Deck 5: The Time Value of Money

Question 1

Find the present value of $5325.00 to be received in one period if the rate is 6.50%.

A) $5,000.00
B) $5,071.43
C) $5,671.13
D) $5,591.25

Answer 1

$5,000.00

Question 2

Beatrice invests $1,000 in an account that pays 4% simple interest.How much more could she have earned over a five-year period if the interest had compounded annually?

A) $15.45
B) $15.97
C) $16.65
D) $17.09
E) $21.67

Answer 2

$16.65

Question 3

The equation [Ct/(1 + r)^t] provides:

A) the compound value of a series of payments with a single interest rate.
B) the compound value of a series of payments with a series of interest rates.
C) the compound value of a single payment.
D) the present value of a series of payments with a single interest rate.
E) the present value of a single payment.

Answer 3

the present value of a single payment.

Question 4

Your parents are giving you $100 a month for four years while you are in college.At a 6% discount rate,what are these payments worth to you when you first start college?

A) $3,797.40
B) $4,167.09
C) $4,198.79
D) $4,258.03
E) $4,279.32

Question 5

What is the future value of the following cash flows at the end of year 3 if the interest rate is 6%? The cash flows occur at the end of each year.

A) $15,916.78
B) $18,109.08
C) $18,246.25
D) $19,341.02
E) $19,608.07

Question 6

Which of the following statements is true?

A) Regardless of the value of the interest rate, increasing the compounding frequency will decrease the future value.
B) Regardless of the value of the interest rate, increasing the compounding frequency will increase the future value.
C) There is a relationship between the future value of investment and the effect of compounding frequency. At high interest rates, increases in compounding frequency will decrease the future value.
D) There is a relationship between the future value of investment and the effect of compounding frequency. At low interest rates, increases in compounding frequency will decrease the future value.

Question 7

If you have a choice to earn simple interest on $10,000 for three years at 8% or compound interest at 7.5% for three years which one will pay more and by how much?

A) Simple interest by $1,500.
B) Compound interest by $22.97.
C) Compound interest by $150.75.
D) Simple interest by $150.00.

Question 8

The future value table provides the factors for the:

A) compound interest rate for 1/N periods for a specified interest rate.
B) compound value of a dollar for 1/N periods for a specified interest rates.
C) single value of a dollar for N periods for a specified interest rate.
D) simple interest rate for N periods.

Question 9

The present value factor is:

A) the dollar amount of the future value.
B) the rate that equates the present value with the future value.
C) the process of calculating future or present values.
D) the value of $1 to be received in T periods at a given interest rate.

Question 10

The discount rate is adjusted:

A) upward to reflect higher risk and to increase the future cash flows.
B) upward to reflect higher risk and to reduce the future cash flows.
C) downward to reflect higher risk and to increase the future cash flows.
D) downward to reflect higher risk and to reduce the future cash flows.

Question 11

The compound value is defined as:

A) the value of a dollar received tomorrow.
B) the value of a sum after investing over one or more periods.
C) the value of a sum today to received in the future.
D) the rate of growth in a sum today.

Question 12

You have a sub-contracting job with a local manufacturing firm.Your agreement calls for annual payments of $50,000 for the next five years.At a discount rate of 12%,what is this job worth to you today?

A) $180,238.81
B) $201,867.47
C) $210,618.19
D) $223,162.50
E) $224,267.10

Question 13

The time value of money concept can be defined as:

A) the time in your life when you receive an inheritance.
B) the relationship between money spent versus money received.
C) the relationship between a dollar to be received in the future and a dollar today.
D) the relationship of interest rate stated and amount paid.

Question 14

In the equation,NPV = -Cost + PV,the term Cost is the:

A) current value of the commitment fee today.
B) current value of the terminal cash flow.
C) initial cash outflow.
D) present value of the variable costs.

Question 15

The present value of future cash flows minus initial cost is called:

A) the future savings of the project.
B) the net present value of the project.
C) the equivalent sum of the investment.
D) the initial investment risk equivalent value.

Question 16

Discounting cash flows involves:

A) reducing cash flows that occur beyond 10 years in the future.
B) discounting expected cash flows beyond a certain number of years in the future, which varies with the riskiness of the project.
C) reducing expected cash flows to achieve certainty equivalence.
D) reducing the value of future cash flows to reflect the time value of money.
E) taking the cash discount offered on trade merchandise.

Question 17

The great grandparents of one of your classmates sold their munitions factory to the government in beginning of 1898 during the Spanish-American War for $150,000.If these proceeds had been invested at 6% from then until the end of 2001,what would the legacy to your classmate's family be worth at the end of 2001 (assume whole years)?

A) $936,000
B) $64,254,159.44
C) $1,086,000
D) $60,617,131.54
E) $60,467,131.54

Question 18

The equation (1 + (r/m))^m -1 gives the:

A) effective annual interest rate, and r is the stated annual interest rate.
B) effective annual interest rate, and m is the number of years to maturity.
C) stated annual interest rate, and r is the effective annual interest rate.
D) stated annual interest rate, and m is the number of years to maturity.

Question 19

Present value may be defined as:

A) future cash flows discounted to the present.
B) official prescribed price.
C) present cash flows compounded into the future.
D) the average of the bid and asked price.

Question 20

Jim Mayer has deposited $7,000 in a guaranteed investment account with a promised rate of 7% compounded annually.He plans to leave it there for 4 full years when he will make a down payment on a car after graduation.How much of a down payment will he be able to make?

A) $8,960.00
B) $1,960.00
C) $2,175.57
D) $9,175.57

Question 21

What is the effective annual rate if a bank charges you 7.64% compounded quarterly?

A) 7.79%
B) 7.86%
C) 7.95%
D) 7.98%
E) 8.01%

Question 22

Aunt Clarisse has promised to leave you an annuity that will pay $60 next year and grow at an annual rate of 4%.The payments are expected to go on indefinitely and the interest rate is 9%.What is the value of the growing perpetuity?

A) $667
B) $693
C) $1,200
D) $1,248

Question 23

The present value of a set of cash flows is:

A) the sum of the present value of the individual cash flows.
B) the sum of individual cash flows which are then discounted.
C) not equal to the sum of the present value of the individual cash flows.
D) always greater than the present value of the investment.

Question 24

Which of the following amounts is closest to the end value of investing $3,000 for 3/4 year at a continuously compounded rate of 12%?

A) $3,163
B) $3,283
C) $3,263
D) $3,287
E) $3,317

Question 25

Which of the following amounts is closest to the end value of investing $9,000 for 7 years at a continuously compounded rate of 11%?

A) $18,685.44
B) $19,369.83
C) $15,930.00
D) $19,437.90

Question 26

A court settlement awarded an accident victim four payments of $50,000 to be paid at the end of each of the next four years.Using a discount rate of 4%,calculate the present value of the annuity.

A) $173,255
B) $178,495
C) $181,495
D) $184,095
E) $200,000

Question 27

Which one of the following statements concerning interest rates is correct?

A) The stated rate is the same as the effective annual rate.
B) An effective annual rate is the rate that applies if interest were charged annually.
C) The annual percentage rate increases as the number of compounding periods per year increases.
D) Banks prefer more frequent compounding on their savings accounts.
E) For any positive rate of interest, the effective annual rate will always exceed the annual percentage rate.

Question 28

Which of the following amounts is closest to the net present value of a project that contributes $10,000 at the end of the first year and $5,000 at the end of the second year.The initial cost is $8,000 and the appropriate interest rate is 10%.

A) $5,223
B) $5,951
C) $7,000
D) $21,223
E) $23,000

Question 29

What is the net present value of a project that contributes $25,000 at the end of the first year and $12,000 at the end of the second year.The initial cost is $33,000.The appropriate interest rate is 7% for the first year and 10% for the second year.

A) $1,579.44
B) $559.90
C) $281.85
D) -$2,148.26

Question 30

Your employer contributes $25 a week to your retirement plan.Assume that you work for your employer for another twenty years and that the applicable discount rate is 5%.Given these assumptions,what is this employee benefit worth to you today?

A) $13,144.43
B) $15,920.55
C) $16,430.54
D) $16,446.34
E) $16,519.02

Question 31

If the compound period is greater than one:

A) the effective annual interest rate is always equal to the annual percentage rate.
B) the effective annual interest rate is always less than the annual percentage rate.
C) the effective annual interest rate is always greater than the annual percentage rate.
D) the effective annual interest rate is never greater than the annual percentage rate.

Question 32

The present value table provides the factors for the:

A) simple interest rate for N periods.
B) discount value of a dollar for N periods for a specified interest rate.
C) discount value of a dollar for 1/N periods for a specified interest rate.
D) simple interest value of an investment for N periods.
E) simple interest value of an investment for 1/N periods.

Question 33

Which of the following amounts is closest to the end value of investing $5,000 for 14 months at a stated annual interest rate of 6 percent compounded monthly?

A) $5,352
B) $5,362
C) $5,350
D) $5,293
E) $6,183

Question 34

You have deposited $1,500 in an account that promises to pay 8% compounded quarterly for the next five years.How much will you have in the account at the end?

A) $1,598.33
B) $2,228.92
C) $2,203.99
D) $6,991.44

Question 35

Which of the following amounts is closest to the end value of investing $10,000 for 1 1/2 years at a stated annual interest rate of 12% compounded quarterly?

A) $11,800
B) $11,852
C) $11,941
D) $11,961

Question 36

Which of the following amounts is closest to the present value of a payment of $21,000 three years from now if the effective annual interest rate is 4%?

A) $18,669
B) $18,658
C) $19,218
D) $18,480
E) $17,951

Question 37

The interest rate charged per period multiplied by the number of periods per year is called the _____ rate.

A) effective annual
B) annual percentage
C) periodic interest
D) compound interest

Question 38

Which of the following amounts is closest to the end value of investing $7,500 for 2 1/2 years at an effective annual interest rate of 12.36%? Interest is compounded semiannually.

A) $7,531
B) $8,427
C) $9,818
D) $9,469
E) $10,122

Question 39

You are to receive $75 per year indefinitely.The market rate of interest for these types of payments is 8%.The price you would pay for this stream is:

A) $9.38
B) $81.00
C) $93.75
D) $937.50

Question 40

You are the beneficiary of a life insurance policy.The insurance company informs you that you have two options for receiving the insurance proceeds.You can receive a lump sum of $50,000 today or receive payments of $641 a month for ten years.You can earn 6.5% on your money.Which option should you take and why?

A) You should accept the payments because they are worth $56,451.91 today.
B) You should accept the payments because they are worth $56,523.74 today.
C) You should accept the payments because they are worth $56,737.08 today.
D) You should accept the $50,000 because the payments are only worth $47,757.69 today.
E) You should accept the $50,000 because the payments are only worth $47,808.17 today.

Question 41

A "little seven" accounting firm offers to pay you a year-end bonus of $5,000 for 3 years if you will accept employment with them and stay for the entire 3-year period.Which of the following amounts is closest to the present value of the bonus if the interest rate is 10%?

A) $5,000.
B) $11,270.
C) $12,434.
D) $15,000.
E) $31,576.

Question 42

As an excellent student in environmental ecology you have been awarded the "Clean Effluent Prize" by state agency.You (or your estate)are to receive $300 forever from the state or the agency will allow you to choose $400 over the next 25 years.Payments are to be received semi-annually and if the market rate of interest is 6% what is the value of the two options respectively?

A) $30,000; $10,000.25
B) $5,000; $5,145.95
C) $10,000; $6,304.74
D) $2,500; $3,859.46
E) $6,666.67; $5,113.34

Question 43

A mortgage instrument pays $1.5 million at the end of each of the next two years.An investor has an alternative investment with the same amount of risk that will pay interest at 8% compounded semiannually.Which of the following amounts is closest to what the investor should pay for the mortgage instrument?

A) $1.28 million.
B) $1.39 million.
C) $2.67 million.
D) $2.72 million.

Question 44

Thorton will receive an inheritance of $500,000 three years from now.Thorton's personal discount rate corresponds to a 10% interest rate compounded semiannually.Which of the following values is closest to the amount that Thorton should accept today for the right to his inheritance?

A) $373,108
B) $375,657
C) $665,500
D) $670,048

Question 45

A perpetuity differs from an annuity because:

A) perpetuity payments vary with the rate of inflation.
B) perpetuity payments vary with the market rate of interest.
C) perpetuity payments are variable while annuity payments are constant.
D) perpetuity payments never cease.
E) annuity payments never cease.

Question 46

The Ajax Co.just decided to save $1,500 a month for the next five years as a safety net for recessionary periods.The money will be set aside in a separate savings account which pays 3.25% interest compounded monthly.It deposits the first $1,500 today.If the company had wanted to deposit an equivalent lump sum today,how much would it have had to deposit?

A) $82,964.59
B) $83,189.29
C) $83,428.87
D) $83,687.23
E) $84,998.01

Question 47

Tina is able to pay $160 a month for five years for a car.If the interest rate is 4.9%,how much can Tina afford to borrow to buy a car?

A) $6,961.36
B) $8,499.13
C) $8,533.84
D) $8,686.82
E) $9,588.05

Question 48

A sports team in an effort to solve the salary cap problem has offered a player a contract of $1 million dollars a year for the next season with the payments growing at 7% per year for the next 25 years.The player believes the discount rate for such payments is 13%.What is the value today of taking this contract?

A) $12,405,955.40
B) $16,666,666.67
C) $884,956.09
D) $5,824,965.76

Question 49

Alan Burnie has just started work and has been wanting to buy a sleek powerboat for sometime.Rather than purchase and finance now,he plans to save every three months and increase the deposits by 3% per annum as he expects raises at least that large.How much must the first deposit be if the boat costs $25,000 today and he expects to earn 10% on the money over the next five years?

A) $1,501.56
B) $2,081.99
C) $1,561.49
D) $6,097.27
E) $2,359.82

Question 50

An S&L provides a loan with 15 yearly repayments of $8,000 with the first payment beginning immediately.Which of the following amounts comes closest to the present value of the loan if the interest rate is 7%?

A) $72,863.
B) $77,964.
C) $115,648.
D) $120,000.

Question 51

An annuity:

A) is a debt instrument that pays no interest.
B) is a stream of payments that varies with current market interest.
C) is a series of equal payments through time.
D) has no value.

Question 52

If a student borrows $20,000 to start a business as a 5 year,10% loan,the annual payment is:

A) $2,000.00
B) $3,275.95
C) $4,000.00
D) $5,275.95

Question 53

Suzette is going to receive $10,000 today as the result of an insurance settlement.In addition,she will receive $15,000 one year from today and $25,000 two years from today.She plans on saving all of this money and investing it for her retirement.If Suzette can earn an average of 11% on her investments,how much will she have in her account if she retires 25 years from today?

A) $536,124.93
B) $541,414.14
C) $546,072.91
D) $570,008.77
E) $595,098.67

Question 54

The BobIU Computer Graphics Co.has just produced a new multimedia graphics chip which will cost $6,000,000 this year to put into production.They anticipate net cash flows of $3 million next year,$2million,$1 million,$.5 million,$.25 million and then $0 over each of the following years.The two owners require a 15% return on their investment.The value of this investment to the firm is:

A) $750,000.10
B) -$811,329.97
C) $556,462.71
D) $652,173.91
E) -$371,782.85

Question 55

An equal stream of payments that lasts forever is:

A) a growing annuity.
B) a zero coupon bond.
C) a perpetuity.
D) valueless.

Question 56

The potential owner/managers of the yet to be formed new In-Line Blade Company are evaluating the prospects for the business.The new equipment is expected to be $5.5 million and have after tax cashflows of $400,000 for the first two years,$750,000 in the next two years,and $1,200,000 thereafter indefinitely.The owners estimate that they require a 15% rate of return.What is the value of the In-Line Blade Company; should they go forward with the investment?

A) $3,872,122; yes.
B) $4,072,236; yes.
C) -$2,000,000; no.
D) $943,596; yes.
E) $105,185; yes.

Question 57

Charles Carr borrowed $3,500 to consolidate his debts.Since Charles had an excellent credit rating,he was able to borrow at a 12% effective annual rate.Charles is required to make monthly payments.Charles will make equal payments for the next 36 months.Which one of the following values is closest to his monthly payments?

A) $121
B) $122
C) $115
D) $118
E) $123

Question 58

An annuity factor:

A) can be used to determine the present value of a level stream of payments.
B) consists entirely of maturation and interest.
C) is a variable that can never be greater than one.
D) is any factor that affects the price of a bond.

Question 59

What is the present value of 10 payments of $500 each received every 24 months at a discount rate of 12%?

A) $1,840.93
B) $1,332.60
C) $2,825.11.
D) $1,761.66

Question 60

You are comparing two investment options.The cost to invest in either option is the same today.Both options will provide you with $20,000 of income.Option A pays five annual payments starting with $8,000 the first year followed by four annual payments of $3,000 each.Option B pays five annual payments of $4,000 each.Which one of the following statements is correct given these two investment options?

A) Both options are of equal value given that they both provide $20,000 of income.
B) Option A is the better choice of the two given any positive rate of return.
C) Option B has a higher present value than option A given a positive rate of return.
D) Option B has a lower future value at year 5 than option A given a zero rate of return.
E) Option A is preferable because it is an annuity due.

Question 61

What is meant by "amortizing a loan"?

Question 62

Mr.Miser,who is 35 years old,has just inherited $11,000 and decides to use the windfall towards his retirement.He places the money in a bank,which promises a return of 6% per year until his planned retirement at age 65.If his funds earn 6% interest compounded annually,how much will he have at retirement? Repeat the analysis for both semi-annual and continuous compounding.

Question 63

Joe,a freshman in college,needs $55,000 in 4 years to buy the car of his dreams.If his investments earn 6% interest per year,how much must he invest today to have that amount at graduation? If he invested once a year for four years beginning today until the end of the 4 years how much must he invest?

Question 64

Your aunt,in her will,left you the sum of $5,000 a year forever with payments starting immediately.However,the news is better.She has specified that the amount should grow at 5% per year to maintain purchasing power.Given an interest rate of 12%,what is the PV of the inheritance?

Question 65

There are three factors that affect the present value of an annuity.Explain what these three factors are and discuss how an increase in each will impact the present value of the annuity.

Question 66

As the winner of the Housecleaners sweepstakes,you are entitled to one of the following prizes:
A. $999,999 immediately.
B. $100,000 per year forever.
C. $180,000 per year for the next 10 years starting immediately.
D. $400,000 payable every 2 years over 20 years.
E. $39,000 next year growing by 6% forever.
In terms of present values, which prize should be chosen if r = 9%?

Question 67

An investment today of $3300 is worth $10,000 in 8 years.At what rate has your investment been growing (annually)over the 8 years?

Question 68

If you invest $100,000 today at 12% per year over the next 15 years,what is the most you can spend in equal amounts out of the fund each year over that time.

Question 69

There are three factors that affect the future value of an annuity.Explain what these three factors are and discuss how an increase in each will impact the future value of the annuity.