Deck 8: Compound Interest: Future Value and Present Value

Question 1

What is meant by the future value of an investment?

Answer 1

The future value of an investment at a future date is the combined value of the investment's principal and interest on that date.

Question 2

What is the maturity value of a $12,000 loan for 18 months at 5.2% compounded quarterly? How much interest is charged on the loan?

Answer 2

Maturity Value = $12,966.95 and Interest charged = $966.95

Question 3

What total interest will be earned by $5,000 invested at 5.4% compounded monthly for 3½ years?

Answer 3

Maturity Value = $6,037.64 and Interest earned = $1,037.64

Question 4

Noori borrowed $5,000 for 4.5 years. For the first 2.5 years, the interest rate on the loan was 8.4% compounded monthly. Then the rate became 5.5% compounded semi-annually. What total amount was required to pay off the loan if no payments were made before the expiry of the 4.5-year term?

Question 5

What amount 15 months ago is equivalent to $2,600, 1½ years from now? Assume money can earn 5.4% compounded monthly.

Question 6

Calculate the original principal:

Question 7

You owe $6,000 payable three years from now. What alternative amount should your creditor be willing to accept today if she can earn 2.1% compounded monthly on a low-risk investment?

Question 8

By calculating the maturity value of $100 invested for 1 year at each rate, determine which rate of return an investor would prefer.
a) 8.0% compounded monthly.
b) 8.1% compounded quarterly.
c) 8.2% compounded semi-annually.
d) 8.3% compounded annually.

Question 9

Why is $100 received today worth more than $100 received at a future date? Is inflation the fundamental reason?

Question 10

By calculating the maturity value of $100 invested for 1 year at each rate, determine which rate of return an investor would prefer.
a) 12.0% compounded monthly.
b) 12.1% compounded quarterly.
c) 12.2% compounded semi-annually.
d) 12.3% compounded annually.

Question 11

Calculate the original principal:

Question 12

For a six-month investment, rank the following interest rates (number 1 being "most preferred"): 6% per annum simple interest, 6% compounded semi-annually, 6% compounded quarterly. Explain your ranking.

Question 13

A $2,300 payment due 1½ years ago has not been paid. If money earns 6.25% compounded semi-annually, what amount in two years from now would be the economic equivalent to the missed payment during the intervening time?

Question 14

If your client's objective is to have $10,000 in four years, how much should he invest today in a product earning 5.5% compounded annually? (Taken from CIFP course materials)

Question 15

Faisal borrowed $3,000, $3,500, and $4,000 from his father on January 1 of 3 successive years at college. Faisal and his father agreed that interest would accumulate on each amount at the rate of 5% compounded semi-annually. Faisal is to start repaying the loan on the January 1 following graduation. What consolidated amount will he owe at that time?

Question 16

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 $2,297.78. How much of this amount is principal and how much is interest?

Question 17

Calculate the original principal:

Question 18

Calculate the combined equivalent value of the scheduled payments on the indicated dates. The rate of return that money can earn is given in the fourth column. Assume that payments due in the past have not yet been made.

Question 19

A $1,000 investment is made today. Calculate its maturity values for the six combinations of terms and annually compounded interest rates in the following table.

Question 20

Interest rates were at historical highs in the early 1980s. In August of 1981, you could earn 17.5% compounded annually on a five-year term deposit with a Canadian bank. Since then, the interest rate offered on five-year term deposits dropped to a low of 1.1% compounded annually in June of 2013. On a $10,000 deposit for a term of five years, how much more would you have earned at the historical high interest rate than at the more recent low rate?

Question 21

The process of discounting is the opposite of doing what?

Question 22

Isaac borrowed $3,000 at 10.5% compounded quarterly 3½ years ago. One year ago he made a payment of $1,200. What amount will extinguish the loan today?

Question 23

Mustafa can receive a $77 dollar discount if he pays his property taxes early. Alternatively, he can pay the full amount of $2,250 when payment is due in 9 months. Which alternative is to his advantage if he can earn 6% compounded monthly on short-term investments? In current dollars, how much is the advantage?

Question 24

Does a smaller discount rate result in a larger or a smaller present value? Explain.

Question 25

What single payment 1 year from now would be equivalent to $2500 due in 3 months, and another $2,500 due in 2 years? Money is worth 7% compounded quarterly.

Question 26

Megan borrowed $1,900 3½ years ago at 7% compounded semi-annually. Two years ago she made a payment of $1,000. What amount is required today to pay off the remaining principal and the accrued interest?

Question 27

Suppose the future value of $1 after x years is $5. What is the present value of $1, x years before its scheduled payment date? (Assume the same interest rate in both cases.)

Question 28

Why does $100 due one year from now have less economic value than $100 has today? What do you need to know before you can determine the difference between the economic values of the two payments?

Question 29

An investment of $2,500 earned interest at 4.5% compounded quarterly for 1½ years, and then 4.0% compounded monthly for two years. How much interest did the investment earn in the 3½ years?

Question 30

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 3% compounded monthly for the first 2½ years and then at 8.25% compounded semi-annually for the remainder of the term. What total amount was required to pay off the loan?

Question 31

What amount three years ago is equivalent to $4,800 on a date 1½ years from now if money earns 8% compounded semi-annually during the intervening time?

Question 32

What is the meaning of the term discount rate?

Question 33

An eight year note for $3,800 with interest at 6% compounded semi-annually was sold after three years and three months to yield the buyer 9% compounded quarterly. What price did the buyer pay?

Question 34

A four year $8,000 promissory note bearing interest at 6.6% compounded monthly was discounted 21 months after issue to yield 4.8% compounded quarterly. What were the proceeds from the sale of the note?

Question 35

A $15,000 loan at 5.5% compounded semi-annually is advanced today. Two payments of $4,000 are to be made 1 year and 3 years from now. The balance is to be paid in 5 years. What will the third payment be?

Question 36

A bond pays $1,000 interest at the end of every year for the next 30 years. What is the current economic value of each of the 15^th and 30^th payments if we discount the payments at:
a) 4% compounded semi-annually?
b) 8% compounded semi-annually?

Question 37

Alicia is considering two offers-to-purchase that she has received on a residential building lot she wishes to sell. One is a cash offer of $145,000. The other offer consists of three payments of $49,000-one now, one in six months, and one in twelve months. Which offer has the larger economic value if Alicia can earn 4.4% compounded quarterly on low-risk investments? How much more (in current dollars) is the better offer worth?

Question 38

Michelle has just received an inheritance from her grandfather's estate. She will be entering college in 3½ years, and wants to immediately purchase three compound-interest investment certificates having the following maturity values and dates: $4,000 at the beginning of her first academic year, $5,000 at the start of her second year, and $6,000 at the beginning of her third year. She can obtain interest rates of 5% compounded semi-annually for any terms between 3 and 5 years, and 5.6% compounded quarterly for terms between 5 and 7 years. What principal amount should she invest in each certificate?

Question 39

Teresa has three financial obligations to the same person: $2,700 due in 1 year, $1,900 due in 1½ years, and $1,100 due in 3 years. She wishes to settle the obligations with a single payment in 2¼ years, when her inheritance will be released from her mother's estate. What amount should the creditor accept if money can earn 6% compounded quarterly?

Question 40

A $6,000 loan at 6% compounded quarterly is to be settled by two payments. The first payment is due after 9 months and the second payment, half the amount of the first payment, is due after 1½ years. Determine the size of each payment.

Question 41

On February 1 of 3 successive years, Roger contributed $3,000, $4,000, 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-annually for the third year. What was the value of his RRSP 3 years after the first contribution?

Question 42

How, if at all, will the future value of a 3-year variable-rate GIC differ if it earns 4%, 5%, and 6% in successive years instead of 6%, 5%, and 4% in successive years?

Question 43

Roger has just invested $60,000 in a five-year Guaranteed Investment Certificate (GIC) earning 3% compounded semi-annually. When the GIC matures, he will reinvest its entire maturity value in a new five-year GIC. What will be the maturity value of the second GIC if it yields:
a) The same rate as the current GIC?
b) 4% compounded semi-annually?
c) 2% compounded semi-annually?

Question 44

Mr. Dickson purchased a 7-year, $30,000 compound-interest GIC with funds in his RRSP. If the interest rate on the GIC is 4.25% compounded semi-annually, what is the GIC's maturity value?

Question 45

The BMO Bank of Montreal advertised rates of 1.8%, 2.25%, 2.6%, 3%, and 3.25% for the five successive years of its five-year compound-interest Rate Optimizer GIC. At the same time, the bank was offering fixed-rate five-year compound-interest GICs yielding 2.75% compounded annually. What total interest would be earned during the five-year term on a $5,000 investment in each type of GIC?

Question 46

Mrs. Sandhu placed $11,500 in a 4-year compound-interest GIC earning 3.75% compounded monthly. What is the GIC's maturity value?

Question 47

On the same date that the CIBC advertised rates of 2%, 2.5%, 3%, 3.25%, and 7% in successive years of its five-year compound-interest Escalating Rate GIC, it offered 2.75% compounded annually on its five-year fixed-rate GIC. How much more will a $10,000 investment be worth at maturity if the Escalating Rate GIC is chosen instead of the fixed-rate GIC?

Question 48

What amount did the owner of a $10,000 face value compound-interest series S120 CSB receive when he redeemed the bond on: a) November 1, 2012? b) May 19, 2013?

Question 49

For a given term of compound-interest GIC, the nominal interest rate with annual compounding is typically 0.125% higher than the rate with semi-annual compounding and 0.25% higher than the rate with monthly compounding. Suppose that the rates for 5-year GICs are 3.00%, 2.875%, and 2.75% for annual, semi-annual, and monthly compounding, respectively. How much more will an investor earn over 5 years on a $10,000 GIC at the most favourable rate than at the least favourable rate?

Question 50

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

Question 51

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 compound-interest GIC.
a) What will be the maturity values of $10,000 invested in each GIC?
b) How much interest will each GIC earn in the third year?

Question 52

Stan purchased a $15,000 compound-interest Series S122 Canada Savings Bond on January 1, 2010. The interest rate in the first year was 0.40% and in the second year was 0.65%. What interest did he receive when he redeemed the CSB on November 1, 2012?

Question 53

A four-year $7,000 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?

Question 54

Krista invested $18,000 in a 3-year regular-interest GIC earning 4.2% compounded semi-annually. What is the semi-annual interest payment?

Question 55

Eric invested $22,000 in a 5-year regular-interest GIC earning 4.5% compounded monthly. What is each monthly interest payment?

Question 56

If an investor has the choice between rates of 5.4% compounded quarterly and 5.5% compounded annually for a six-year GIC, which rate should be chosen?

Question 57

A trust company offers 3-year compound-interest GICs earning 4.8% compounded monthly or 4.9% compounded semi-annually. Which rate should an investor choose?

Question 58

What was the redemption value of a $300 face value compound-interest series S108 CSB on March 8, 2013?

Question 59

What amount did the owner of a $5,000 face value compound-interest series S114 Canada Savings Bond receive when she redeemed the bond on: a) November 1, 20012? b) August 21, 2013?

Question 60

A five-year, compound-interest GIC purchased for $1,000 earns 6% compounded annually.
a) How much interest will the GIC earn in the fifth year?
b) If the rate of inflation during the five-year term is 2.5% per year, what will be the percent increase in the purchasing power of the invested funds over the entire five years?

Question 61

Use the data in Table 8.2 to determine the redemption value of a $500 face value compound-interest series S108 Canada Savings Bond on:
a) November 1, 2012.. b) April 15, 2013.

Question 62

Should we conclude that the owner of a strip bond earns nothing until the full face value is received at maturity? Explain.

Question 63

If a quantity declines by x% per year (compounded) for 2 years, will the overall percent decrease be more or less than 2x%? Explain.

Question 64

Give two examples of advertisements or news items that routinely ignore the time value of money.

Question 65

How much money was needed 15 years ago to have the purchasing power of $1,000 today if the average (compound annual) rate of inflation has been:
a) 2%? b) 4%?

Question 66

The late 1970s and early 1980s were years of historically high rates of inflation in Canada. For the years 1978, 1979, 1980, 1981, and 1982 the rates of inflation were 8.8%, 9.2%, 10.9%, 12.6%, and 10.0%, respectively.
a) Suppose your hourly wage at the beginning of 1978 was $10 per hour. What wage did you need to earn at the end of 1982 just to keep pace with inflation?
b) What percentage of its purchasing power did money lose over these five years?

Question 67

What price should be paid for a $5,000 face value strip bond with 19.5 years remaining to maturity if it is to yield the buyer 4.1% compounded semi-annually?

Question 68

In 2003 the number of workers in the forest industry was forecast to decline by 3% per year, reaching 80,000 in 2013. How many were employed in the industry in 2003?

Question 69

A pharmaceutical company had sales of $28,600,000 in the year just completed. Sales are expected to decline by 4% per year for the next three years until new drugs, now under development, receive regulatory approval. Then sales should grow at 8% per year for the next four years. What are the expected sales for the final year of the seven year period?

Question 70

How much will you need 20 years from now to have the purchasing power of $100 today if the (compound annual) rate of inflation during the period is:
a) 2%? b) 3%? c) 4%?

Question 71

A $1,000 face value strip bond has 19 years remaining until maturity. What is its price if the market rate of return on such bonds is 3.9% compounded semi-annually?

Question 72

Why must the Finance Department keep the interest rates on existing CSBs at least as high as the rate on a new CSB issue?

Question 73

If a quantity increases by x% per year (compounded) for two years, will the overall percent increase be more or less than 2x%? Explain.

Question 74

A 1995 study predicted that employment in base metal mining would decline by 3.5% per year for the next five years. What percentage of total base metal mining jobs was expected to be lost during the five-year period?

Question 75

Mrs. Janzen wishes to purchase 13 year-maturity strip bonds with $12,830 cash she now has in her RRSP. If these strip bonds are currently priced to yield 4.25% compounded semi-annually, how many $1,000 denomination bonds can she purchase?

Question 76

If the inflation rate for the next 10 years is 3% per year, what hourly rate of pay in 10 years will be equivalent to $15 per hour today?

Question 77

A $1,000 face value compound-interest series S114 Canada Savings Bond was redeemed on March 14, 2013. What amount did the bond's owner receive? (Obtain the issue date and the interest rates paid on the bond from Table 8.2)

Question 78

If the inflation rate for the next 10 years is 3.5% per year, what hourly rate of pay in 10 years will be equivalent to $15/hour today?

Question 79

A city's population stood at 120,000 after 5 years of 3% annual growth. What was the population 5 years previously?

Question 80

If two payment streams are equivalent at one interest rate, will they be equivalent at another interest rate?