Deck 5: The Time Value of Money

Question 1

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 percent compounded annually to cover this amount?

A)$952
B)$1,600
C)$1,728
D)$3,973 $20,000 = x(1.08)²¹
$20,000 = 5.0338x

Answer 1

$3,973 $20,000 = x(1.08)²¹
$20,000 = 5.0338x

Question 2

What is the relationship between an annually compounded rate and the annual percentage rate (APR) which is calculated for truth in lending laws for a loan requiring monthly payments?

A)The APR is lower than the annually compounded rate
B)The APR is higher than the annually compounded rate
C)The APR equals the annually compounded rate
D)The answer depends on the interest rate

Answer 2

The APR is lower than the annually compounded rate

Question 3

What will be the approximate population of the United States, if its current population of 275 million grows at a compound rate of 2 percent annually for 25 years?

A)413 million
B)430 million
C)451 million
D)466 million

Answer 3

451 million

Question 4

What EAR is being earned on a deposit of $5,000 made ten years ago today if the deposit is worth $9,948.94 today? The deposit pays interest semi-annually.

A)3.56 percent
B)6.76 percent
C)7.00 percent
D)7.12 percent $9,948.94 = $5,000

Question 5

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

A)$88
B)$100
C)$112
D)$200 The investment will again pay $100 plus interest on the previous interest:

Question 6

In most cases it will save money for consumers to select their loans based on the lowest:

A)Annual percentage rate
B)Effective annual rate
C)Number of compounding periods per year
D)Simple interest rate

Question 7

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

A)$107.69
B)$133.10
C)$134.49
D)$313.84 FV = PV (1 + r)²

Question 8

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

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

Question 9

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 percent compounded annually?

A)9
B)14
C)22
D)25 $3,000 = 1,000(1.08)ⁿ
3 = (1.08)ⁿ
14)27, or approx.14 yrs.= N

Question 10

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

A)4.02 percent
B)10.02 percent
C)14.50 percent
D)15.19 percent (1.1608).²⁵ = 1 + quarterly rate
1)0380 - 1 = quarterly rate
)0380 = quarterly rate

Question 11

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 12

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

A)$100.00
B)$105.17
C)$110.50
D)$115.70 Interest = $1,000 x e.¹ - $1,000
= $1,000 x 1.1052 - $1,000
= $1,105.17 - $1,000

Question 13

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 non-taxable to the investor
D)Interest is earned only on the original investment

Question 14

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

A)$70.00
B)$80.14
C)$105.62
D)$140.00 100 x (1.07)² = $1,144.90 after 2 years.

Question 15

If interest is paid m times per year, then the per-period interest rate equals the:

A)Effective annual rate divided by m
B)Compound interest rate times m
C)Effective annual rate
D)Annual percentage rate divided by m

Question 16

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

A)16.08 percent; 15.00 percent
B)14.55 percent; 16.08 percent
C)12.68 percent; 15.00 percent
D)15.00 percent; 14.55 percent Annually compounded rate = (1.0125)¹²-1 = 16.08%

Question 17

An interest rate that has been annualized using compound interest is termed the:

A)simple interest rate
B)Annual percentage rate
C)Discounted interest rate
D)Effective annual interest rate

Question 18

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

A)$87,200.00
B)$675,764.89
C)$736,583.73
D)$802,876.27 PV = 2000

Question 19

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

A)$7,472.58
B)$10,303.62
C)$13,000.00
D)$13,382.26 FV = PV + (PV x r x t)

Question 20

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 multi-year period of time
D)Determining the APR of the investment

Question 21

Other things being equal, the more frequent the compounding period, the:

A)Higher the APR
B)Lower the APR
C)Higher the effective annual interest rate
D)Lower the effective annual interest rate

Question 22

What is the APR on a loan with an effective annual rate of 15.01 percent and weekly compounding of interest?

A)12.00 percent
B)12.50 percent
C)13.00 percent
D)14.00 percent 1.1501 =

Question 23

What is the present value of the following payment stream, discounted at 8 percent 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 PV =

Question 24

Which account would be preferred by a depositor: an 8 percent APR with monthly compounding or 8.5 percent APR with semi-annual compounding?

A)8 percent with monthly compounding
B)8.5 percent with semi-annual compounding
C)The depositor would be indifferent
D)The time period must be known to select the preferred account (1.0667)¹²-1 = 8.3%
(1)0425)²-1 = 8.68%

Question 25

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

A)3 percent
B)4 percent
C)5 percent
D)6 percent $6,939.91 = $500/(1 + i)⁰ + $2,000/(1 + i)¹ + $5,000/(1 + i)²

Question 26

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 27

"Give me $5,000 today and I'll return $20,000 to you in five years," offers the investment broker.To the nearest percent, what annual interest rate is being offered?

A)25 percent
B)29 percent
C)32 percent
D)60 percent $5,000 =

Question 28

An APR will be equal to an effective annual rate if:

A)Simple interest is used
B)Compounding occurs continuously
C)Compounding occurs annually
D)An error has occurred; these terms cannot be equal

Question 29

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 percent compounded annually?

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

Question 30

A cash-strapped young professional offers to buy your car with four, equal annual payments of $3,000, beginning two years from today.Assuming you're indifferent to cash versus credit, that you can invest at 10 percent, 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 PV = $3,000 [1/.1-1/(.1 (1.1)⁴)]/1.1
= $3,000 [10-6.8301]/1.1
= $3,000 [3.1699]/1.1
= $9,509.60/1.1

Question 31

What is the effective annual interest rate on a 9 percent APR automobile loan that has monthly payments?

A)9.00 percent
B)9.38 percent
C)9.81 percent
D)10.94 percent Effective rate = (1 + (.09 + 12))¹²-1
= (1.0075)¹²-1
= 1)0938-1

Question 32

If a borrower promises to pay you $1,900 nine years from now in return for a loan of $1,000 today, what effective annual interest rate is being offered?

A)5.26 percent
B)7.39 percent
C)9.00 percent
D)10.00 percent PV =

Question 33

What is the present value of the following set of cash flows at an interest rate of 7 percent; $1,000 today, $2,000 at end of year one, $4,000 at end of year three, and $6,000 at end of year five?

A)$9,731
B)$10,412
C)$10,524
D)$11,524 PV = $1,000/(1.07)⁰ + $2,000/(1.07)¹ = $4,000/(1.07)³ + $6,000/(1.07)⁵
= $1,000 + 1,869.16 + 3,265.19 + 4,277.92

Question 34

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 35

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

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

Question 36

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

A)$130.00
B)$138.83
C)$169.00
D)$353.34 1000 (e.¹³) =
1000 x 1.1388 = $1,138.83

Question 37

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

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

Question 38

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

A).4693
B).5500
C).6000
D).6806 Discount factor = 1/ (1.08)⁵
= 1/1.4693

Question 39

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 percent
B)7.37 percent
C)8.00 percent
D)9.50 percent discount factor =

Question 40

What is the present value of $100 to be deposited today into an account paying 8.0 percent, compounded semi-annually for two years?

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

Question 41

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

A)$3,604,78
B)$3,746.25
C)$4,037.35
D)$4,604.78 PV =

Question 42

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

A)$297.21
B)$323.86
C)$356.85
D)$388.97 PV₁ = 100

Question 43

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 percent 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 PV = $500

Question 44

If $120,000 is borrowed for a home mortgage, to be repaid at 9 percent 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 a five period annuity of $3,000 if the interest rate is 12 percent and the first payment is made today?

A)$9,655.65
B)$10,814.33
C)$12,112.05
D)$13,200.00 PV = 3,000

Question 46

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

A)Approximately 268 payments
B)Approximately 180 payments
C)Approximately 92 payments
D)Approximately 68 payments $50,000 = $733.76 [1/.08-1/.08 (1.0067)ⁿ

Question 47

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 48

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 49

According to the Rule of 72, what approximate interest rate is being offered on a deposit that doubles in value over an eight-year period?

A)7.2 percent
B)8.0 percent
C)9.0 percent
D)12.5 percent

Question 50

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 51

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

A)6 percent
B)9 percent
C)11 percent
D)12 percent 21,000 = 522.59

Question 52

An amortizing loan is one in which:

A)Payments are made monthly
B)Accrued interest is paid regularly
C)The maturity of the loan is known
D)The principal balance is reduced with each payment

Question 53

A furniture store is offering free credit on purchases of 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 percent
B)The "free" credit costs about 9.13 percent
C)The "free" credit costs about 9.59 percent
D)The "free" credit effectively costs zero percent

Question 54

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 55

$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)$201.06
B)$500.00
C)$1,510.57
D)$2,010.57

Question 56

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 percent and payments begin in one month.What is the present value of this two-year loan?

A)$6,246.34
B)$6,389.78
C)$6,428.57
D)$6,753.05 PV = $200

Question 57

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

A)$70.00
B)$258.42
C)$629.56
D)$857.43 PV = $1,000/(1.07)²⁰
= $1,000/3.8697

Question 58

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

A)$33,333.33
B)$37,681.16
C)$38,333.33
D)$65,217.39 PV = $5,000 +

Question 59

$3,000 is deposited into an account paying 10 percent 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)$1,096.67
D)$587.32

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 percent interest rate and cash flows at end of period.

A)$297.29
B)$1,486.44
C)$1,635.08
D)$2,000.00 Difference= $1,000/.10 - $1,000[1/.10-1/.10(1.10)²⁰]
= $10,000 - $8,513.56

Question 61

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

A)5.00 percent
B)5.66 percent
C)6.00 percent
D)9.46 percent 1 + real rate = 1.12/1.06

Question 62

What is the minimum nominal rate of return should you accept, if you require a 4 percent real rate of return and the rate of inflation is expected to average 3.5 percent during the investment period?

A)7.36 percent
B)7.50 percent
C)7.64 percent
D)8.01 percent 1.04 =

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 percent annually, and the first payment occurs one year from now?

A)$1,067,000
B)$1,250,000
C)$2,315,000
D)$2,500,000 PV = $100,000
= $100,000 x (12.5 -1.8252)

Question 64

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

Question 65

Which of the following statements best describes the real interest rate?

A)Real interest rates exceed inflation rates
B)Real interest rates can decline only to zero
C)Real interest rates can be negative, zero, or positive
D)Real interest rates traditionally exceed nominal rates

Question 66

Appleton University seeks to setup a scholarship for its students in perpetuity.Every six months, $5,000 will be provided to students.If interest is 4.8% compounded monthly, determine the amount that must be invested in order to deliver on the semi-annual scholarship.

A)$206,260
B)$210,505
C)$212,222
D)$219,905

Question 67

Which of the following strategies will allow real retirement spending to remain approximately equal, assuming savings of $1,000,000 invested at 8 percent, a 25-year horizon, and 4 percent 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 Real Rate = -1 = 3.85%
$1,000,000 = pmt

Question 68

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

A)$771.46
B)$775.90
C)$1,028.61
D)$1,034.53 75,000 = PMT

Question 69

Assume your uncle recorded his salary history during a 40-year career and found that it had increased ten-fold.If inflation averaged 5 percent annually during the period, how would you describe his purchasing power, on average?

A)His purchasing power remained on par with inflation
B)He "beat" inflation by nearly 1 percent annually
C)He "beat" inflation by slightly over 2 percent annually
D)He "beat" inflation by 5 percent annually

Question 70

The present value of an annuity stream of $100 per year is $614 when valued at a 10 percent 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 71

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 percent interest.What is the approximate size of the mortgage with these terms?

A)$128,035
B)$147,940
C)$149,140
D)$393,120 PV = $1,200

Question 72

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 percent
B)7.24 percent
C)9.80 percent
D)10.07 percent

Question 73

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

A)$3,291
B)$3,587
C)$4,500
D)$4,587 $50,000 = pmt
= pmt
= pmt [15.1929]

Question 74

If inflation in Wonderland averaged about 20% per month in 2008, what was the annual inflation rate?

A)20%
B)240%
C)790%
D)890%

Question 75

How much must be deposited today in an account earning 6 percent annually to accumulate a 20 percent 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 percent?

A)$3,774
B)$3,782
C)$3,925
D)$4,080 Need $20,800 x .2 = $4,160
PV = $4,160/(1.06)

Question 76

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 77

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 percent interest with monthly compounding?

A)$261,500.00
B)$323,800.00
C)$578,700.00
D)$690,000.00 PV = $2,500
= $2,500 [149.925-20.405]
= $2,500 [129.52]

Question 78

You're ready to make the last of four equal, annual payments on a $1,000 loan with a 10 percent 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

Considering the past economic history of Canada, high rates of price inflation are typically accompanied by:

A)Low nominal interest rates
B)High nominal interest rates
C)Negative nominal interest rates
D)No correlation with nominal interest rates

Question 80

With $1.5 million in an account expected to earn 8 percent 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 $1,500,000 = pmt