Deck 5: Time Value of Money-The Basics

Question 1

The end of one time period and the beginning of the next occupy the same place on a timeline.

Answer 1

True

Question 2

Which of the following statements is FALSE?

A) A dollar received one year from now will be worth more than a dollar received today.
B) A dollar received one year from now will be worth more than a dollar received two years from now.
C) Compounding essentially means earning interest on interest on an initial balance.
D) Perpetuities pay an equal payment forever.

Answer 2

A

Question 3

On timeline, the present is represented as

A) time sub n.
B) time zero
C) time sub i
D) time 1

Answer 3

B

Question 4

Sketch a timeline that represents an immediate investment of $20,000 with $25,000 to be received at the end of 4 years.

Question 5

A timeline is a linear representation of the timing of cash flows.

Question 6

Timelines can be expressed in terms of

A) years.
B) months.
C) days.
D) any of the above

Question 7

Timelines used to visualize cash flows normally represent present values on the left and future values on the right.

Question 8

The last amount shown on a timeline represents the future value of all amounts invested up to that point.

Question 9

Should you prefer to receive $100,000 right now or $10,000 at the end of each of the next 12 years?

A) $100,000 now.
B) $10,000 at the end of each of the next 12 years.
C) The answer depends on the time value of money.
D) Either alternative is equally valuable.

Question 10

An investor will invest $1,000 now and expect to receive $10 for each of the next 10 years plus $1,000 at the end of the 10th year. Her cash flow at time period 0 is

A) $1,000.
B) -$1,000.
C) $-990.
D) $1,010.

Question 11

Timelines are always expressed in years.

Question 12

A diagram for visualizing future cash flows is known as

A) a future value vector.
B) a cash flow chart.
C) an FV/PV plot.
D) a timeline.

Question 13

A timeline typically represents cash flows as an exponential growth curve.

Question 14

The first amount on a timeline represent the present value of all the future amounts at a given interest rate.

Question 15

Money has a greater time value time value

A) when rates of return are higher.
B) when rates of return are lower.
C) when the future is uncertain.
D) when investors are willing to assume greater risks.

Question 16

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 17

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 18

Which of the following is the formula for compound value?

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

Question 19

A timeline represents the value of a sum invested now at the end of a series of time periods.

Question 20

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 21

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 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 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 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

An increase in future value can be caused by

A) an increase in the: annual interest rate.
B) an increase in the: number of compounding periods.
C) deferring the original investment by one or more periods.
D) both A and B.

Question 26

When using a financial calculator, which of the following is the correct way to find the future value of $200 deposited today in an account for four years paying annual interest of 3%?

A) N=4, i=.03, PV=-200, PMT=0, solve for FV
B) N=4, i=3, PV=-200, PMT=0, solve for FV
C) N=4, i=3, PV=0, PMT=$200, solve for FV
D) N=4, i=3, FV=200, PMT=0, solve for PV

Question 27

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 28

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 29

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 30

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 31

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 32

Alva Thomas has decided to place $10,000 in an account payable to his alma matter when he dies. If the account grows at an annual rate of 6% compounded monthly and he lives for another 10 years, the university will receive

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

Question 33

Dawn Swift discovered that 20 years ago, the average tuition for one year at an Ivy League school was $15,000. Today, the average cost is $60,000. What is the growth rate in tuition cost over this 20-year period?

A) 15.5%
B) 4.2%
C) 7.18%
D) 10.6%

Question 34

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 35

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 36

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 37

If you put $6,000 in a savings account that yields an 1% rate of interest compounded daily, what will the investment be worth at the end of one year?

A) $6060.00
B) $6,060.30
C) $6,006.03
D) $6,760.95

Question 38

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 39

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 40

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 41

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 42

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 43

If you plotted the future value of $1,000 growing at any interest rate greater than 0 with dollars on the vertical axis and time on the horizontal axis, the resulting curve would

A) slope upward at a constant rate.
B) eventually become parallel to the horizontal axis.
C) slope upward at a decreasing rate.
D) slope upward at an increasing rate.

Question 44

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 45

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 46

High discount rates favor

A) neither long-term nor short-term investments.
B) both long-term and short-term investments.
C) long-term investments.
D) short-term investments.

Question 47

Which of the following is the formula for present value?

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

Question 48

When performing time value of money computations with a financial calculator or EXCEL, PV and FV must have opposite signs.

Question 49

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

Question 50

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 51

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

Question 52

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 53

When using a financial calculator, which of the following is a correct way to find the future value of $200 deposited today in an account for four years paying annual interest of 2% compounded quarterly?

A) N=16, i=.005, PV=-200, PMT=0, solve for FV
B) N=4, i=.5, PV=$200, PMT=0, solve for FV
C) N=16, i=.5, PV=-200, PMT=0, solve for FV
D) N=16, i=.03, FV=200, PMT=0, solve for PV

Question 54

When using a financial calculator, which of the following is a correct way to find the future value of $200 deposited today in an account for four years paying annual interest of 2% compounded quarterly?

A) N=16, i=.005, PV=200, PMT=0, solve for FV
B) N=4, i=.5, PV=200, PMT=0, solve for FV
C) N=16, i=.5, PV=-200, PMT=0, solve for FV
D) N=16, i=.03, FV=-200, PMT=0, solve for PV

Question 55

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.

Question 56

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 57

When using EXCEL to find the future value of $2,000 invested in an account that would earn interest of 7.5% for 18 years, the correct entry would be

A) =FV(7.5,18,0,-1,000).
B) =PV(.075,18,0,-1,000).
C) =FV(7.5,18,0,1,000).
D) =FV(.075,18,0,-1,000).

Question 58

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 59

Assuming equal annual rates, the more frequent the compounding periods in a year, the higher the future value.

Question 60

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 61

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 62

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 63

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

Question 64

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 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

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 67

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

A) the investment is discounted at a higher interest rate.
B) the investment is discounted for fewer years.
C) the investment is discounted at a lower interest rate.
D) both B & C.

Question 68

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 $1.00.

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

Question 69

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

Question 70

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 71

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 72

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 73

Using a financial calculator, which of the following would be a correct way to find how long it would take for a sum to triple at a rate of 3%?

A) i=5, PV=-1, PMT=0, FV=3, solve for N
B) i=5, PV=1, PMT=0, FV=3, solve for N
C) i=.05, PV=-1, PMT=0, FV=3, solve for N
D) Financial calculators cannot be used to solve this problem.

Question 74

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

Question 75

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 76

To find the present value of $1000 discounted for 20 years at 8%, when using a financial calculator, the correct entry is

A) N=20, i=.08,PMT=0, FV=1000 solve for PV.
B) N=20, i=8,PMT=0, FV=1000 solve for PMT.
C) N=20, i=.08,PMT=0, PV=1000 solve for FV.
D) N=20, i=8,PMT=0, FV=1000 solve for PV.

Question 77

Stephen's grandmother deposited $100 in an investment account for him when he was born, 25 years ago. The account is now worth $1,500. What was the average rate of return on the account?

A) 6.00%
B) 16.67%
C) 15.00%
D) 11.44%

Question 78

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?

A) 330 years
B) 3.6 years
C) 9.5 years
D) 4.8 years

Question 79

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 80

Stephen's grandmother deposited $100 in an investment account for him when he was born, 25 years ago. The account is now worth $1,500. What was the average rate of return on the account? Which of the following is a correct way to solve this problem using EXCEL?

A) =PV(25,i,-100,1500)
B) =rate(25,0,100,1500)
C) =rate(25,0,-100,1500)
D) =rate(0,-100,1500,25)