Deck 5: Time Value of Money-The Basics

Question 1

Which of the following is the formula for compound value?

A)FV_n = P(1 + i)ⁿ
B)FV_n = (1 + i)/P
C)FV_n = P/(1 + i)ⁿ
D)FV_n = P(1 + i)^-n

Answer 1

A

Question 2

Why is the concept of the time value of money so important to financial managers?

Answer 2

The concept of the time value of money is important to financial managers because it is this concept that drives managerial decision making.Management decisions are driven by cash flow and these cash flows must be adjusted for the time value of money.This would be most closely reflected in the project evaluation.In addition,the value of a firm's common stock is driven by discounted cash flows.Management pays close attention as to how their decisions affect the value of ownership in their firm.

Question 3

Which of the following provides the lowest return to an investor?

A)12%,compounded annually
B)12%,compounded semiannually
C)12%,compounded quarterly
D)12%,compounded monthly
E)12%,compounded daily

Answer 3

A

Question 4

A bank pays a quoted annual (nominal)interest rate of 4.25%,compounded daily (365-day year).What is the annual percentage yield (APY)?

A)4.25%
B)5.56%
C)4.75%
D)6.20%
E)4.34%

Question 5

The discount rate for the time value of money should reflect delaying consumption.

Question 6

If you are an investor,which of the following would you prefer?

A)Earnings on funds invested would compound annually.
B)Earnings on funds invested would compound daily.
C)Earnings on funds invested would compound monthly.
D)Earnings on funds invested would compound quarterly.

Question 7

Which of the following statements is true about the time value of money?

A)The present value of a future amount will be greater if funds earn 5% instead of 10%.
B)The present value of a single sum will be unaffected by the rate of return at which funds grow.
C)The present value of a future amount will be greater if funds earn 12% instead of 6%.
D)The present value of a future amount will be unaffected by how far in the future funds would be received.

Question 8

At 8% compounded annually,how long will it take $750 to double?

A)6.5 years
B)48 months
C)9 years
D)12 years

Question 9

An investment has a nominal interest rate of 12% annually,but interest on the investment is compounded monthly.Therefore,the annual percentage yield on the investment is:

A)12%.
B)12.68%.
C)13.89%.
D)12.36%.

Question 10

You have $10,000 to invest.You do not want to take any risk,so you will put the funds in a savings account at the local bank.Of the following choices,which one will produce the largest sum at the end of 22 years?

A)An account that compounds interest annually.
B)An account that compounds interest daily.
C)An account that compounds interest quarterly.
D)An account that compounds interest monthly.

Question 11

Financial managers use the time value of money to:

A)make business decisions.
B)compare cash flows of different projects.
C)determine the price of common stock.
D)both A and B.
E)all of the above.

Question 12

If you are a borrower,which of the choices would lower your APR?

A)Repay your loan in monthly installments
B)Repay your loan in quarterly installments
C)Repay your loan in semiannual installments
D)Repay your loan in annual installments
E)You would be indifferent to how frequent your loan payments are.

Question 13

Northwest Bank pays a quoted annual (nominal)interest rate of 4.75%.However,it pays interest (compounds)daily using a 365-day year.What is the effective annual rate of return (APY)?

A)4.75%
B)5.02%
C)3.61%
D)4.86%

Question 14

Which of the following statements is FALSE?

A)The effective annual rate (APR)of a loan is always the same as the quoted rate.
B)The payments of an ordinary annuity are made or received at the end of each period.
C)The effective annual rate (APR)of a loan is always equal to or greater than the quoted rate.
D)A perpetuity is a series of equal payments,which are made for an infinite period of time.

Question 15

Which of the following statements is true about the time value of money?

A)The future value of a single sum will be greater if funds earn 5% instead of 10%.
B)The future value of a single sum will be unaffected by the rate of return at which funds grow.
C)The future value of a single sum will be greater if funds earn 12% instead of 6%.
D)The future value of a single sum will be unaffected by the length of time funds are invested.

Question 16

Which of the following provides the greatest annual interest?

A)10%,compounded annually
B)10%,compounded semiannually
C)10%,compounded quarterly
D)10%,compounded monthly
E)10%,compounded daily

Question 17

An investment has a nominal interest rate of 12% annually,but interest on the investment is compounded semiannually.Therefore,the annual percentage yield on the investment is:

A)12%.
B)12.68%.
C)13.89%.
D)12.36%.

Question 18

The time value of money is created by:

A)the existence of profitable investment alternatives and interest rates.
B)the fact that the passing of time increases the value of money.
C)the elimination of the opportunity cost as a consideration.
D)the fact that the value of saving money for tomorrow could be more or less than spending it today.

Question 19

Which of the following statements is FALSE?

A)Quarterly compounding has a higher annual percentage yield than monthly compounding.
B)On monthly compounding loans,the annual percentage yield will be less than the nominal or quoted rate of interest.
C)Compounding essentially means earning interest on interest on an initial balance.
D)Perpetuities pay an equal payment forever.

Question 20

As the number of compounding periods increases,the ________ increases.

A)quoted
B)annual percentage yield
C)effective annual rate
D)both B and C

Question 21

Shorty Jones wants to buy a one-way bus ticket to Mule-Snort,Pennsylvania.The ticket costs $142,but Mr.Jones has only $80.If Shorty puts the money in an account that pays 9% interest compounded monthly,how many months must Shorty wait until he has $142 (round to the nearest month)?

A)73 months
B)75 months
C)77 months
D)79 months

Question 22

Which of the following formulas represents the future value of $500 invested at 8% compounded quarterly for five years?

A)500(1 + .08)⁵
B)500(1 + .08)²⁰
C)500(1 + .02)⁵
D)500(1 + .02)²⁰

Question 23

What is the value of $750 invested at 7.5% compounded quarterly for 4.5 years (round to the nearest $1)?

A)$1,048
B)$1,010
C)$1,038
D)$808

Question 24

At what rate must $400 be compounded annually for it to grow to $716.40 in 10 years?

A)6%
B)5%
C)7%
D)8%

Question 25

Dawn Swift discovered that 20 years ago,the average tuition for one year at an Ivy League school was $4,500.Today,the average cost is $29,000.What is the growth rate in tuition cost over this 20-year period? Round off to the nearest 0.1%.

A)15.5%
B)4.2%
C)9.8%
D)10.6%

Question 26

If you place $50 in a savings account with an interest rate of 7% compounded weekly,what will the investment be worth at the end of five years (round to the nearest dollar)?

A)$72
B)$70
C)$71
D)$57

Question 27

An increase in future value can be caused by an increase in the:

A)annual interest rate.
B)number of compounding periods.
C)original amount invested.
D)both A and B.
E)all of the above.

Question 28

If you want to have $1,200 in 27 months,how much money must you put in a savings account today? Assume that the savings account pays 14% and it is compounded monthly (round to the nearest $10).

A)$910
B)$890
C)$880
D)$860

Question 29

You just purchased a parcel of land for $10,000.If you expect a 12% annual rate of return on your investment,how much will you sell the land for in 10 years?

A)$25,000
B)$31,060
C)$38,720
D)$34,310

Question 30

What will the dollar amount be if the interest is compounded semiannually for those four years?

A)$3,100
B)$3,188
C)$3,240
D)$3,290

Question 31

If you put $600 in a savings account that yields an 8% rate of interest compounded weekly,what will the investment be worth in 37 weeks (round to the nearest dollar)?

A)$648
B)$635
C)$634
D)$645

Question 32

What will the dollar amount be in four years,assuming that interest is paid annually?

A)$2,800
B)$3,100
C)$3,111
D)$3,148

Question 33

How much money must be put into a bank account yielding 5.5% (compounded annually)in order to have $250 at the end of five years (round to nearest $1)?

A)$237
B)$191
C)$187
D)$179

Question 34

You bought a painting 10 years ago as an investment.You originally paid $85,000 for it.If you sold it for $484,050,what was your annual return on investment?

A)47%
B)4.7%
C)19%
D)12.8%

Question 35

A friend plans to buy a big-screen TV/entertainment system and can afford to set aside $1,320 toward the purchase today.If your friend can earn 5.0%,compounded yearly,how much can your friend spend in four years on the purchase? Round off to the nearest $1.

A)$1,444
B)$1,604
C)$1,764
D)$1,283

Question 36

If you want to have $90 in four years,how much money must you put in a savings account today? Assume that the savings account pays 8.5% and it is compounded monthly (round to the nearest $1).

A)$64
B)$65
C)$66
D)$71

Question 37

How many periods would it take for the deposit to grow to $6,798 if the interest is compounded semiannually?

A)17
B)19
C)21
D)25

Question 38

If you want to have $1,700 in seven years,how much money must you put in a savings account today? Assume that the savings account pays 6% and it is compounded quarterly (round to the nearest $10).

A)$1,120
B)$1,130
C)$1,110
D)$1,140

Question 39

If you put $700 in a savings account with a 10% nominal rate of interest compounded monthly,what will the investment be worth in 21 months (round to the nearest dollar)?

A)$827
B)$833
C)$828
D)$1,176

Question 40

If you want to have $10,000 in 10 years,which of the following formulas represents how much money you must put in a savings account today? Assume that the savings account pays 6% and it is compounded monthly.

A)10,000/(1 + .05)¹⁰
B)10,000/(1 + .005)¹²⁰
C)10,000/(1 + .06)¹⁰
D)10,000/(1 + .006)¹²⁰

Question 41

How many years will it take for an initial investment of $200 to grow to $544 if it is invested today at 8% compounded annually?

A)8 years
B)10 years
C)11 years
D)13 years

Question 42

The future value of $500 deposited into an account paying 8% annually for three years is:

A)$500.
B)$630.
C)$700.
D)$620.

Question 43

If you deposit $1,000 each year in a savings account earning 4%,compounded annually,how much will you have in 10 years?

Question 44

When George Washington was president of the United States in 1797,his salary was $25,000.If you assume an annual rate of inflation of 2.5%,how much would his salary have been in 1997?

A)$1,025,000
B)$954,719
C)$2,525,548
D)$4,085,920
E)$3,489,097

Question 45

The future value of $200 deposited today in an account for four years paying semiannual interest when the annual interest rate is 12% is:

A)$309.40.
B)$318.80.
C)$320.20.
D)$296.00.

Question 46

Determining the specified amount of money that you will receive at the maturity of an investment is an example of a future value equation.

Question 47

The future value of a single sum:

A)increases as the compound rate decreases.
B)decreases as the compound rate increases.
C)increases as the number of compound periods decreases.
D)increases as the compound rate increases.
E)none of the above.

Question 48

If you were to deposit $2,000 in an IRA that would earn interest of 7.5%,compounded quarterly for 18 years,how much would you have accumulated?

A)$9,621
B)$36,000
C)$22,419
D)$12,363
E)$7,619

Question 49

If we invest money for 10 years at 8% interest,compounded semi-annually,we are really investing money for 20 six-month periods,during which we receive 4% interest each period.

Question 50

The more frequent the compounding periods in a year,the higher the future value.

Question 51

You deposit $5,000 today in an account drawing 12% compounded quarterly.How much will you have in the account at the end of 2 1/2 years?

A)$7,401
B)$5,523
C)$7,128
D)$6,720

Question 52

The same basic formula is used for computing both the computation of future value and of present value.

Question 53

If you purchased a share of Mico.com stock on March 1,1993 for $45 and you sold the stock at $168 on February 28,1998,what was your annual rate of return on the stock?

A)83%
B)75%
C)20%
D)30%
E)50%

Question 54

The future value of a lump sum deposited today increases as the number of years of compounding at a positive rate of interest declines.

Question 55

At 8%,compounded annually,how long will it take $750 to double?

A)9 years
B)8 years
C)12 years
D)4 years
E)6 years

Question 56

Your bank has agreed to loan you $3,000 if you agree to pay a lump sum of $5,775 in five years.What annual rate of interest will you be paying?

Question 57

Earnings per share for XYZ,Inc.grew constantly from $7.99 in 1974 to $12.68 in 1980.What was the compound annual growth rate in earnings-per-share over the period?

Question 58

Middletown,USA currently has a population of 1.5 million people.It has been one of the fastest growing cities in the nation,growing by an average of 4% per year for the last five years.If this city's population continues to grow at 4% per year,what will the population be 10 years from now?

A)1,560,000
B)2,220,366
C)2,100,000
D)1,824,979

Question 59

If you invest $450 today and it increases to $6,185 at the end of 20 years,what rate of return have you earned?

Question 60

Briefly discuss how non-annual compounding (more than one compounding period per year)is preferable to annual compounding if you are an investor.

Question 61

The present value of a single future sum:

A)increases as the number of discount periods increases.
B)is generally larger than the future sum.
C)depends upon the number of discount periods.
D)increases as the discount rate increases.

Question 62

What is the present value of the following uneven stream of cash flows? Assume a 6% discount rate and end-of-period payments.Round to the nearest whole dollar.

A)PV = $3,000/[1.06]¹ + $4,000/[1.06]² + $5,000/[1.06]³
B)PV = $3,000[1.06]₁ + $4,000[1.06]² + $5,000[1.06]³
C)PV = $3,000/[1.06]⁰ + $4,000/[1.06]¹ + $5,000/[1.06]²
D)PV = $3,000[1.06]^-0 + $4,000[1.06]^-1 + $5,000[1.06]^-2

Question 63

California Investors recently advertised the following claim: Invest your money with us at 21%,compounded annually,and we guarantee to double your money sooner than you imagine.Ignoring taxes,how long would it take to double your money at a nominal rate of 21%,compounded annually? Round off to the nearest year.

A)Approximately two years
B)Approximately four years
C)Approximately six years
D)Approximately eight years

Question 64

How much money do I need to place into a bank account which pays a 6% rate in order to have $500 at the end of seven years?

A)$332.53
B)$381.82
C)$423.77
D)$489.52

Question 65

The present value of $1,000 to be received at the end of five years,if the discount rate is 10%,is:

A)$621.
B)$784.
C)$614.
D)$500.

Question 66

If you want to have $875 in 32 months,how much money must you put in a savings account today? Assume that the savings account pays 16% and it is compounded monthly (round to the nearest $10).

A)$630
B)$570
C)$650
D)$660

Question 67

Bobby's grandmother deposited $100 in a savings account for him when he was born.The money has been earning an annual rate of 12% interest,compounded quarterly for the last 25 years.He is getting married and would like to take his new bride on a fabulous honeymoon.How much does he have in this account to use?

A)$4,165
B)$1,700
C)$5,051
D)$1,922

Question 68

You are considering two investments: A and B.Both investments provide a cash flow of $100 per year for n years.However,investment A receives the cash flow at the beginning of each year,while investment B receives the cash at the end of each year.If the present value of cash flows from investment A is P,and the discount rate is c,what is the present value of the cash flows from investment B?

A)P/(1 + c)
B)P(1 + c)
C)P/(1 + c)ⁿ
D)P(1 + c)ⁿ

Question 69

All else constant,the future value of an investment will increase if:

A)the investment involves more risk.
B)the investment is compounded for fewer years.
C)the investment is compounded at a higher interest rate.
D)both B & C.

Question 70

The present value of a single sum:

A)increases as the discount rate decreases.
B)decreases as the discount rate decreases.
C)increases as the number of discount periods increases.
D)increases as the discount rate increases.
E)none of the above.

Question 71

As the discount rate increases,the present value of future cash flows increases.

Question 72

An increase in ________ will decrease present value.

A)the discount rate per period
B)the original amount invested
C)the number of periods
D)both A and C
E)all of the above

Question 73

Assuming two investments have equal lives,a high discount rate tends to favor:

A)the investment with large cash flow early.
B)the investment with large cash flow late.
C)the investment with even cash flow.
D)neither investment since they have equal lives.

Question 74

Discounting is the opposite of:

A)compounding.
B)future value.
C)opportunity costs.
D)both A and C.

Question 75

To compound $100 quarterly for 20 years at 8%,we must use:

A)40 periods at 4%.
B)five periods at 12%.
C)10 periods at 4%.
D)80 periods at 2%.

Question 76

What is the present value of $12,500 to be received 10 years from today? Assume a discount rate of 8% compounded annually and round to the nearest $10.

A)$5,790
B)$11,574
C)$9,210
D)$17,010

Question 77

What is the present value of $1,000 to be received 10 years from today? Assume that the investment pays 8.5% and it is compounded monthly (round to the nearest $1).

A)$893
B)$3,106
C)$429
D)$833

Question 78

The present value of $400 to be received at the end of 10 years,if the discount rate is 5%,is:

A)$400.00.
B)$248.40.
C)$313.60.
D)$245.60.

Question 79

Three years from now,Barbara Waters will purchase a laptop computer that will cost $2,250.Assume that Barbara can earn 6.25% (compounded monthly)on her money.How much should she set aside today for the purchase? Round off to the nearest $1.

A)$1,250
B)$900
C)$1,866
D)$3,775

Question 80

What is the present value of an investment that pays $400 at the end of three years and $700 at the end of 10 years if the discount rate is 5%?

A)$1,100.00
B)$675.30
C)$775.40
D)$424.60