Deck 5: The Time Value of Money

Question 1

When a loan is amortized over a five-year term, the ____.

A) rate of interest is reduced each year
B) amount of interest paid is reduced each year
C) payment is reduced each year
D) balance is paid as a balloon payment in the fifth year

Answer 1

B

Question 2

If the present value of a given sum is equal to its future value, then ____.

A) the discount rate must be very high
B) there is no inflation
C) the discount rate must be zero
D) None of these are correct

Answer 2

C

Question 3

When using a present value of an annuity table (e.g., Table IV at the back of the book), _____.

A) payments are assumed to be made at the beginning of each period
B) PVIFA factors decrease with an increase in the interest rate
C) PVIFA factors decrease with an increase in the number of periods
D) All of these are correct

Answer 3

B

Question 4

When using a future value of an annuity table (e.g., Table III at the back of the book), _____.

A) payments are assumed to be made at the end of each period
B) FVIFA factors increase with an increase in the interest rate
C) FVIFA factors increase with an increase in the number of periods
D) All of these are correct

Question 5

The future value of a single payment equation is given by ____.

A) FV_n = PV₀(PVIF_i,n)
B) FV_n = PV₀(FVIFA_i,n)
C) FV_n = PV₀(1/(1 + i)ⁿ)
D) FV_n = PV₀(FVIF_i,n)

Question 6

The more frequent the compounding, the _____.

A) greater the present value
B) greater the amount deposited
C) greater the effective interest rate
D) lesser the future value

Question 7

The present value of a single payment can be represented as _____.

A) ​PV₀ = FV_n ÷ (PVIF_i,n)
B) ​PV₀ = FV_n(PVIFA_i,n)
C) ​PV₀ = FV_n [1/(1 + i)ⁿ]
D) None of these are correct

Question 8

You have just won a $5 million lottery to be received in twenty annual equal payments of $250,000. What will happen to the present value of your winnings if the interest rate increases during the next 20 years?

A) It will be worth less.
B) It will be worth more.
C) It will not change.
D) It will increase during the first ten years.

Question 9

The amount of simple interest is equal to the product of the principal times ____ times ____.

A) (1 + rate per time period); the number of time periods
B) (1 + rate per time period); (the number of time periods - 1)
C) rate per time period; the number of time periods
D) rate per time period; (the number of time periods - 1)

Question 10

The present value of an ordinary annuity is the ____.

A) sum of the present value of a series of equal periodic payments
B) future value of an equal series of payments
C) receipt of equal cash flows for a specified amount of time
D) sum of the future value of an equal series of payments

Question 11

An annuity due is one in which _____.

A) payments or receipts occur at the end of each period
B) payments or receipts occur at the beginning of each period
C) payments or receipts occur forever
D) cash flows occur continuously

Question 12

The process of finding present values is frequently called ____.

A) annualizing
B) compounding
C) discounting
D) leasing

Question 13

Finding the discounted current value of $1,000 to be received at the end of each of the next 5 years requires calculating the ____.

A) future value of an annuity
B) future value of an annuity due
C) present value of an annuity
D) present value of an annuity due

Question 14

The present value of a single payment can be represented as ____.

A) PV₀ = FV_n(PVIF_i,n)
B) PV₀ = FV_n(PVIFA_i,n)
C) PV₀ = FV_n[1/(1 - i)ⁿ]
D) None of these are correct

Question 15

A(n) ____ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e., forever).

A) annuity
B) annuity due
C) sinking fund
D) perpetuity

Question 16

The values shown in ordinary annuity tables (either present value or compound value) can be adjusted to the annuity due form by ____ the ordinary annuity interest factor by ____.

A) dividing; (1 + i)
B) dividing; (1 + i)ⁿ
C) multiplying; (1 + i)
D) multiplying; (1 + i)ⁿ

Question 17

Finding the compound sum of $1,000 to be received at the beginning of each of the next 5 years requires calculating the _____.

A) future value of an annuity
B) present value of an annuity
C) future value of an annuity due
D) present value of an annuity due

Question 18

The effective rate of interest will always be ____ the nominal rate.

A) greater than
B) equal to
C) less than
D) equal to or greater than

Question 19

Using the "Rule of 72," about how long will it take a sum of money to double in value if the annual interest rate is 9 percent?

A) 9 years
B) 7 years
C) 8 years
D) 10 years

Question 20

Annuity due calculations are especially important when dealing with ____.

A) term loans
B) lease contracts
C) capital investments
D) capital recovery problems

Question 21

The difference between an ordinary annuity and an annuity due is the _____.

A) interest rate
B) timing of the payments
C) amount of the payments
D) number of periods

Question 22

Comet Powder Company has purchased a piece of equipment costing $100,000. It is expected to generate a ten-year stream of benefits amounting to $16,273 per year. Determine the rate of return Comet expects to earn from this equipment.

A) 16.3%
B) 62.7%
C) 10%
D) 20%

Question 23

____ is the return earned by someone who has forgone current consumption.

A) The present value
B) Principle
C) An annuity
D) Interest

Question 24

Determine how much $1,000 deposited in a savings account paying 8% (compounded annually) will be worth after 5 years.

A) $5,526
B) $784
C) $1,400
D) $1,469

Question 25

Determine how much you would be willing to pay for a bond that pays $60 annual interest indefinitely and never matures (i.e., a perpetuity), assuming you require an 8 percent rate of return on this investment.

A) $480
B) $743
C) $1,000
D) $750

Question 26

Air Atlantic (AA) has been offered a 3-year-old jet airliner under a 12-year lease arrangement. The lease requires AA to make annual lease payments of $500,000 at the beginning of each of the next 12 years. Determine the present value of the lease payments if the opportunity cost of funds is 14 percent.

A) $2,830,000
B) $13,635,500
C) $6,000,000
D) $3,226,200

Question 27

Mr. Moore is 35 years old today and is beginning to plan for his retirement. He wants to set aside an equal amount at the end of each of the next 25 years so that he can retire at age 60. He expects to live to the maximum age of 80 and wants to be able to withdraw $25,000 per year from the account on his 61st through 80th birthdays. The account is expected to earn 10 percent per annum for the entire period of time. Determine the size of the annual deposits that must be made by Mr. Moore.

A) $212,850
B) $23,449
C) $2,164
D) $8,514

Question 28

The payment or receipt of a series of equal cash flows per period, at the end of each period, for a specified amount of time is called a(n) ____.

A) annuity due
B) perpetuity
C) ordinary annuity
D) simple interest

Question 29

The earnings of Omega Supply Company have grown from $2.00 per share to $4.00 per share over a nine-year time period. Determine the compound annual growth rate.

A) 11.1%
B) 8%
C) 22.2%
D) 100%

Question 30

The annual effective rate of interest (i_eff) is a function of _____.

A) the annual nominal rate of interest (i_nom) only
B) the number of compounding intervals per year (m) only
C) the number of years (n) only
D) both the nominal rate of interest and the number of compounding periods per year

Question 31

More frequent compounding results in ____ future values and ____ present values than does less frequent compounding at the same interest rate.

A) higher; higher
B) lower; higher
C) higher; lower
D) lower; lower

Question 32

The ____ of a perpetual stream of equal, annual returns (PMT) discounted at i% per year is equal to ____.

A) present value; PMT/i
B) present value; PMT × i
C) future value; PMT/i
D) future value; PMT × i

Question 33

An annuity that begins more than 1 year in the future is referred to as a(n) ____.

A) perpetuity
B) annuity due
C) uneven annuity
D) deferred annuity

Question 34

Annuity due calculations are common when dealing with _____.

A) cash dividends
B) loan repayments
C) rental contracts
D) interest payments

Question 35

Your grandparents put $1,000 into a savings account for you when you were born 20 years ago. This account has been earning interest at a compound rate of 7 percent. What is its value today?

A) $3,870
B) $1,967
C) $3,026
D) $3,583

Question 36

Which of the following is worth more?

A) Future value of an ordinary annuity of PMT dollars per year for n years discounted at i percent
B) Future value of an annuity due of PMT dollars per year for n years discounted at i percent
C) Both are worth the same amount
D) Cannot be determined from the information given

Question 37

You sold 100 shares of stock today for $30 per share that you paid $20 for 6 years ago. Determine the average annual rate of return on your investment, assuming the stock paid no dividends.

A) 25%
B) 8.33%
C) 150%
D) 7%

Question 38

If you invest $10,000 in a 4-year certificate of deposit (CD) paying 10 percent interest compounded annually, determine how much the CD will be worth at the end of 4 years.

A) $13,600
B) $45,730
C) $14,640
D) $15,958

Question 39

The present value of a(n) ____ is determined by dividing the annual cash flow by the interest rate.

A) annuity
B) annuity due
C) perpetuity
D) lease

Question 40

____ interest is paid not only on the principal but also on any interest earned but not withdrawn during earlier periods.

A) Basic
B) Simple
C) Future
D) Compound

Question 41

An insurance company offers you an end-of-year annuity of $48,000 per year for the next 20 years. They claim your return on the annuity is 9 percent. What should you be willing to pay today for this annuity?

A) $429,600
B) $438,192
C) $408,672
D) $398,144

Question 42

Your firm, New Sunrise, has just leased a $28,000 BMW for you. The lease requires six beginning-of-the-year payments that will fully amortize the cost of the car. What is the amount of the payments if the interest rate is 12 percent?

A) $6,810.99
B) $7,766.99
C) $6,423.74
D) $6,081.25

Question 43

Idlewild Bank has granted you a seven-year loan for $50,000. If your seven annual end-of-the-year payments are $11,660.45, what is the rate of interest Idlewild is charging?

A) 14%
B) 23%
C) 12.6%
D) 11%

Question 44

BB&C bank has agreed to lend you $30,000 today, but you must repay $42,135 in 3 years. What rate is the bank charging you?

A) 10%
B) 11%
C) 12%
D) 13%

Question 45

In six years, your daughter will be going to college. You wish to have a fund that will provide her $10,000 per year (end of year) for each of her four years in college. How much must you put into that fund today if the fund will earn 10 percent in each of the 10 years?

A) $29,744.65
B) $29,783.76
C) $17,878.80
D) $21,651.10

Question 46

The lease on a new office requires an immediate payment of $24,000 plus $24,000 per year at the end of each of the next 10 years. At a discount rate of 14 percent, what is the present value of this stream of lease payments?

A) $130,872
B) $149,194
C) $142,710
D) $264,000

Question 47

You have just won a $50,000 bond that pays no interest and matures in 20 years. If the discount rate is 10%, what is the present value of your bond?

A) $7,450
B) $8,175
C) $8,900
D) $1,490

Question 48

Columbia Bank & Trust has just given you a $20,000 term loan to pay for a new concrete mixer. The loan requires five equal annual end-of-the-year payments. If the loan provides the bank with a 12 percent return, what will be your annual payments?

A) $5,547.85
B) $3,148.12
C) $6,000
D) $1,666.67

Question 49

New Jersey Mutual has offered you a single premium annuity that will pay you $12,000 per year (end of year) for the next 15 years. If you must pay $109,296 today for this annuity, what is your expected rate of return?

A) 8%
B) 9%
C) 7%
D) 10%

Question 50

Joe Brady just won a $450,000 lottery in Pennsylvania. Instead of receiving a lump sum, he found that he would receive $22,500 annually (end of year) for 20 years. Joe is 75 years old and wants his money now. He has been offered $140,827 to sell his ticket. What rate of return is the buyer expecting to make if Joe accepts the offer?

A) less than 1%
B) 15%
C) 18%
D) 12%

Question 51

Alabama Power has preferred stock that pays an annual dividend of $9.44. If the security has no maturity, what is its value to an investor who wishes to obtain a 9 percent rate of return?

A) $84.96
B) $104.89
C) $95.34
D) $94.40

Question 52

Baggos has seen its EPS increase from $0.30 to $3.16 in seven years. What has been the growth rate of Baggos's EPS?

A) about 30%
B) about 40%
C) about 20%
D) about 10%

Question 53

John is 25 years old and wishes to retire in 30 years. His plan is to invest in a mutual fund earning a 12 percent annual return and have a $1 million retirement fund at age 55. How much must he invest at the end of each year to achieve this goal?

A) $7,499.96
B) $5,024.60
C) $4,143.65
D) $33,333.33

Question 54

Designs Now is opening a showcase office to display and sell its computer-designed poster art. Designs expects cash flows to be $120,000 in the first year, $180,000 in the second year, $240,000 in the third year. If Designs uses 11 percent as its discount rate, what is the present value of the cash flows?

A) $429,720
B) $457,620
C) $456,000
D) $424,820

Question 55

What is the effective rate of interest on a CD that has a nominal rate of 9.5 percent with interest compounded monthly?

A) 9.93%
B) 9.74%
C) 10.02%
D) 9.86%

Question 56

The Florida lottery agrees to pay the winner $250,000 at the end of each year for the next 20 years. What is the future value of this lottery if you plan to put each payment in an account earning 9 percent?

A) $2.28 million
B) $12.79 million
C) $14.32 million
D) $ 5.00 million

Question 57

Jane wants to have $200,000 in an account in 20 years. If her account earns 11 percent per annum over the accumulation period, how much must she save per year (end of year) to have the $200,000?

A) $25,116
B) $3,115
C) $10,000
D) $3,492

Question 58

Many IRA fund managers argue that investors should invest at the beginning of the year rather than at the end. What is the difference to an investor who invests $2,000 per year at 11 percent over a 30-year period?

A) $43,785
B) $36,189
C) $54,244
D) There is no difference

Question 59

Billy Bob has decided to put $2,400 a year (at the end of each year) into an IRA over his 40-year working life and then retire. What will Billy have if the account will earn 10 percent compounded annually?

A) $394,786
B) $23,470
C) $1,062,223
D) $810,917

Question 60

What is the future value of a $10,000 college tuition fund if the nominal rate of interest is 12 percent compounded monthly for five years?

A) $17,623.42
B) $18,170
C) $16,105.10
D) $16,122.26

Question 61

When using a financial calculator, PV stands for the ____.

A) interest rate per period
B) number of periods
C) present value amount
D) future value amount

Question 62

John borrowed $20,000 to finance his college education. If the finance charge on the loan is 6 percent, and he will pay off the loan in 10 equal, annual, end-of-year payments, how much total interest will he pay?

A) $7,173.90
B) $2,717.39
C) $12,000.00
D) $25,924.23

Question 63

Seebee makes quarterly (end-of-period) payments of $30,000 into a pension fund earning 12 percent per year compounded quarterly for 10 years. How much interest will it have earned in 10 years?

A) $2,262,030
B) $2,105,880
C) $905,880
D) $1,062,030

Question 64

When using a financial calculator, n stands for the ____.

A) interest rate per period
B) number of periods
C) present value amount
D) future value amount

Question 65

You just purchased a new $25,000 car and agreed to pay for the car in 50 monthly payments. If the monthly interest rate is 1 percent, what is your total financing cost?

A) $637.82
B) $12,500
C) $574.25
D) $6,891

Question 66

Your local bank offers 4-year certificates of deposit (CD) at a 12 percent annual nominal interest rate compounded quarterly. Determine how much additional interest you will earn over 4 years on a $10,000 CD that is compounded quarterly compared with one that is compounded annually.

A) $6,050
B) $0
C) $310
D) $220

Question 67

How much will you have at the end of 5 years in a European vacation account if you deposit $200 a month in an account that is paying a nominal 12 percent per year, compounded monthly?

A) $16,334
B) $15,247
C) $16,497
D) $15,817

Question 68

When using a financial calculator, FV stands for the ____.

A) interest rate per period
B) number of periods
C) present value amount
D) future value amount

Question 69

Jackie plans to open her own bookstore in 10 years. To raise the "seed" money, she has committed the $10,000 she now has in a mutual fund. In addition, she plans to save $2,000 per year (end of year) for the next 5 years and $3,000 per year (end of year) for the following 5 years. How much "seed" money will Jackie have in 10 years if the investments earn 10 percent per year compounded annually?

A) $76,129
B) $63,925
C) $44,255
D) $159,370

Question 70

What is the most you should pay to receive the following cash flows if your required rate of return is 12 percent? $\begin{array}{ll}\text { Year 1 } & \$ 5,000 \\\text { Year 2 } & \$ 8,000 \\\text { Year 3 } & \$ 12,000 \\\text { Years 4-10 } & \$ 15,000\end{array}$

A) $58,580
B) $104,135
C) $68,105
D) $40,000

Question 71

Your brother, who is 6 years old, just received a trust fund that will be worth $25,000 when he is 21 years old. If the fund earns 10 percent interest compounded annually, what is the value of the fund today?

A) $104,602
B) $6,575
C) $5,975
D) $6,875

Question 72

Five years after an accident, you received $100,000 to pay the medical expenses incurred at the time of the accident. What is the present value (at the time of the accident) of the payment? Assume interest rates are 9%.

A) $153,900
B) $68,100
C) $65,000
D) $70,800

Question 73

You wish to save $500,000 in the next 25 years. You put your savings into a corporate bond fund that earns about 11 percent per year. How much must you save each year to obtain your goal?

A) $20,000.00
B) $3,749.98
C) $4,370.13
D) $2,000.00

Question 74

A bank has agreed to loan you $10,000 at 11% for 5 years. You are required to make equal, annual, end-of-year payments that include both principal and interest on the outstanding balance. Determine the amount of these annual payments (to the nearest dollar).

A) $2,000
B) $3,100
C) $2,706
D) $1,100

Question 75

You purchased a piece of property for $30,000 nine years ago and sold it today for $83,190. What was the rate of return on your investment?

A) 12%
B) 11%
C) 10%
D) 9%

Question 76

Calculate the present value of the following net cash flows if the discount rate is 12%. $$\begin{array} { l l } \text { Year } & \text { Cash Flow } \\1 - 5 & \$ 10,000 \text { each year } \\6 - 10 & \$ 15,000 \text { each year } \\11 - 15 & \$ 17,000 \text { each year }\end{array}$$

A) $151,400
B) $86,462
C) $144,037
D) $79,252

Question 77

If you invest the $10,000 you receive at graduation (age 22) in a mutual fund that averages a 12% annual return, how much will you have at retirement in 40 years?

A) $909,090
B) $930,510
C) $783,879
D) $510,285

Question 78

Roy, who has just turned 40, would like to have an annual annuity of $20,000 paid over a 20-year period, the first payment occurring on his 66th birthday. How much must Roy save each year (end of year) for the next 25 years to have this annuity, if the investment will earn 12 percent compounded annually?

A) $16,000
B) $19,046
C) $1,120
D) $944.10

Question 79

If the discount rate is 12%, what is the present value of the following cash flows? $$\begin{array} { l l } \text { Year } & \text { Cash Flow } \\1 & \$ 10,000 \\2 & \$ 11,000 \\3 & \$ 12,000 \\4 & \$ 13,000 \\5 & \$ 14,000 \\6 - 15 & \$ 15,000 \text { each year }\end{array}$$

A) $144,618
B) $127,923
C) $127,197
D) $90,537

Question 80

When using a financial calculator, i stands for the ____.

A) interest rate per period
B) number of periods
C) present value amount
D) future value amount