Deck 6: Time Value of Money

Question 1

You have just calculated the present value of the expected cash flows of a potential investment. Management thinks your figures are too low. Which of the following actions would increase the present value of your cash flows?

A) Assume a longer stream of cash flows of the same amount
B) Increase the discount rate
C) Decrease the discount rate
D) a and c

Answer 1

D

Question 2

Which of the following is not a time value key?

A) n
B) I/Y
C) LN
D) PMT
E) FV

Answer 2

C

Question 3

Which of the following statements about time lines is false?

A) A time line is a graphic portrayal of a time value problem.
B) Time zero is the present point in time.
C) Future time periods are to the right of zero.
D) Time is portrayed along a vertical line.

Answer 3

D

Question 4

The present value factor (PVF) and the future value factor (FVF) are related:

A) exponentially.
B) arithmetically.
C) as reciprocals.
D) as compliments.

Question 5

If the interest rate is 0%:

A) future amounts have zero present value.
B) future amounts have an infinite present value.
C) the present value of amounts to be received in the future is equal to the sum of those amounts.
D) the future value of an investment is less than the sum of its cash flows.

Question 6

The higher the rate of interest:

A) the larger the present value of a future sum of money.
B) the smaller the future value of an amount invested today.
C) the smaller the present value of a future sum of money.
D) All of the above

Question 7

Which of the following formulas can be used to solve amount problems?

A) FV_n = PV[FVF_k,n]
B) FV_n = PV[1+k]ⁿ
C) PV = FV[1+k]^-n
D) PV = FV_n[PVF_k,n]
E) All of the above

Question 8

The present value of a future amount is:

A) that sum which if deposited today will grow into the future amount.
B) referred to as the discounted value of the future amount.
C) always smaller than the future amount, for positive interest rates.
D) All of the above

Question 9

The process of finding present values is frequently called:

A) annualizing.
B) compounding.
C) discounting.
D) leasing.

Question 10

If an investor is indifferent between $1.00 today and $1.33 in three years:

A) $1.00 must be the present value of $1.33 in three years.
B) $1.33 must be the future value of $1.00 today.
C) the relevant interest rate is positive.
D) a and b.
E) All of the above

Question 11

Opportunity cost is the:

A) benefit that would have been available from the next best use of money.
B) prime rate for large firms.
C) unemployment rate.
D) rate on standard savings accounts.

Question 12

Holding all other variables constant, an increase in the interest rate will cause ____ to decrease.

A) future values
B) present values
C) annuity payments
D) growth rates

Question 13

If the present value of a given sum is equal to its future value, then:

A) the discount rate must be very high.
B) there is no inflation.
C) the discount rate must be zero.
D) none of the above are correct.

Question 14

Which of the following would increase the future value of an amount?

A) An increase in the interest rate
B) An increase in the amount
C) An increase in the time until future value is to be received
D) a and b
E) All of the above

Question 15

Which of the following is a FALSE statement?

A) Future values and interest rates move in the same direction.
B) The EAR is generally less than the nominal or quoted rate of interest.
C) Compounding means earning interest on interest.
D) Future values decrease with decreases in interest rates

Question 16

The principle behind time value of money is based on the fact that:

A) a sum of money in hand today is worth more than the same sum in the future.
B) a sum of money in hand today is worth less than the same sum in the future.
C) a sum of money in the future is worth less than the same sum in hand today.
D) a and c

Question 17

The present value of an amount can be represented as:

A) PV = FVn[PVF_k,n].
B) PV = FVn[PVFA_k,n].
C) PV = FV_n[1 / (1 + k)ⁿ].
D) a and c

Question 18

If an investor prefers the present value of an investment to its future value:

A) he has selected an interest rate that is too high.
B) he has selected an interest rate that is too low.
C) he has a zero time value of money.
D) None of the above

Question 19

The present value of the cash flows expected to come from owning a share of stock:

A) is the maximum price an investor should be willing to pay for the share.
B) is the minimum price an investor should be willing to pay for the share.
C) is not related to the price that an investor should be willing to pay for the share.
D) All of the above

Question 20

Effective annual rates decrease as ____ decrease:

A) annual percentage rates
B) number of compounding periods
C) quoted rates
D) All of the above

Question 21

The present value of an annuity:

A) is equal to the sum of the present values of each period's cash flow.
B) has a future value (as an amount) equal to the future value of the annuity.
C) has a future value (as an amount) equal to the sum of the annuity's cash flows.
D) a and b.

Question 22

The payment or receipt of equal amounts, at the end of a series of equal periods, for a specified amount of time is called a(n):

A) annuity due.
B) perpetuity.
C) ordinary annuity.
D) simple interest.

Question 23

The more frequent the compounding the:

A) greater the present value.
B) greater the amount deposited.
C) greater the effective interest rate.
D) lower the future value.

Question 24

The annual effective rate of interest is a function of:

A) the annual nominal rate of interest.
B) the number of compounding intervals per year.
C) the imbedded annuity.
D) a and b

Question 25

When a loan is amortized over a five year term, the:

A) rate of interest is reduced each year.
B) amount of interest paid is reduced each year.
C) payment is reduced each year.
D) balance is paid as a balloon payment in the fifth year.

Question 26

When using a future value of an annuity table:

A) payments are assumed to be made at the end of each period.
B) FVFA factors increase with an increase in the interest rate.
C) FVFA factors increase with an increase in the number of periods.
D) All of the above

Question 27

You have just won a $5 million lottery to be received in twenty annual equal payments of $250,000. What will happen to the present value of your winnings if the interest rate increases?

A) It will be worth less.
B) It will be worth more.
C) It will not change.
D) None of the above

Question 28

Holding all other variables constant, an increase in the ____ will increase the future value of an annuity.

A) annuity payment
B) rate of interest
C) number of periods
D) Both a & b
E) All of the above

Question 29

More frequent compounding results in ____ future values and ____ present values than less frequent compounding at the same nominal interest rate.

A) higher, higher
B) lower, higher
C) higher, lower
D) lower, lower

Question 30

Which of the following is most correct?

A) The present value of an annuity due is always larger than the present value of an ordinary annuity with the same cash flows.
B) The future value of an annuity due is always larger than the future value of an ordinary annuity with the same cash flows.
C) The future value of an ordinary annuity is always larger than the future value of an annuity due with the same cash flows.
D) Both a and b are correct.
E) Both a and c are correct.

Question 31

Finding the discounted value of $1,000 to be received at the end of each of the next five years requires calculating the:

A) future value of an annuity.
B) future value of a deferred annuity.
C) present value of an annuity.
D) present value of a deferred annuity.

Question 32

Which of the following phrases would not be utilized if the payments were an annuity due?

A) End-of-period payments
B) Starting immediately
C) Starting now
D) Starting today

Question 33

The effective rate of interest will always be ____ the nominal rate.

A) greater than
B) equal to
C) less than
D) equal to or greater than

Question 34

The present value factor for an annuity:

A) is less than the number of years in the annuity.
B) approaches a value of infinity for a perpetuity.
C) is greater than the number of years in an annuity.
D) a and b
E) None of the above

Question 35

The ____ of a resource is the benefit that would have been available from its next best use.

A) opportunity cost
B) present value
C) future value
D) all of the above
E) none of the above

Question 36

If the interest rate is 6%, which expression will determine the appropriate price to pay for a business that you expect to earn $5,000 in each of the next ten years and be sold for $25,000 in the eleventh year.

A) PV = $5,000[FVFA_6,10] + $25,000[FVF_6,11]
B) PV = $5,000[PVFA_6,10] + $25,000[FVF_6,11]
C) PV = $5,000[PVFA_6,10] + $25,000[PVF_6,11]
D) None of the above

Question 37

You expect to receive $1,000 at the end of each of the next three years that you plan to deposit in a bank account paying 6%. Which of the following expressions will calculate your bank balance just after the last payment is deposited?

A) FV = $1,000 [FVF_6,1] + $1,000 [FVF_6,2] + $1,000 [FVF_6,3]
B) FV = $1,000 [1.06]¹ + $1,000 [1.06]² + $1,000 [1.06]³
C) FVA₃ = $1,000 [FVFA_6,3]
D) All of the above

Question 38

The present value of an annuity will be decreased by:

A) a decrease in the number of payments.
B) a decrease in the discount rate.
C) a decrease in the amount of the payment in each per period.
D) a and c.
E) all of the above.

Question 39

When using a present value of an annuity table:

A) payments are assumed to be made at the beginning of each period.
B) PVFA factors decrease with an increase in the interest rate.
C) PVFA factors increase with an increase in the number of periods.
D) b and c only

Question 40

Interest rates are quoted by stating the ____ followed by the compounding period.

A) effective annual rate
B) nominal rate
C) yield
D) coupon rate
E) none of the above

Question 41

The present value of a perpetuity:

A) conceptually doesn't make sense.
B) is infinite.
C) is zero.
D) is not affected by changes in the discount rate.
E) None of the above

Question 42

Which of the following series of cash flows includes an imbedded annuity?

A) 10, 5, 6, 7, 8, 9, 10
B) 6, 6, 6, 6, 6, 6, 6
C) 5, 6, 7, 7, 7, 6, 7
D) 8, 7, 6, 5, 4, 3, 2
E) None of the above has an embedded annuity.

Question 43

A series of equal payments that occur at equal intervals and go on forever is called a(n):

A) ordinary annuity.
B) annuity due.
C) perpetuity.
D) non-ending stream.
E) None of the above

Question 44

What is the most you should pay to receive the following cash flows if you require a return of 12 percent? $\begin{array}{ll}\text { Year 1 } & \$ 5,000 \\\text { Year 2 } & \$ 8,000 \\\text { Year 3 } & \$ 12,000 \\\text { Year 4-10 } & \$ 15,000\end{array}$

A) $58,580
B) $104,135
C) $68,105
D) None of the above

Question 45

$3,947 deposited four years ago has grown to $5,000. What semiannually compounded rate of interest has the bank been paying?

A) 5.26%
B) 6.00%
C) 3.00%
D) 6.67%

Question 46

You purchased a piece of property for $30,000 nine years ago and sold it today for $83,190. What was the annual rate of return on your investment?

A) 12%
B) 11%
C) 10%
D) 9%

Question 47

Designs Now is opening a showcase office to display and sell its computer designed poster art. Designs expects cash flows to be $120,000 in the first year, $180,000 in the second year, $240,000 in the third year. If Designs uses 11 percent as its discount rate, what is the present value of the cash flows?

A) $429,720
B) $457,620
C) $456,000
D) $424,820

Question 48

Determine how much $1,000 deposited in a savings account paying 8% compounded annually will be worth after 5 years.

A) $5,526
B) $784
C) $1,400
D) $1,469

Question 49

Using an annual interest rate of 9%, how long will it take a deposit of $1,000 to grow to $3,000, assuming no additional deposits are made?

A) 8.04 years
B) 10.00 years
C) 11.11 years
D) 12.75 years
E) 13.50 years

Question 50

Which of the following interest rates will come closest to doubling invested money in five years?

A) 13%
B) 14%
C) 15%
D) 16%

Question 51

At an effective interest rate of 12%, a single sum invested today will double itself in approximately:

A) 8 years.
B) 12 years.
C) 6 years.
D) insufficient data to determine answer.

Question 52

What is the rate of return on an investment if you lend $1,000 and are repaid $1,254.70 two years later?

A) 12%
B) 25%
C) 6%
D) 18%
E) 4%

Question 53

If a series of equal payments is paid regularly out of a bank account which earns a constant rate of interest, the ____ is the amount that must be in the bank at the beginning of the series to just fund all of the payments.

A) future value of an annuity due
B) present value of an annuity due
C) future value of an ordinary annuity
D) present value of an ordinary annuity
E) None of the above

Question 54

Your bank balance is exactly $10,000. Three years ago you deposited $7,938 and have not touched the account since. What annually compounded rate of interest has the bank been paying?

A) 8.65%
B) 26.00%
C) 8.00%
D) 6.87%

Question 55

If you invest the $10,000 you receive at graduation (age 22) in a mutual fund which averages a 12% annual return, how much will you have at retirement in 40 years?

A) $909,090
B) $930,510
C) $783,879
D) $510,285

Question 56

If a series of equal payments is received regularly at the end of the year, and each is deposited immediately at the same interest rate, the ____ is the sum of all the payments and all the interest earned at the end of the series.

A) future value of an annuity due
B) present value of an annuity due
C) future value of an ordinary annuity
D) present value of an ordinary annuity
E) none of the above

Question 57

Five years after an accident, you received $100,000 to pay the medical expenses incurred at the time of the accident. What is the present value (at the time of the accident) of the payment? Assume interest rates are 9%.

A) $153,900
B) $68,100
C) $65,000
D) $70,800

Question 58

How much must be invested today to have $1,000 in two years if the interest rate is 5%?

A) $909.09
B) $900.00
C) $907.00
D) $950.00

Question 59

A(n) ____ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e. forever).

A) imbedded annuity
B) annuity due
C) sinking fund
D) perpetuity

Question 60

Find the present value of $100 to be received at the end of two years if the discount rate is 12% compounded monthly.

A) $66.50
B) $78.76
C) $68.80
D) $91.80
E) $79.75

Question 61

Your local bank offers 4-year certificates of deposit (CDs) 12 % compounded quarterly. How much additional interest will you earn over 4 years on a $10,000 CD that is compounded quarterly, compared with one that is compounded annually?

A) $6,050
B) $0
C) $312
D) $220

Question 62

The Florida lottery agrees to pay the winner $250,000 at the end of each year for the next 20 years. What is the future value of this prize if each payment is put in an account earning 9 percent?

A) $2.28 million
B) $12.79 million
C) $14.32 million
D) $5.00 million

Question 63

If Susan and Joe set aside $10,000 for college tuition when their daughter is 13, how much will be available when she starts college at 18 if the account in which the money is deposited pays 12 percent compounded monthly?

A) $17,623.42
B) $18,170
C) $16,105.10
D) $16,122.26

Question 64

Your brother, who is 6 years old, just received a trust fund that will be worth $25,000 when he is 21 years old. If the fund earns 10 percent interest compounded annually, what is the value of the fund today?

A) $104,602
B) $6,575
C) $5,975
D) $6,875

Question 65

What is the future value of $1,000, placed in a saving account for four years if the account pays 8%, compounded quarterly?

A) $1,320.45
B) $1,360.50
C) $1,372.80
D) None of the above

Question 66

Joan is saving to open her own dress shop in 10 years. She currently has $10,000. In addition, she plans to save $2,000 per year for the next 5 years and $3,000 per year for the following 5 years. How much will Joan have in 10 years if she earns a 10 % return on her savings?

A) $76,129
B) $63,925
C) $44,255
D) $159,370

Question 67

You deposited $2,000 seven years ago and haven't touched the account since. Now you have $3,656 in the bank. What was the interest rate?

A) 6%
B) 7%
C) 8%
D) 9%

Question 68

If you deposit $3500 in a bank account paying 6% interest and leave it there for fifteen years, how much will you have?

A) $1,460.55
B) $3,399.27
C) $8,388.10
D) $81,466.00

Question 69

The First National Bank has agreed to lend you $30,000 today, but you must repay $42,135 in 3 years. What rate is the bank charging you?

A) 10%
B) 11%
C) 12%
D) 13%

Question 70

Which of the following cash flows has the highest present value (PV) at a 15 percent discount rate?

A) $1,150 received one year from today
B) $2,000 received 5 years from today
C) $200 received every year (at the end of the year) for 10 years
D) $300 received every year (at the end of the year) for 5 years

Question 71

Find the future value in two years of $100 that is deposited in an account, which pays 12%, compounded monthly.

A) $160.00
B) $112.70
C) $118.80
D) $125.40
E) $126.97

Question 72

Your grandparents put $1,000 into a savings account for you when you were born 20 years ago. This account has been earning interest at a compound rate of 7 percent. What is its value today?

A) $3,870
B) $1,967
C) $3,026
D) $3,583

Question 73

Calculate the amount today that is equivalent to $150 at the end of year 1, $450 at the end of year 2, and $300 at the end of year 3, given a discount rate of 10%.

A) $695
B) $710
C) $755
D) $734
E) $1,100

Question 74

Your grandparents have just given you a $50,000 savings bond that matures in 20 years. If the discount rate is 10%, what did they pay for the bond?

A) $7,450
B) $8,175
C) $8,900
D) $1,490

Question 75

What amount received at the end of 20-years is equivalent to $100 today, given an interest rate of 14%?

A) $87,346
B) $1,152
C) $1,638
D) $1.374
E) $91,029

Question 76

What is the rate of interest on a $10,000 loan that is to be repaid in 10 equal annual installments of $1,917.

A) 8%
B) 10%
C) 14%
D) 16%
E) 15%

Question 77

Ralph has decided to put $2,400 a year (at the end of each year) into an IRA over his 40 year working life and then retire. What will Ralph have at retirement if the account earns 10 percent compounded annually?

A) $394,786
B) $23,470
C) $1,062,223
D) $810,917

Question 78

Six years ago you paid $20 per share for 100 shares of stock. Today you sold the 100 shares for $30 per share. Determine the average annual rate of return on your investment, assuming the stock paid no dividends.

A) 25%
B) 8.33%
C) 150%
D) 7%

Question 79

Suppose you put $100 into a savings account today, the account pays 8% compounded semiannually, and you withdraw $50 one year after your initial deposit. What would your ending balance be 20 years after the initial $100 deposit was made, assuming that you make no additional deposits?

A) $250.31
B) $257.45
C) $258.16
D) $430.10
E) $480.10

Question 80

What present amount is equivalent to $100 received at the end of 5 years, given an interest rate of 16%?

A) $47.60
B) $327.40
C) $40.20
D) $163.60
E) $32.30