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

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

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

A dollar tomorrow is worth more than a dollar today.

Question 13

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 14

Accrued interest declines with each payment on an amortizing loan.

Question 15

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 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

A perpetuity is a special form of an annuity.

Question 21

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 22

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

Question 23

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 24

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 25

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 26

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

Question 27

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

Question 28

Nominal dollars refer to the amount of purchasing power.

Question 29

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 30

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 31

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

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

Question 32

A loan officer states,"Thousands of dollars can be saved by switching to a 15-year mortgage from a 30-year mortgage." Calculate the difference in payments on a 30-year mortgage at 9% interest versus a 15-year mortgage with 8.5% interest.Both mortgages are for $100,000 and have monthly payments.What is the difference in total dollars that will be paid to the lender under each loan? (Round the monthly payment amounts to 2 decimal places.Both interest rates are compounded monthly.)

A) $89,211
B) $98,406
C) $112,410
D) $124,300

Question 33

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 34

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 35

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 36

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 37

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

Question 38

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 39

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 40

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 41

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 42

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 43

Eighteen years from now,4 years of college are expected to cost $150,000.How much more must be deposited into an account today to fund this expense if you could only earn 8% rather than the 11% you had hoped to earn on your savings?

A) $12,211.18
B) $13,609.21
C) $14,006.41
D) $14,614.03

Question 44

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 45

What is the present value of your trust fund if you have projected that it will provide you with $50,000 on your 30^th birthday (7 years from today)and it earns 10% compounded annually?

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

Question 46

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 47

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 48

$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 49

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 compounded monthly.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 50

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 51

Miller's Hardware plans on saving $42,000,$54,000,and $58,000 at the end of each year for the next three years,respectively.How much will the firm have saved at the end of the three years if it can earn 4.5% by reinvesting its saving?

A) $160,295.05
B) $158,098.15
C) $167,508.33
D) $165,212.57

Question 52

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 53

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 54

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 55

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 56

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 57

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 58

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,compounded monthly." Calculate the "appropriate" down payment.

A) $1,000.00
B) $4,519.04
C) $5,127.24
D) $8,000.00

Question 59

What is the present value of a four-year annuity of $100 per year that begins 2 years from today (end of year 1)if the discount rate is 9%?

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

Question 60

Prizes are often not "worth" as much as claimed.Place a value on a prize of $5,000,000 that is to be received in equal payments over 20 years,with the first payment beginning today.Assume an interest rate of 7%.

A) $2,833,898.81
B) $2,911,015.68
C) $2,609,144.14
D) $2,738,304.13

Question 61

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 62

What is the APR on a loan that charges interest at the rate of 1.4% per month?

A) 10.20%
B) 14.00%
C) 16.80%
D) 18.16%

Question 63

If the effective annual rate of interest is known to be 16.08% on a debt that has quarterly payments,what is the annual percentage rate?

A) 4.02%
B) 10.02%
C) 14.50%
D) 15.19%

Question 64

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 65

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 66

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 67

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 68

What is the APR on a loan with an effective annual rate of 15.26% and weekly compounding of interest?

A) 14.35%
B) 14.49%
C) 13.97%
D) 14.22%

Question 69

A credit card account that charges interest at the rate of 1.25% per month would have an annually compounded rate of _____ and an APR of ____.

A) 16.08%; 15.00%
B) 14.55%; 16.08%
C) 12.68%; 15.00%
D) 15.00%; 14.55%

Question 70

A car dealer offers payments of $522.59 per month for 48 months on a $25,000 car after making a $4,000 down payment.What is the loan's APR?

A) 6%
B) 9%
C) 11%
D) 12%

Question 71

What APR is being earned on a deposit of $5,000 made 10 years ago today if the deposit is worth $9,848.21 today? The deposit pays interest semiannually.

A) 3.56%
B) 6.76%
C) 6.89%
D) 7.12%

Question 72

Lester's just signed a contract that will provide the firm with annual cash inflows of $28,000,$35,000,and $42,000 over the next three years with the first payment of $28,000 occurring one year from today.What is this contract worth today at a discount rate of 7.25%?

A) $88,311.08
B) $89,423.91
C) $90,580.55
D) $91,341.41

Question 73

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

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

Question 74

What is the annually compounded rate of interest on an account with an APR of 10% and monthly compounding?

A) 10.00%
B) 10.47%
C) 10.52%
D) 11.05%

Question 75

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 76

After reading the fine print in your credit card agreement,you find that the "low" interest rate is actually an 18% APR,or 1.5% per month.What is the effective annual rate?

A) 18.47%
B) 19.56%
C) 18.82%
D) 19.41%

Question 77

You are considering the purchase of a home that would require a mortgage of $150,000.How much more in total interest will you pay if you select a 30-year mortgage at 5.65% rather than a 15-year mortgage at 4.9%? (Round the monthly payment amount to 2 decimal places.Both interest rates are compounded monthly.)

A) $86,311.18
B) $78,487.92
C) $99,595.80
D) $102,486.68

Question 78

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 79

"Give me $5,000 today and I'll return $10,000 to you in 5 years," offers the investment broker.To the nearest percent,what annual interest rate is being offered?

A) 12.29%
B) 13.67%
C) 14.87%
D) 12.84%

Question 80

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