or the effective interest rate?

What is the effective rate of interest on a credit card that calculates interest at the rate of 1.8% per month?

If an invoice indicates that interest at the rate of 2% per month will be charged on overdue amounts, what effective rate of interest will be charged?

If the nominal rate of interest paid on a savings account is 2% compounded monthly, what is the effective rate of interest?

A company reports that its sales have grown 3% per quarter for the last eight fiscal quarters. What annual growth rate has the company been experiencing for the last two years?

If a $5,000 investment grew to $6,450 in 30 months of monthly compounding, what effective rate of return was the investment earning?

After 27 months of quarterly compounding, a $3,000 debt had grown to $3,810. What effective rate of interest was being charged on the debt?

Lisa is offered a loan from a bank at 4.2% compounded monthly. A credit union offers similar terms but a rate of 4.4% compounded semiannually. Which loan should she accept? Present calculations that support your answer.

Craig can buy a three-year compound-interest GIC paying 4.6% compounded semiannually or 4.5% compounded monthly. Which option should he choose? Present calculations that support your answer.

Camille can obtain a residential mortgage loan from a bank at 5.5% compounded semiannually, or from an independent mortgage broker at 5.4% compounded monthly. Which source should she pick if other terms and conditions of the loan are the same? Present calculations that support your answer.

ABC Ltd. reports that its sales are growing at the rate of 1.3% per month. DEF Inc. reports sales increasing by 4% each quarter. What is each company's effective annual rate of sales growth?

Columbia Trust wants its annually, semiannually, and monthly compounded five-year GICs all to have an effective interest rate of 3.75%. What nominal annual rates should it quote for the three compounding options?

Belleville Credit Union has established interest rates on its three-year GICs so that the effective rate of interest is 4% on all three compounding options. What are the monthly, semiannually, and annually compounded rates?

A department store chain currently charges 18% compounded monthly on its credit card. To what amount should it set the monthly compounded annual rate if it wants to add 2% to the effective interest rate?

An oil company wants to drop the effective rate of interest on its credit card by 3%. If it currently charges a periodic rate of 1.7% per month, at what amount should it set the periodic rate?

What is the significance of two nominal interest rates being equivalent?

What semiannually compounded rate is equivalent to 4% compounded monthly?

What quarterly compounded rate is equivalent to 3.5% compounded semiannually?

What monthly compounded rate is equivalent to 6% compounded quarterly?

What semiannually compounded rate is equivalent to 8.5% compounded quarterly?

For a three-year GIC investment, what nominal rate compounded monthly would put you in the same financial position as 5.5% compounded semiannually?

A trust company pays 3.5% compounded semiannually on its three-year GICs. For you to prefer an annually compounded GIC of the same maturity, what value must its nominal interest rate exceed?

You are offered a loan at a rate of 9% compounded monthly. Below what nominal rate of interest would you choose semiannual compounding instead?

Banks usually quote residential mortgage interest rates on the basis of semiannual compounding. An independent mortgage broker is quoting rates with monthly compounding. What rate would the broker have to give to match 6.5% compounded semiannually available from a bank?

A credit union pays 5.25% compounded annually on five-year compound interest: GICs. It wants to set the rates on its semiannually and monthly compounded GICs of the same maturity so that investors will earn the same total interest. What should be the rates on the GICs with the higher compounding frequencies?

A bank offers a rate of 5.0% compounded semiannually on its four-year GICs. What monthly compounded rate should the bank offer on four-year GIC's to make investors indifferent between the alternatives?

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?

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?

If the Consumer Price Index rose from 109.6 to 133.8 over an 8½-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 double in value if it earns 7.5% compounded semiannually?

An investor paid $4217.17 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 that each half-year is exactly 182 days long.

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, when did Terry make the payment?

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

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?

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%?

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 portfolio's annually compounded real rate of return?

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?

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 3,000?

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?

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

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?

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

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 calculations that support your answer.

If a $15,000 investment grew to $21,805 in 4½ years of quarterly compounding, what effective rate of return was the investment earning?

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

You are offered a loan at a rate of 9% compounded monthly. What would a semiannually compounded nominal rate would a competing bank need to offer in order to provide an equivalent rate?

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?

A trust company pays 5.375% compounded annually on its 5-year GICs. What semiannually compounded nominal interest rate would provide the same maturity value?

The Consumer Price Index rose from 131.2 to 132.1 during the second quarter of a year. What was the effective annualized rate of inflation during the quarter?

The Calgary Real Estate Board reports that house prices increased by 5% during the first seven months of the year. If prices continue to rise at the same rate for the subsequent five months, what will be the (compound) increase for the entire year?

A T-bill with 125 days remaining to maturity is discounted to yield 4.6% pa simple interest. What is the effective annualized rate of return on the T-bill?

The current (simple annualized) yield on a money market mutual fund, based on the return for the most recent seven days, is 4.12%. What effective (annualized) yield will be reported for the fund?

The current (simple annualized) yield, based on the holding-period return for the most recent seven days, is reported for a money market mutual fund as 4.54%. What is the fund's corresponding effective (annualized) yield?

What is meant by the "total return" from an investment?

Can the income yield from an investment be negative? Explain or give an example.

Is it possible for the capital gain yield to exceed 100%? Explain or give an example.

Is it possible for a capital loss to be worse than -100%? Explain or give an example.

Does the combined effect of a 20% increase followed by a 20% decrease differ from the combined effect of a 20% decrease followed by a 20% increase? Justify your answer.

Rose purchased units of the Trimark Fund 1 year ago at $24.10 per unit. Today they are valued at $25.50. On the intervening December 31, there was a distribution of $0.83 per unit. ("Distribution" is the term used by most mutual funds for income paid to unit holders.) Calculate Rose's income yield, capital gain yield, and rate of total return for the year.

The market value of Stephanie's bonds has declined from $1053.25 to $1021.75 per bond during the past year. In the meantime she has received two semiannual interest payments of $35. Calculate Stephanie's income yield, capital gain yield, and rate of total return for the year.

How much will an investment of $100 be worth after 20 years if it increases in value by 25% in half of the years, but declines by 20% in the other years?

One year ago, Art Vandelay bought Norwood Industries shares for $37 per share. Today they are worth $40 per share. During the year, Art received dividends of $0.60 per share. What was his income yield, capital gain yield, and rate of total return for the year?

The federal government cut transfer payments to the provinces by a total of 20% over a five-year period. In the next budget speech, the Minister of Finance announced "the level of transfer payments will be restored to their former level by a 20% increase to be phased in over the next two years." Is this an accurate statement? Explain briefly.

The price of Bionex Inc. shares rose by 25% in each of 2 successive years. If they began the 2-year period at $12 per share, what was the percent increase in price over the entire 2 years?

The price of Biomed Corp. shares began a two-year period at $12, but fell 25% in each year. What was their overall percent decline in price?

What rate of return in the second year of an investment will wipe out a 50% gain in the first year?

What rate of return in the second year of an investment will nullify a 25% return on investment in the first year?

What rate of return in the second year of an investment is required to break even after a 50% loss in the first year?

Vitaly's shares of Dominion Petroleum have dropped in value from $36.75 to $32.25 during the past year. The shares paid a $0.50 per share dividend 6 months ago. Calculate Vitaly's income yield, capital gain yield, and rate of total return for the year.

What rate of return in the second year of an investment is required to break even after a rate of return of -20% in the first year?

After two consecutive years of 10% rates of return, what rate of return in the third year will produce a cumulative gain of 30%?

After two consecutive years of 10% losses, what rate of return in the third year will produce a cumulative loss of 30%?

Assume that the TD Bank shares in Table 9.3 will pay a $2.54 per share dividend in 2013. What would the share price have needed to be at the end of 2013 for a total rate of return in 2013 of 7%?

One year ago, Morgan invested $5,000 to purchase 400 units of a mutual fund. He has just noted in the Financial Post that the fund's rate of return on investment for the year was 22% and that the current price of a unit is $13.75. What amount did the fund distribute as income per unit during the year?

The Globe and Mail Web site noted that the shares of Compact Computers produced a 55% rate of total return in the past year. The shares paid a dividend of $0.72 per share during the year, and they currently trade at $37.50. What was the price of the shares 1 year ago?

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Monty purchased a strip bond for his RRSP. He paid $3,800 for a $5,000 face value bond with three years remaining until maturity. What semiannually compounded rate of return will he realize over the three years?

If the number of workers in the forest industry in Canada declined by 41% from the end of 1993 to the beginning of 2009, what was the compound annual rate of attrition in the industry?

A number of years ago, your client invested $6,000 at a rate of return of 9% compounded annually. If the investment is currently worth $10,968.25, for how long has she held the investment?

The maturity value of a four-year, $1,000 investment, is $1175.65. Calculate the nominal rate of interest paid on the investment if interest was compounded quarterly.

How long will it take a $1,000 investment to grow to $1500 if it earns 3.8% compounded annually?

Your client wants to invest a $250,000 inheritance and grow it to $325,000. Rounded to the nearest month, how long will this take if the investment earns 7% compounded annually?

Your client invests $10,000 today at a rate of return of 7.7% compounded quarterly. Rounded to the nearest month, how long will it take the investment to grow to $22,000?

How long will it take a $2,000 investment to grow to $2501.50 if it earns 4.5% compounded quarterly?

The Consumer Price Index (based on a value of 100 in 1986) rose from 67.2 in 1980 to 119.5 in 1990. What was the (equivalent) annual rate of inflation in the decade of the 1980s?

If money is worth 8% compounded quarterly, how long (to the nearest day) before a scheduled payment of $6,000 is $5,000 an equivalent payment? For the purpose of determining the number of days in a partial calendar quarter, assume that a full quarter has 91 days.

The Canadian Consumer Price Index (based on a value of 100 in 1971) rose from 97.2 in 1970 to 210.6 in 1980 and (based on a value of 100 in 1986) rose from 67.2 in 1980 to 119.5 in 1990. Calculate the annual rate of inflation for the period 1970-1990.

For three successive years, an investment paid annual rates of return of 3.5%, 4.8%, and 2.75%. Calculate the funds equivalent annually compounded rate of return over the three years.

The Canadian Consumer Price Index (based on a value of 100 in 1971) rose from 97.2 in 1970 to 113.5 in 1980. What was the (equivalent) annual rate of inflation in the decade of the 1970s?

An investment grew in value from $5,630 to $8,485 during a five-year period. The annual rate of inflation for the 5 years was 2.3%. What was the compound annual real rate of return during the five years?

An investment earned 6% compounded semiannually for two years and 8% compounded annually for the next three years. What was the equivalent annually compounded rate of return for the entire five-year period?

Kristina was earning $10.00 an hour four years ago. Today, she earns $13.50 an hour. At what equivalent compound annual rate has her salary grown over the four years?

A $5,000 investment was purchased for $4220.50. The bond paid interest at a rate of 3.8% compounded semi-annually until the maturity date. What was the term of the investment?

At the end of 2009, the Industrial Alliance (IA) Group Dividends Fund had the best 10-year compound annual return of any Canadian diversified equity mutual fund. During the 10-year period, this fund invested primarily in the shares of large Canadian companies. The fund's annual returns in successive years from 2000 to 2009 inclusive were 33.5%, 9.2%, 2.2%, 25.8%, 17.9%, 27.9%, 19.7%, 6.3%, -26.0%, and 21.5%, respectively. For 3-year, 5-year, and 10-year periods ended December 31, 2009, what was the fund's equivalent annual compounded return?

At the end of 2012, the Trans IMS Canadian Growth Fund had one of the worst 10-year compound annual returns of any Canadian diversified equity mutual fund. The fund's annual returns in successive years from 2000 to 2009 inclusive were -12.8%, -38.3%, -24.1%, 25.4%, 9.2%, 18.6%, 12.0%, -0.2%, -38.5%, and 15.6%, respectively. For 3-year, 5-year, and 10-year periods ended December 31, 2012, what was the fund's equivalent annually compounded return?

Advances in technology have improved the rate of production of widgets over the last 10 years and the number of plant workers required has declined by 25%. What is the equivalent annual rate of decrease during the period?

How long will it take an investment to double in value if it earns 4.5% compounded quarterly?

At the end of 2012, the RBC Canadian Dividend Fund was the largest equity mutual fund in Canada. The aggregate market value of its holdings at the end of 2012 was $9.995 billion. The fund's annual returns in successive years from 2003 to 2012 inclusive were 28.3%, 4.4%, -0.5%, 23.5%, 12.9%, 21.1%, 15.1%, 3.0% - 27.0%, and 27.3% respectively. For the 3-year, 5-year, and 10-year periods ending December 31, 2012, what were the fund's equivalent annually compounded returns?

A few years ago, Larissa invested $1500 at 3.75% compounded quarterly. If the investment is worth $1693.46 today, how many years ago did Larissa make the investment?

A $6,000, three-year promissory note bearing interest at 11% compounded semiannually was purchased 15 months into its term for $6,854.12. What monthly compounded discount rate was used in pricing the note?

Rounded to the nearest month, how long before a scheduled payment of $10,000 would a payment of $5,000 be an economically equivalent alternative? Assume money is worth 5% compounded annually.

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?

For three successive years, an investment paid annual rates of return of 5.8%, 3.4%, and -2.25%. Calculate the funds equivalent annually compounded rate of return over the three years.

Over a five-year period, Hardip's $2,000 investment grew to $2675. At the same time, the CPI increased from 106.1 to 109.1. What was Hardip's real compound rate of return?

The proceeds from the sale of a $3500 four-year promissory note bearing interest at 5% compounded quarterly were $3612.31. The note was discounted to yield 6.8% compounded semiannually. When was the note sold?

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Calculate the missing interest rate (to the nearest 0.01%)

Calculate the missing interest rate (to the nearest 0.01%)

If an interest rate of 8.9% compounded semiannually is charged on a car loan, what effective rate of interest should be disclosed to the borrower?

Calculate the effective rate of interest if $1,000 grows to $1459.74 in five years with semiannual compounding.

A department store credit card quotes a rate of 2% per month on any unpaid balance. Calculate the effective rate of interest being charged.

What rate of interest compounded quarterly has an effective rate of 6%?

Enrique wants to borrow $15,000 for a new car. The bank has personal loans at 5.25% compounded monthly, whereas the credit union at his company is offering personal loans at 5.5% compounded annually. Which should Enrique accept?

A bank quotes 7.25% compounded monthly on a loan. What is the effective rate of interest charged?

A furniture company has decided to drop the effective rate on its credit card by 2%. The store currently charges a periodic rate of 1.85% per month. What new periodic rate should the store advertise?

A department store currently charges an effective rate of 18% on its credit card. The store wants to add .25% per month to its monthly compounded rate. What new monthly compounded rate will the store charge?

Calculate the equivalent interest rate (to the nearest 0.01%)

Calculate the equivalent interest rate (to the nearest 0.01%)

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Calculate the equivalent interest rate (to the nearest 0.01%)

Calculate the equivalent interest rate (to the nearest 0.01%)

For a two-year GIC, what nominal rate compounded quarterly would pay the same amount of interest as 3.8% compounded annually?