Deck 5: Time Value of Money

Question 1

If I invest $1,000 in a financial instrument that pays 10% simple interest payable at the end of each year, I will

A)not receive any interest for the first year.
B)receive the same amount of interest each year.
C)receive interest only for the first year.
D)receive less interest in year ten than in year two.
E)receive interest on both the principal and first year's interest in year two.

Answer 1

receive the same amount of interest each year.

Question 2

Ingrid has invested $10,000 in a Guaranteed Investment Certificate that promises her 12% per year for the first 5 years and 4% per year for the next 10 years.The interest is compounded annually.At the end of the 15 years, the value of the investment will be closest to which value? (Round your answer to two decimals.)

A)$26,086.96
B)$31,721.69
C)$32,425.86
D)$36,372.55

Answer 2

$31,721.69

Question 3

As interest rates rise, future values

A)increase.
B)decrease.
C)stay the same.
D)cannot be determined, need compounding frequency.

Answer 3

increase.

Question 4

Earl has invested $12,000 in a security that pays 2% annual simple interest.How much interest does he earn in the 3^rd year?

A)$160
B)$240
C)$720
D)$12,735

Question 5

The interest earned on both the original investment and the accumulated interest, over time is called

A)growth rate.
B)compound interest.
C)simple interest.
D)cost of capital.

Question 6

Which one of the following is/are an example(s)of opportunity cost?

A)quitting your job to go to university
B)using a piece of land that you owned to build a house
C)spending time caring for an elder in your family instead of working
D)All of the above are examples of opportunity costs.

Question 7

You invested $2,000 at 5.0% compounded annually.What is the value of the investment in five years? (Round your answer to two decimals.)

A)$500.00
B)$552.56
C)$2,500.00
D)$2,552.56

Question 8

Gianni invested $10,000 at a rate of 6% compounded annually.How long will it take for the investment to grow to $40,000?

A)1.33 years
B)4.00 years
C)23.79 years
D)50.00 years

Question 9

Franklin needs to have $1,000 in 8 years.If his investment earns 5% compounded annually, how much must he invest today to achieve his goal? (Round your answer to two decimals.)

A)$676.84
B)$680.58
C)$1,477.46
D)$1,469.33

Question 10

The present value is always ______ the future value if the opportunity cost is ______ zero.

A)less than; greater than
B)equal to; equal to
C)greater than; less than
D)All of the above are true.

Question 11

Charles has $12,000 to invest.Charles' bank offers him the following investment accounts:

Assuming that all the accounts have the same risk as the investment, Charles' opportunity cost is closest to

A)1%.
B)3%.
C)5%.
D)8%.

Question 12

If Frank is indifferent between receiving $1,000 today and $1,100 in one year, his opportunity cost is approximately

A)1.10%.
B)10%.
C)110%.
D)100%.

Question 13

Lottery A pays $1,000 today and Lottery B pays $1,750 at the end of five years.If the discount rate is 5%, which lottery should you choose

A)Lottery A, because its future value is $1,276.
B)Lottery B, because its present value is $1,371 which is more than that of Lottery A.
C)Lottery B, because it pays $1,750 which is more than $1,000 from Lottery A.
D)Either option gives the same value over time.

Question 14

Consider two investments: PDQ and XPD.Each investment pays interest at the end of each year and the interest rate does not change over time.The interest earned each year is given below:

Which of the following statements is most correct?

A)PDQ and XPD earn simple interest.
B)PDQ earns simple interest, XPD earns compound interest.
C)PDQ earns compound interest, XPD earns simple interest.
D)PDQ and XPD earn compound interest.

Question 15

You invested $2,000 at 5% compounded annually.Determine how much interest was earned in the fifth year.(Round your answer to two decimals.)

A)$100.00
B)$121.55
C)$500.00
D)$552.56

Question 16

An equal-payment mortgage is calculated using the interest on the remaining balance of the capital every month, whereas interest paid on a line of credit is deducted from your account every month.So, mortgage payments are calculated using ______ where line of credit interest is calculated using ______.

A)simple interest, compound interest
B)compound interest, simple interest
C)simple interest, simple interest
D)compound interest, compound interest

Question 17

ABC Bank pays 2% simple interest annually on an investment of $10,000.What is the interest earned in the fifth year?

A)$2000
B)$200
C)$1000
D)$100
E)$500

Question 18

The current interest rate is 3.04%.If the interest rate increases by 10 basis points, the new interest rate will be (Round your answer to two decimals.)

A)2.94%.
B)3.03%.
C)3.05%.
D)3.14%.

Question 19

As interest rates fall, present values

A)increase.
B)decrease.
C)stay the same.
D)cannot be determined; need compounding frequency.

Question 20

Eduardo bought a house for $320,000 five years ago.He has just sold it for $480,000.What annual rate of return did he earn on this investment?

A)10%
B)8.45%
C)1.08%
D)3.13%

Question 21

Montreal Financial Services Company offers a perpetuity of $5,000 per year with the first payment made one year from year.If your opportunity cost is 8% compounded annually, the present value of the perpetuity today is

A)$57,500
B)$62,500
C)$67,500
D)$125,000

Question 22

Your mother has just retired.The balance in her investment account is $600,000 and she wants to receive monthly payments of $5,000.If she receives the payments at the end of the month, and the current interest rate is 7%, compounded quarterly, how many months will her investment account last for approximately?

A)98 months
B)120 months
C)170 months
D)206 months

Question 23

Montreal Financial Services Company offers a perpetuity of $5,000 per year with the first payment occurring immediately.If your opportunity cost is 8% compounded annually, the present value of the perpetuity today is

A)$57,500.
B)$62,500.
C)$67,500.
D)$125,000.

Question 24

Xiang invests $25,000 per year, starting in one year, for 20 years at an interest rate of 7%.What is the value of the investment at the end of the 20 years?

A)$1,096,629
B)$1,024,887
C)$283,390
D)$264,850

Question 25

Marie is considering investing a part of her future income in an investment account that offers 0.5% a month.She will start work in 6 months and her contract extends for 2 years.If the investment amount is $300 a month, what is the present value of this investment?

A)$6,768.86
B)$8,338.22
C)$6,569.30
D)$8,903.62

Question 26

An investment pays $2,000 every month for 2 years.Your opportunity cost is 10% compounded annually.The present value of this investment is approximately

A)$43,342
B)$43,529
C)$47,405
D)$48,000

Question 27

ABC Bank offers a return of 9% on a savings account for five years using simple interest while XYZ Bank offers a return of 9% for five years using compound interest.An investor should choose

A)the simple interest option because both have the same basic interest rate.
B)the compound interest option because it provides a higher overall return.
C)the compound interest option only if interest is compounded monthly.
D)the simple interest option only if interest is compounded monthly.
E)the compound interest option because both have the same basic interest rate.

Question 28

An annuity due pays out

A)equal payments at the beginning of each time period and continues forever.
B)unequal payments at the beginning of each time period for a fixed number of periods.
C)equal payments at the beginning of each time period for a fixed number of periods.
D)unequal payments at the end of each time period for a fixed number of periods.
E)equal payments at the end of each time period and continues forever.

Question 29

Which of the following is the most appropriate timeline for the cash flows of a three-year annuity due with annual cash flows of $5,000?

A)
B)
C)
D)

Question 30

A pension fund pays out $50,000 a year in perpetuity, based on a cost of capital of 5%, to retiring employees.Alternatively, the employee can take out a lump sum of $1 million payable immediately.The employee should choose

A)the lump sum, because its future value is $25 million.
B)the pension fund, because its present value is $1.25 million.
C)the pension fund, because it offers steady payments in perpetuity.
D)either option gives the same value over time.

Question 31

Xiang invests $25,000 per year, starting today, for 20 years at an interest rate of 7%.What is the value of the investment at the end of the 20 years?

A)$1,096,629
B)$1,024,887
C)$283,390
D)$264,850

Question 32

An investment pays $1,000 per year for the first four years and $2,000 per year for six years following.If the required rate of return is 8% compounded annually, how much will this investment have returned to the investor?

A)$12,557.89
B)$10,108.04
C)$9,604.64
D)$9,138.52

Question 33

Felix has been offered a three-year ordinary annuity with annual payments of $1,500.The current price to purchase this annuity is $2,700.Which of the following is the most appropriate timeline for this investment?

A)
B)
C)
D)

Question 34

Montreal Financial Services Company offers a perpetuity of $50,000 per year with the first payment on January 1 next year.If your opportunity costs are constant over time, the price you are willing to pay for this perpetuity ______ over time.

A)increases
B)decreases
C)stays the same
D)can't determine without the opportunity cost

Question 35

Elvira is considering buying a 20-year annuity due to provide her retirement income.The annuity will make annual payments of $25,000.If her opportunity cost is 7%, what is the present value of the annuity?

A)$1,096,629
B)$1,024,887
C)$283,390
D)$264,850

Question 36

At the age of 65 your grandfather decides to retire and use the money he saved in his RRSPs.He decided to get a fixed amount every quarter starting the day he retires.What type of payment is this?

A)an ordinary annuity
B)an annuity due
C)a reverse ordinary annuity
D)a reverse annuity due

Question 37

Ellie is considering an investment that will require her to deposit $500 per month for 6 years with the first payment occurring today.This is an example of

A)an ordinary annuity.
B)an annuity due.
C)a reverse ordinary annuity.
D)a reverse annuity due.

Question 38

Montreal Financial Services Company offers a 50-year annuity of $50,000 per year with the first payment on January 1 next year.If your opportunity costs are constant over time, the price you are willing to pay for this annuity ______ over time.

A)increases
B)decreases
C)stays the same
D)can't determine without the opportunity cost

Question 39

Consols are British bonds that were issued during the 18^th century that paid a constant coupon and were not redeemable.What type of payment is this?

A)an ordinary annuity
B)an annuity due
C)a perpetuity
D)a growing perpetuity

Question 40

Elvira is considering buying a 20-year ordinary annuity to provide her with retirement income.The annuity will make annual payments of $25,000.If her opportunity cost is 7%, what is the maximum Elvira should pay for the annuity?

A)$1,096,629
B)$1,024,887
C)$283,390
D)$264,850

Question 41

The R&M Bank currently offers an investment account with an interest rate of 6% compounded monthly.R&M wants to offer customers another account with interest compounded quarterly.If R&M wants the effective rates to be equal, what interest rate should R&M quote for the second account?

A)2.00%
B)6.00%
C)6.03%
D)6.17%

Question 42

How much should a monthly compounded account with an EAR of 10% earn semi-annually?

A)4.88%
B)5.00%
C)4.76%
D)5.11%

Question 43

Eloise has deposited $2,000 in an investment account that pays 5% compounded continuously.How much will she have in her account in two years?

A)$2,205.00
B)$2,210.34
C)$2,105.54
D)$1,809.67

Question 44

Your credit card has a quoted rate of 18.5% compounded daily.What is the effective annual rate? (Assume 360 days a year.)

A)66.60%
B)20.32%
C)51.39%
D)18.50%

Question 45

How much should a weekly compounded account with an EAR of 10% earn semi-annually?

A)4.88%
B)5.00%
C)5.36%
D)5.12%

Question 46

Your investment account pays interest at a rate of 8% compounded semi-annually.If you deposit $1,000 today, how much will you have in two years?

A)$1,081.60
B)$1,166.40
C)$1,169.86
D)$1,360.49

Question 47

To compare interest rates, we should compare the

A)quoted rates.
B)nominal rates.
C)effective rates.
D)periodic rates.

Question 48

Which one of the following will increase the present value of an annuity?

A)lowering the discount rate
B)reducing the cash flow amount
C)decreasing the number of payments
D)reducing the future value of the cash flow
E)lowering the payment amount

Question 49

In 30 years, you plan to set up a fellowship fund for your university that pays out $100,000 each year in perpetuity with an annually compounded discount rate of 5%.In order to set up the fund in 30 years, how much do you need to save each year (starting at the end of this year)assuming you can get a semi-annually compounded return of 10% on your savings for the next 30 years?

A)$66,666.67
B)$11,595.56
C)$21,215.49
D)$30,744.90
E)$30,000.00

Question 50

The following four different financing schemes have been offered to you for the purchase of a $30,000 car.Which one should you choose?

A)$5,000 down with the balance paid in equal monthly payments of $624.70 per month for 48 months
B)$0 down with equal monthly payments of $960 per month for 36 months
C)$15,000 down and a final payment of $18,550 two years from now
D)have it financed with a bank loan at a quoted rate of 9.75% with loan repayments made monthly

Question 51

For a given effective annual rate, the quoted rate ______ as the compounding frequency increases.

A)does not change
B)increases
C)decreases
D)There is no connection between the effective annual rate and the quoted rate.

Question 52

The R&M Bank has offered you the choice between two loans:
$\bullet$ #1 charges interest at a rate of 9% compounded quarterly.
$\bullet$ #2 charges interest at a rate of 9.50% compounded semi-annually.
Which loan do you prefer and why?

A)#1, lower effective rate
B)#2, lower effective rate
C)#1, higher effective rate
D)#2, higher effective rate

Question 53

For a given quoted rate, the effective annual rate ______ as the compounding frequency increases.

A)does not change
B)increases
C)decreases
D)There is no connection between the effective annual rate and the quoted rate.

Question 54

Your credit card has a quoted rate of 17% compounded weekly.What is the effective annual rate?

A)884%
B)18.50%
C)32.69%
D)17.00%

Question 55

Wilma borrows $10,000 from "Jaw Breaker Joe" and promises to repay Joe a total of $10,500 in one month.What is the effective annual interest rate charged by Joe?

A)5.00%
B)60.00%
C)79.59%
D)179.59%

Question 56

The R&M Bank has offered you the choice between two investment accounts:
$\bullet$ #1 pays interest at a rate of 12% compounded semi-annually.
$\bullet$ #2 pays interest at a rate of 11% compounded monthly.
Which investment account do you prefer and why?

A)#1, 12% is greater than 11%
B)#2, greater compounding frequency
C)#1, higher effective rate
D)#2, higher effective rate

Question 57

The R&M Bank currently offers an investment account with an interest rate of 8% compounded semi-annually.R&M wants to offer customers another account with interest compounded monthly.If R&M wants the effective rates to be equal, what interest rate should R&M quote for the second account?

A)7.87%
B)8.00%
C)8.16%
D)24.00%

Question 58

Your investment account has an interest rate of 10% compounded semi-annually.This is the equivalent of an effective annual interest rate of

A)1.1025%.
B)5%.
C)10%.
D)10.25%.

Question 59

How much should a monthly compounded account with an EAR of 18% earn semi-annually?

A)2.80%
B)3.00%
C)2.77%
D)8.63%

Question 60

Valentino will receive $25,000 in 3 years.His opportunity cost is 8% compounded continuously.The present value of this cash flow is closest to

A)$31,781.23.
B)$31,492.80.
C)$19,845.81.
D)$19,665.70.

Question 61

Kangaroo Motors has a used car for sale at $4,300, which you want to buy for driving to school.Your parents are willing to lend you the money and charge only 3.60 % APR compounded monthly.They want the loan repaid in equal payment over 48 months, with the first payment due at the end of the month in which you buy the car.You estimate that the monthly cost of operating the car, including gas, insurance, maintenance, and licence fees, will be $160 and payable at the start of each month.The cost of a monthly bus pass is $95.You expect that the car will be totally worn out in four years, with zero resale value, when you are finished school.Your discount rate is 5% EAR, compounded annually.
a)What is the monthly interest rate on the parents' car loan?
b)What is the monthly car repayment?
c)What is the monthly opportunity cost of funds?
d)What is the present value of the car costs?
e)If you have three roommates who also need transportation to and from school, how much do you and your roommates each need to pay a month in order to cover all your costs?

Question 62

Josh Ackerman, having saved up a nest egg of $1.5 million, retires this year and looks forward to a 30-year retirement.If his nest egg is expected to earn 9% APR and is compounded monthly, what will be his monthly income during retirement?

A)$50,000.00
B)$17,205.12
C)$14,600.45
D)$12,069.34

Question 63

Explain why the interest rates publicized by credit card companies do not reflect the real cost of borrowing incurred on the charges to these cards.

Question 64

Explain the difference between simple interest and compound interest.

Question 65

As the term of a mortgage increases, holding interest rates constant, the monthly payments will

A)stay about the same.
B)increase.
C)decrease.
D)There is no connection between the term and the size of the payments.

Question 66

Amir has obtained a $250,000 mortgage.The mortgage is amortized over 25 years and the term of the mortgage is 25 years.The mortgage interest rate is 9% compounded annually.Amir will begin making annual payments of $25,451.56 at the end of the year.How much of Amir's third payment is interest?

A)$22,500.00
B)$21,944.81
C)$18,470.51
D)$2,290.64

Question 67

You have just obtained a $150,000 10-year 6% fixed-rate mortgage.The mortgage is amortized over 25 years.The interest rate is compounded semi-annually and you make monthly payments at the end of each month.
Immediately after you signed the paperwork, mortgage rates dropped to 5%.Your bank has offered you the opportunity to renegotiate the mortgage for a penalty of $10,000.Should you take this opportunity? Assume your opportunity cost equals the mortgage rate.

Question 68

Carmen's grandfather died five years ago and left Carmen a perpetuity paying $50,000 a year.Carmen's cost of capital is 4%.After receiving the fifth payment, Carmen received an offer of $1.4 million from The Bizet Hedge Fund for the remainder of the perpetuity.Should Carmen accept the offer?

Question 69

Lucy has just obtained a five-year fixed-rate mortgage to buy her first home.The mortgage is amortized over 30 years.Which of the following statements is most correct?

A)Lucy's payments won't change for the next 30 years.
B)Lucy's payments won't change for the next 5 years.
C)Lucy's payments will increase as the term of the mortgage increases.
D)Lucy's payments will decrease as the term of the mortgage increases.

Question 70

As the amortization period of a mortgage increases, holding interest rates constant, the monthly payments will

A)stay the same.
B)increase.
C)decrease.
D)There is no connection between the amortization period and the size of the payment.

Question 71

Amir has obtained a $250,000 mortgage.The mortgage is amortized over 25 years and the term of the mortgage is 25 years.The mortgage interest rate is 9% compounded annually.Amir will begin making annual payments of $25,451.56 at the end of the year.What is the principal outstanding immediately after Amir makes his third payment?

A)$50,903.12
B)$173,645.32
C)$185,574.60
D)$240,324.46

Question 72

When comparing different investment opportunities (each with the same risk)with different interest rates reported in different ways you should

A)convert each interest rate to an annual nominal rate.
B)convert each interest rate to a monthly nominal rate.
C)convert each interest rate to an effective annual rate.
D)compare them by using the published annual rates.
E)convert each interest rate to an APR.

Question 73

Explain what the effective (or equivalent)annual interest rate is and why we use it.

Question 74

Your bank offers two options: Account A compounds semi-annually while account B compounds monthly.If both accounts have the same effective annual rate of interest, you should choose

A)account A as it offers a higher APR.
B)account B as it offers a higher APR.
C)account B because it is compounded more often.
D)account A because it is compounded less often.
E)either since you would be indifferent between the two.

Question 75

A lakefront cottage is selling for $200,000, with a $125,000 down payment, and the remainder mortgaged at 12% APR, to be amortized over 30 years.What is the monthly mortgage payment?

A)$771.46
B)$792.90
C)$931.77
D)$1,906.11

Question 76

You won the lottery and you were asked to choose between the following two options:
$\bullet$ Get $1,000 every week forever.
$\bullet$ Get $1,000,000 in a lump sum.
You expect to earn an effective annual rate of 4% on your investments.Assuming there is no risk between the two, which option do you prefer?

Question 77

You have currently accumulated $50,000 thus far for your retirement, and are planning to have $1,000,000 in 30 years when you retire.If you can add $6,000 each year to your retirement fund, what interest rate do you need to have in order to achieve your retirement goal?

A)6.17%
B)7.24%
C)9.04%
D)10.71%

Question 78

You have received two job offers:
ABC is offering to pay you $5,000 at the end of each month for five years and then $8,000 at the end of each month for the next five years.
PQR is offering you $2,500 twice a month for the first five years and then $4,000 twice a month for the next five years.
If your decision is based solely on money, which job offer do you prefer? Why? Note: no calculations are necessary.

Question 79

Amir has obtained a $250,000 mortgage.The mortgage is amortized over 25 years and the term of the mortgage is five years.The mortgage interest rate is 9% compounded semi-annually.Amir will begin making monthly payments at the end of the month.Amir's monthly payment will be approximately

A)$2,069.94.
B)$2,097.99.
C)$5,169.68.
D)$5,189.59.

Question 80

You borrow $50,000 on a line of credit to finance your start-up company, to be repaid in three equal, annual payments.Interest on the line of credit is 10% interest.Approximately how much of the principal is paid off on the first payment?

A)$5000.00
B)$16,666.67
C)$15,105.74
D)$20,105.74