Deck 9: Compound Interest: Further Topics and Applications

Question 1

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

Answer 1

9 years, 9 months

Question 2

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

Answer 2

4.3% compounded annually

Question 3

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?

Answer 3

14 years, 6 months

Question 4

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.

Question 5

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

Question 6

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?

Question 7

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?

Question 8

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?

Question 9

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?

Question 10

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?

Question 11

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?

Question 12

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?

Question 13

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?

Question 14

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?

Question 15

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

Question 16

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?

Question 17

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?

Question 18

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

Question 19

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)?

Question 20

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?

Question 21

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%?

Question 22

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?

Question 23

For an investment to double in value during a 10-year period.
a) What annually compounded rate of return must it earn?
b) What monthly compounded rate of return must it earn?

Question 24

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?

Question 25

Rounded to the nearest month, how long will it take an investment to double if it earns:
a) 8.4% compounded annually?
b) 10.5% compounded semiannually?

Question 26

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.

Question 27

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?

Question 28

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.

Question 29

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?

Question 30

$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.

Question 31

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?

Question 32

Rounded to the nearest month, how long will it take an investment to triple if it earns:
a) 9% compounded annually?
b) 8% compounded quarterly?

Question 33

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?

Question 34

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?

Question 35

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.

Question 36

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.

Question 37

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?

Question 38

Consider the Province of Ontario strip bond in Table 9.1.
a) Present calculations to verify, to the nearest dollar, the bond's price on July 4, 2013, based on the quoted yield of 4.01% compounded semiannually. b) What would the price be on July 4, 2020 if the bond's yield remains the same?

Question 39

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?

Question 40

Consider the Newfoundland strip bond in Table 9.1.
a) Present calculations to verify, to the nearest dollar, the bond's price on July 4, 2013, based on the quoted yield of 1.68% compounded semiannually. b) What would the bond's price be on July 4, 2014 if the yield remains the same?

Question 41

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

Question 42

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?

Question 43

What is meant by the effective rate of interest?

Question 44

What is the effective interest rate corresponding to a nominal annual rate of:
a) 9% compounded semiannually?
b) 9% compounded monthly?

Question 45

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?

Question 46

According to Statistics Canada, undergraduate students paid an average of $5581 in tuition fees for the 2012/2013 academic year compared to fees of $4747 for the 2008/2009 year. During the same period, the Consumer Price Index rose from 115.7 to 122.0.
a) What would have been the average tuition fees for the 2012/2013 year if tuition fees had grown just at the rate of inflation since the 2008/2009 year?
b) What was the (equivalent) compound annual rate of increase of tuition fees during the period?
c) What was the (equivalent) compound annual rate of inflation during the period?

Question 47

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?

Question 48

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

Question 49

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?

Question 50

What is the effective interest rate corresponding to a nominal annual rate of:
a. 6% compounded semiannually?
b. 6% compounded quarterly?

Question 51

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?

Question 52

Rounded to the nearest month, how long will it take money to lose half of its purchasing power if the annual inflation rate is:
a) 2.5%
b) 3.5%

Question 53

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

Question 54

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.

Question 55

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

Question 56

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

Question 57

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

Question 58

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?

Question 59

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?

Question 60

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

Question 61

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?

Question 62

Suppose the periodic rate for one month is 0.5%. Is the equivalent periodic rate for six months (pick one):
(i) equal to 6(0.5%) = 3%?
(ii) less than 3%?
(iii) greater than 3%?
Answer the question without doing calculations. Explain your choice.

Question 63

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

Question 64

To be equivalent to 5.5% compounded annually, what must be the nominal rate with:
a. semiannual compounding?
b. quarterly compounding?
c. monthly compounding?

Question 65

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

Question 66

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.

Question 67

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

Question 68

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?

Question 69

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

Question 70

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?

Question 71

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?

Question 72

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

Question 73

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.

Question 74

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?

Question 75

Suppose the periodic rate for 6 months is 4%. Is the equivalent periodic rate for three months (pick one):
(i) equal to ?
(ii) less than 2%?
(iii) greater than 2%?
Answer the question without doing any calculations. Explain your choice.

Question 76

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?

Question 77

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

Question 78

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?

Question 79

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

Question 80

To be equivalent to 7% compounded quarterly, what must be the nominal rate with:
a. annual compounding?
b. semiannual compounding?
c. monthly compounding?