Deck 9: Compound Interest: Further Topics and Applications

Question 1

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%

Answer 1

7.00%

Question 2

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

Answer 2

30 years

Question 3

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%

Answer 3

2.25%

Question 4

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%

Question 5

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

Question 6

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

Question 7

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%

Question 8

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%

Question 9

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

Question 10

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

Question 11

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%

Question 12

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%

Question 13

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

Question 14

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%

Question 15

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%

Question 16

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

Question 17

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

Question 18

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%

Question 19

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

Question 20

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

Question 21

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

Question 22

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%

Question 23

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

Question 24

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

Question 25

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%

Question 26

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

Question 27

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%

Question 28

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%

Question 29

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%

Question 30

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%

Question 31

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

Question 32

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%

Question 33

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

Question 34

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%

Question 35

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%

Question 36

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%

Question 37

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%

Question 38

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%

Question 39

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%

Question 40

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%

Question 41

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%

Question 42

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%

Question 43

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%

Question 44

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%

Question 45

$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

Question 46

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%

Question 47

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%

Question 48

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%

Question 49

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%

Question 50

Calculate the effective annual rate for 18% compounded annually.

A) 19.8%
B) 16.8%
C) 18.0%
D) 19.0%
E) 20.6%

Question 51

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%

Question 52

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

Question 53

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%

Question 54

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%

Question 55

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%

Question 56

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%

Question 57

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%

Question 58

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%

Question 59

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%

Question 60

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%

Question 61

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%

Question 62

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.

Question 63

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

Question 64

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

Question 65

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%

Question 66

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

Question 67

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%

Question 68

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%

Question 69

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%

Question 70

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%

Question 71

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%

Question 72

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%

Question 73

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

Question 74

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%

Question 75

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%

Question 76

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%

Question 77

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%

Question 78

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%

Question 79

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%

Question 80

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 %