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

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

Answer 2

False

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

Question 5

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

Question 6

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

Question 7

Accrued interest declines with each payment on an amortizing loan.

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

In 2013, the U.S. inflation rate was below 2% and a few countries were even experiencing deflation.

Question 16

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

Question 17

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

Question 18

A dollar tomorrow is worth more than a dollar today.

Question 19

A perpetuity is a special form of an annuity.

Question 20

Nominal dollars refer to the amount of purchasing power.

Question 21

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 22

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 23

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 24

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 25

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 26

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 27

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 28

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 29

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) 9.81 years
B) 14.27 years
C) 22.01 years
D)25.00 years

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

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

Question 32

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 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

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

Question 35

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) $3,774.61
B) $3,782.20
C) $3,924.53
D)$4,080.08

Question 36

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 37

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

Question 38

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 39

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

Question 40

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 41

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

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

Question 42

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 43

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 an interest rate of 7%, compounded semiannually. Approximately how much should an investor pay for each bond?

A) $70.00
B) $252.57
C) $629.56
D)$857.43

Question 44

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 45

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 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

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 49

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 50

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 51

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 52

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 53

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 54

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 55

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 91 payments
D)Approximately 68 payments

Question 56

Three thousand dollars 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 57

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

A) Present value
B) Payment amount
C) Interest rate
D)Discount rate

Question 58

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 59

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 60

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 $9,510.08
B) Yes; present value is $11,372.67
C) No; present value is $8,645.09
D)No; present value is $7,461.17

Question 61

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 62

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 63

Your retirement account has a current balance of $50,000. What interest rate would need to be earned in order to accumulate a total of $1,000,000 in 30 years, by adding $6,000 annually?

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

Question 64

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 65

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

Question 66

If inflation in Wonderland averaged about 3% per month in 2013, what was the annual rate of inflation?

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

Question 67

$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 68

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 6% interest with monthly compounding?

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

Question 69

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 70

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 71

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 72

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 73

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 74

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 75

Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 9% interest. 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 76

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 77

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 78

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 79

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 80

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