Deck 5: The Time Value of Money

Question 1

An annuity factor represents the future value of $1 that is deposited today.

Answer 1

False

Question 2

You should never compare cash flows occurring at different times without first discounting them to a common date.

Answer 2

True

Question 3

To calculate present value,we discount the future value by some interest rate r,the discount rate.

Answer 3

True

Question 4

The Excel function for future value is FV (rate,nper,pmt,PV).

Question 5

When money is invested at compound interest,the growth rate is the interest rate.

Question 6

The discount factor is used to calculate the present value of $1 received in year t.

Question 7

The Excel function for present value is PV (rate,nper,pmt,FV).

Question 8

The term "constant dollars" refers to equal payments for amortizing a loan.

Question 9

A dollar tomorrow is worth more than a dollar today.

Question 10

Converting an annuity to an annuity due decreases the present value.

Question 11

For a given amount,the lower the discount rate,the less the present value.

Question 12

Any sequence of equally spaced,level cash flows is called an annuity.An annuity is also known as a perpetuity.

Question 13

A mortgage loan is an example of an amortizing loan."Amortizing" means that part of the monthly payment is used to pay interest on the loan and part is used to reduce the amount of the loan.

Question 14

An annuity due must have a present value at least as large as an equivalent ordinary annuity.

Question 15

The more frequent the compounding,the higher the future value,other things equal.

Question 16

A perpetuity is a special form of an annuity.

Question 17

Accrued interest declines with each payment on an amortizing loan.

Question 18

Comparing the values of undiscounted cash flows is analogous to comparing apples to oranges.

Question 19

The present value of an annuity due equals the present value of an ordinary annuity times the discount rate.

Question 20

Compound interest pays interest for each time period on the original investment plus the accumulated interest.

Question 21

The concept of compound interest refers to:

A) earning interest on the original investment.
B) payment of interest on previously earned interest.
C) investing for a multiyear period of time.
D) determining the APR of the investment.

Question 22

What is the future value of $10,000 on deposit for 5 years at 6% simple interest?

A) $7,472.58
B) $10,303.62
C) $13,000.00
D) $13,382.26

Question 23

Under which of the following conditions will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate?

A) The interest rate is very high.
B) The investment period is very long.
C) The compounding is annually.
D) This is not possible with positive interest rates.

Question 24

How much must be deposited today in an account earning 6% annually to accumulate a 20% down payment to use in purchasing a car one year from now,assuming that the car's current price is $20,000,and inflation will be 4%?

A) $3,774
B) $3,782
C) $3,925
D) $4,080

Question 25

The Excel function for interest rate is RATE (nper,pmt,PV,FV).

Question 26

In 2002,the U.S.inflation rate was below 2% and a few countries were even experiencing deflation.

Question 27

How much interest will be earned in the next year on an investment paying 12% compounded annually if $100 was just credited to the account for interest?

A) $88
B) $100
C) $112
D) $200

Question 28

How much will accumulate in an account with an initial deposit of $100,and which earns 10% interest compounded quarterly for 3 years?

A) $107.69
B) $133.10
C) $134.49
D) $313.84

Question 29

An annual percentage rate (APR)is determined by annualizing the rate using compound interest.

Question 30

How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually?

A) $70.00
B) $80.14
C) $105.62
D) $140.00

Question 31

How much interest can be accumulated during one year on a $1,000 deposit paying continuously compounded interest at an APR of 10%?

A) $100.00
B) $105.17
C) $110.50
D) $115.70

Question 32

How much interest will be earned in an account into which $1,000 is deposited for one year with continuous compounding at a 13% rate?

A) $130.00
B) $138.83
C) $169.00
D) $353.34

Question 33

What will be the approximate population of the United States,if its current population of 300 million grows at a compound rate of 2% annually for 25 years?

A) 413 million
B) 430 million
C) 488 million
D) 492 million

Question 34

Nominal dollars refer to the amount of purchasing power.

Question 35

What is the discount factor for $1 to be received in 5 years at a discount rate of 8%?

A) .4693
B) .5500
C) .6000
D) .6806

Question 36

Assume the total expense for your current year in college equals $20,000.Approximately how much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount?

A) $952.00
B) $1,600.00
C) $1,728.00
D) $3,973.00

Question 37

Approximately how long must one wait (to the nearest year)for an initial investment of $1,000 to triple in value if the investment earns 8% compounded annually?

A) 9 years
B) 14 years
C) 22 years
D) 25 years

Question 38

When an investment pays only simple interest,this means:

A) the interest rate is lower than on comparable investments.
B) the future value of the investment will be low.
C) the earned interest is nontaxable to the investor.
D) interest is earned only on the original investment.

Question 39

The appropriate manner of adjusting for inflationary effects is to discount nominal cash flows with real interest rates.

Question 40

An effective annual rate must be greater than an annual percentage rate.

Question 41

Which of the following will increase the present value of an annuity,other things equal?

A) Increasing the interest rate
B) Decreasing the interest rate
C) Decreasing the number of payments
D) Decreasing the amount of the payment

Question 42

Cash flows occurring in different periods should not be compared unless:

A) interest rates are expected to be stable.
B) the flows occur no more than one year from each other.
C) high rates of interest can be earned on the flows.
D) the flows have been discounted to a common date.

Question 43

Given a set future value,which of the following will contribute to a lower present value?

A) Higher discount rate
B) Fewer time periods
C) Less frequent discounting
D) Lower discount factor

Question 44

What is the present value of $100 to be deposited today into an account paying 8%,compounded semiannually for 2 years?

A) $85.48
B) $100.00
C) $116.00
D) $116.99

Question 45

A cash-strapped young professional offers to buy your car with four,equal annual payments of $3,000,beginning 2 years from today.Assuming you're indifferent to cash versus credit,that you can invest at 10%,and that you want to receive $9,000 for the car,should you accept?

A) Yes; present value is $9,510.
B) Yes; present value is $11,372.
C) No; present value is $8,645.
D) No; present value is $7,461.

Question 46

What is the present value of the following set of cash flows at an interest rate of 7%: $1,000 today,$2,000 at end of year 1,$4,000 at end of year 3,and $6,000 at end of year 5?

A) $9,731
B) $10,412
C) $10,524
D) $11,524

Question 47

What is the present value of your trust fund if it promises to pay you $50,000 on your 30^th birthday (7 years from today)and earns 10% compounded annually?

A) $25,000.00
B) $25,657.91
C) $28,223.70
D) $29,411.76

Question 48

What is the present value of the following payment stream,discounted at 8% annually: $1,000 at the end of year 1,$2,000 at the end of year 2,and $3,000 at the end of year 3?

A) $5,022.11
B) $5,144.03
C) $5,423.87
D) $5,520.00

Question 49

A corporation has promised to pay $1,000 20 years from today for each bond sold now.No interest will be paid on the bonds during the 20 years,and the bonds are discounted at a 7% interest rate.Approximately how much should an investor pay for each bond?

A) $70.00
B) $258.42
C) $629.56
D) $857.43

Question 50

The present value of a perpetuity can be determined by:

A) Multiplying the payment by the interest rate.
B) Dividing the interest rate by the payment.
C) Multiplying the payment by the number of payments to be made.
D) Dividing the payment by the interest rate.

Question 51

Your car loan requires payments of $200 per month for the first year and payments of $400 per month during the second year.The annual interest rate is 12% and payments begin in one month.What is the present value of this 2-year loan?

A) $6,246.34
B) $6,389.78
C) $6,428.57
D) $6,753.05

Question 52

Which of the following factors is fixed and thus cannot change for a specific perpetuity?

A) PV of a perpetuity
B) Cash payment of a perpetuity
C) Interest rate on a perpetuity
D) Discount rate of a perpetuity

Question 53

The salesperson offers,"Buy this new car for $25,000 cash or,with appropriate down payment,pay $500 per month for 48 months at 8% interest." Assuming that the salesperson does not offer a free lunch,calculate the "appropriate" down payment.

A) $1,000.00
B) $4,520.64
C) $5,127.24
D) $8,000.00

Question 54

What is the present value of a five-period annuity of $3,000 if the interest rate is 12% and the first payment is made today?

A) $9,655.65
B) $10,814.33
C) $12,112.05
D) $13,200.00

Question 55

A perpetuity of $5,000 per year beginning today is said to offer a 15% interest rate.What is its present value?

A) $33,333.33
B) $37,681.16
C) $38,333.33
D) $65,217.39

Question 56

A stream of equal cash payments lasting forever is termed:

A) an annuity.
B) an annuity due.
C) an installment plan.
D) a perpetuity.

Question 57

How much more would you be willing to pay today for an investment offering $10,000 in 4 years rather than the normally advertised 5-year period? Your discount rate is 8%.

A) $544.47
B) $681.48
C) $740.74
D) $800.00

Question 58

$3,000 is deposited into an account paying 10% annually,to provide three annual withdrawals of $1,206.34 beginning in one year.How much remains in the account after the second payment has been withdrawn?

A) $1,326.97
B) $1,206.34
C) $1,096.69
D) $587.32

Question 59

How much must be invested today in order to generate a 5-year annuity of $1,000 per year,with the first payment 1 year from today,at an interest rate of 12%?

A) $3,604.78
B) $3,746.25
C) $4,037.35
D) $4,604.78

Question 60

How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume a 10% interest rate and cash flows at end of period.

A) $297.29
B) $1,486.44
C) $1,635.08
D) $2,000.00

Question 61

Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years,during which time the fund will earn 8% interest with monthly compounding?

A) $261,500.00
B) $323,800.00
C) $578,700.00
D) $690,000.00

Question 62

How many monthly payments remain to be paid on an 8% mortgage with a 30-year amortization and monthly payments of $733.76,when the balance reaches one-half of the $100,000 mortgage?

A) Approximately 268 payments
B) Approximately 180 payments
C) Approximately 92 payments
D) Approximately 68 payments

Question 63

Approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8% annually,and the first payment occurs 1 year from now?

A) $1,067,000
B) $1,250,000
C) $2,315,000
D) $2,500,000

Question 64

If $120,000 is borrowed for a home mortgage,to be repaid at 9% interest over 30 years with monthly payments of $965.55,how much interest is paid over the life of the loan?

A) $120,000
B) $162,000
C) $181,458
D) $227,598

Question 65

What is the present value of a four-period annuity of $100 per year that begins 2 years from today if the discount rate is 9%?

A) $297.21
B) $323.86
C) $356.85
D) $388.97

Question 66

The present value of the following cash flows is known to be $6,939.91; $500 today,$2,000 in 1 year,and $5,000 in 2 years.What discount rate is being used?

A) 3%
B) 4%
C) 5%
D) 6%

Question 67

In calculating the present value of $1,000 to be received 5 years from today,the discount factor has been calculated to be .7008.What is the apparent interest rate?

A) 5.43%
B) 7.37%
C) 8.00%
D) 9.50%

Question 68

A furniture store is offering free credit on purchases over $1,000.You observe that a big-screen television can be purchased for nothing down and $4,000 due in one year.The store next door offers an identical television for $3,650 but does not offer credit terms.Which statement below best describes the "free" credit?

A) The "free" credit costs about 8.75%.
B) The "free" credit costs about 9.13%.
C) The "free" credit costs about 9.59%.
D) The "free" credit effectively costs zero%.

Question 69

The present value of an annuity stream of $100 per year is $614 when valued at a 10% rate.By approximately how much would the value change if these were annuities due?

A) An increase of $10
B) An increase of $61
C) An increase of $100
D) Unknown without knowing number of payments

Question 70

You're ready to make the last of four equal,annual payments on a $1,000 loan with a 10% interest rate.If the amount of the payment is $315.47,how much of that payment is accrued interest?

A) $28.68
B) $31.55
C) $100.00
D) $315.47

Question 71

What will be the monthly payment on a home mortgage of $75,000 at 12% interest,to be amortized over 30 years?

A) $771.46
B) $775.90
C) $1,028.61
D) $1,034.53

Question 72

How much can be accumulated for retirement if $2,000 is deposited annually,beginning 1 year from today,and the account earns 9% interest compounded annually for 40 years?

A) $87,200.00
B) $675,764.89
C) $736,583.73
D) $802,876.27

Question 73

An amortizing loan is one in which:

A) the principal remains unchanged with each payment.
B) accrued interest is paid regularly.
C) the maturity of the loan is variable.
D) the principal balance is reduced with each payment.

Question 74

How much must be saved annually,beginning 1 year from now,in order to accumulate $50,000 over the next 10 years,earning 9% annually?

A) $3,291
B) $3,587
C) $4,500
D) $4,587

Question 75

$50,000 is borrowed,to be repaid in three equal,annual payments with 10% interest.Approximately how much principal is amortized with the first payment?

A) $2,010.60
B) $5,000.00
C) $15,105.74
D) $20,105.74

Question 76

Which of the following strategies will allow real retirement spending to remain approximately equal,assuming savings of $1,000,000 invested at 8%,a 25-year horizon,and 4% expected inflation?

A) Spend approximately $63,000 annually.
B) Spend approximately $78,225 annually.
C) Spend approximately $93,680 annually.
D) Spend approximately $127,500 annually.

Question 77

If the future value of an annuity due = $25,000 and $24,000 is the future value of an ordinary annuity that is otherwise similar to the annuity due,what is the implied discount rate?

A) 1.04%
B) 4.17%
C) 5.00%
D) 8.19%

Question 78

With $1.5 million in an account expected to earn 8% annually over the retiree's 30 years of life expectancy,what annual annuity can be withdrawn,beginning today?

A) $112,150
B) $120,000
C) $123,371
D) $133,241

Question 79

Your real estate agent mentions that homes in your price range require a payment of approximately $1,200 per month over 30 years at 9% interest.What is the approximate size of the mortgage with these terms?

A) $128,035
B) $147,940
C) $149,140
D) $393,120

Question 80

Which of the following characteristics applies to the amortization of a loan such as a home mortgage?

A) The amortization decreases with each payment.
B) The amortization increases with each payment.
C) The amortization is constant throughout the loan.
D) The amortization fluctuates monthly with changes in interest rates.