Deck 5: The Time Value of Money

Question 1

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

Answer 1

True

Question 2

Present values decline as the time to the cash flows increases.

Answer 2

True

Question 3

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

Answer 3

True

Question 4

The effective annual interest rate cannot be less than the annual percentage rate.

Question 5

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

Question 6

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

Question 7

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

Question 8

Nominal dollars refer to their purchasing power.

Question 9

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

Question 10

A dollar tomorrow is worth more than a dollar today.

Question 11

A perpetuity is a special form of an annuity.

Question 12

When inflation is positive,the nominal interest rate is larger than the real rate.

Question 13

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

Question 14

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

Question 15

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

Question 16

It is important to discount both real and nominal cash flows at the real interest rate.

Question 17

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

Question 18

With a fixed-rate mortgage,the proportion of each payment used to pay interest on the loan declines over time.

Question 19

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

Question 20

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

Question 21

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 22

If the five-year discount factor is d,what is the present value of $1 received in five years' time?

A) 1/(1 + d)⁵
B) 1/d.
C) 5d.
D) d.

Question 23

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 24

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 25

The five-year discount factor is less than the four-year discount factor.

Question 26

An investment offers to pay $100 a year forever starting at the end of year 6.If the interest rate is 8%,what is the investment's value today?

A) $787.71
B) $850.73
C) $1,250
D) $1,586.87

Question 27

Present values can always be calculated by dividing the cash flow by a discount factor.

Question 28

A car's price is currently $20,000 and is expected to rise by 4% a year.If the interest rate is 6%,how much do you need to put aside today to buy the car one year from now?

A) $18,182
B) $19,231
C) $19,623
D) $4,080.08

Question 29

Given the 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 30

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

Question 31

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 32

If interest is compounded semi-annually rather than annually,then:

A) future values and present values will both be higher.
B) futures values and present values will both be lower.
C) future values will be lower and present values will be higher.
D) Future values will be higher and present values will be lower.

Question 33

As long as the interest rate is positive,the future value will always be larger than the present value given any period of time.

Question 34

What is the future value of $10,000 on deposit for 2 years at 6% simple interest?

A) $10,600
B) $11,236
C) $11,200
D) $13,382.26

Question 35

An investment of $100 pays interest of 2.5% per quarter.What will be the value of this investment at the end of 3 years?

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

Question 36

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 37

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

A) $952.46
B) $1,600.00
C) $1,728.08
D) $3,973.11

Question 38

If the 5-year discount factor is 0.7008,what is the interest rate?

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

Question 39

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

Question 40

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 41

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

A) $297.22
B) $323.97
C) $356.85
D) $272.68

Question 42

If the future value of an annuity due is $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 43

A perpetuity of $5,000 per year beginning today offers a 15% return.What is its present value?

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

Question 44

Someone offers to buy your car for four,equal annual payments,beginning 2 years from today.If you think that the present value of your car is $9,000 and the interest rate is 10%,what is the minimum annual payment that you would accept?

A) $2,839.24
B) $3,435.48
C) $3,123.16
D) $2,250

Question 45

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 cost of the "free" credit?

A) 8.75%
B) 9.13%
C) 9.59%
D) 0%

Question 46

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 47

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 48

A bond promises to pay $1,000 20 years from today.No interest will be paid on the bonds during the 20 years If the interest rate is 7%,what is the bond's present value?

A) $50
B) $258.42
C) $629.56
D) $1,000

Question 49

Suppose you take out a 30-year mortgage for $100,000 with annual payments.The interest rate on the mortgage is 8%.When you have paid off half the mortgage,so that the value of the remaining payments is reduced to $50,000,how many more payments need to be made?

A) Approximately 15 payments
B) Approximately 12 payments
C) Approximately 8 payments
D) Approximately 20 payments

Question 50

You will be receiving cash flows of: $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.What is the present value of these cash flows at an interest rate of 7%?

A) $9,731.13
B) $10,412.27
C) $10,524.08
D) $11,524.91

Question 51

The salesperson offers,"Buy this new car for $25,000 cash or,with an 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) $4,519.04
C) $5,127.24
D) $8,000.00

Question 52

What is the present value of a five-period annuity of $3,000 if the interest rate per period 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 53

The sum of $3,000 is deposited into an account paying 10% annually.If $1,206 is withdrawn at the end of years 1 and 2,how much then remains in the account?"

A) $1,326.97
B) $1,206.34
C) $1,097.40
D) $587.32

Question 54

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 55

Your car loan requires payments of $200 per month for the first year and payments of $400 per month during the second year.The APR 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 56

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

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

Question 57

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) $5,022.10
B) $5,144.03
C) $5,423.87
D) $5,520.00

Question 58

You invested $1,200 three years ago.During the three years,you earned annual rates of return of 4.8%,9.2%,and 11.6%.What is the value of this investment today?

A) $1,498.08
B) $1,512.11
C) $1,532.60
D) $1,549.19

Question 59

Which one 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 60

If the interest rate is 6%,which of these investments would you prefer?

A) A single payment of $500 in year 3.
B) A payment of $40 a year for 20 years starting in one year's time.
C) A perpetuity of $30 a year starting in one year's time.
D) A payment of $342.17 today

Question 61

What happens over time to the real cost of purchasing a home if the mortgage payments are fixed in nominal terms and inflation is in existence?

A) The real cost is constant.
B) The real cost is increasing.
C) The real cost is decreasing.
D) The price index must be known to answer this question.

Question 62

If $120,000 is borrowed for a home mortgage,to be repaid at 9% interest over 30 years with annual payments of $11,680.36,how much interest (as opposed to return of capital)is paid in the last year of the loan?

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

Question 63

How much must be saved at the end of each year for the next 10 years in order to accumulate $50,000,if you can earn 9% annually? Assume you contribute the same amount to your savings every year.

A) $3,291.00
B) $3,587.87
C) $4,500.33
D) $4,587.79

Question 64

You have just retired with savings of $1.5 million.If you expect to live for 30 years and to earn 8% a year on your savings,how much can you afford to spend each year? Assume that you spend the money at the start of each year.

A) $112,148.50
B) $120,000.00
C) $123,371.44
D) $133,241.15

Question 65

How much can be accumulated for retirement if $2,000 is put aside at the end of each of the next 40 years? Assume that you can earn 9% a year on your savings.

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

Question 66

What will be the monthly payment on a $75,000 30-year home mortgage at 1% interest per month?

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

Question 67

What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually?

A) 5.00%
B) 5.66%
C) 6.00%
D) 9.46%

Question 68

Real interest rates:

A) always exceed inflation rates.
B) can decline to zero but no lower.
C) can be negative, zero, or positive.
D) traditionally exceed nominal rates.

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) $10
B) $61.40
C) $10 ×Number of years in annuity stream
D) $6.14 × Number of years in annuity stream

Question 70

If inflation in Wonderland was 3% per month in 2016,what was the annual rate of inflation?

A) 36.00%
B) 42.58%
C) 40.09%
D) 41.27%

Question 71

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 one year from now?

A) $1,067,477.62
B) $1,128,433.33
C) $1,487,320.09
D) $1,250,000.00

Question 72

$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 73

Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 0.75% interest per month.What is the size of the mortgage with these terms?

A) $128,035.05
B) $147,940.29
C) $149,138.24
D) $393,120.03

Question 74

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 75

On the day you retire you have $1,000,000 saved.You expect to live another 25 years during which time you expect to earn 6.19% on your savings while inflation averages 2.5% annually.Assume you want to spend the same amount each year in real terms and die on the day you spend your last dime.What real amount will you be able to spend each year?

A) $61,334.36
B) $79,644.58
C) $79,211.09
D) $61,931.78

Question 76

Assume you are making $989 monthly payments on your amortized mortgage.The amount of each payment that is applied to the principal balance:

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

Question 77

Your retirement account has a current balance of $50,000.You plan to add $6,000 a year to the account for each of the next 30 years.Use a financial calculator or Excel to find what interest rate you need to earn in order to have $1,000,000 in the account at the end of the 30 years.?

A) 5.02%
B) 7.24%
C) 9.80%
D) 10.07%

Question 78

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 79

Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10-fold.If inflation averaged 4% annually during the period,then over his career his purchasing power:

A) remained on par with inflation.
B) increased by nearly 1% annually.
C) increased by nearly 2% annually.
D) decreased.

Question 80

How much do you need when you retire to provide a $2,500 monthly check that will last for 25 years? Assume that your savings can earn 0.5% a month.

A) $361,526.14
B) $388,017.16
C) $402,766.67
D) $414,008.24