Deck 4: Introduction to Valuation: The Time Value of Money

Question 1

The interest rate used to compute the present value of a future cash flow is called the:

A)prime rate.
B)current rate.
C)discount rate.
D)compound rate.
E)simple rate.

Answer 1

discount rate.

Question 2

Terry invested $2,000 today in an investment that pays 6.5 percent annual interest.Which one of the following statements is correct,assuming all interest is reinvested?

A)Terry will earn the same amount of interest each year.
B)Terry could have the same future value and invest less than $2,000 initially if he could earn more than 6.5 percent interest.
C)Terry will earn an increasing amount of interest each and every year even if he should decide to withdraw the interest annually rather than reinvesting the interest.
D)Terry's interest for year two will be equal to $2,000 × 0.065 × 2.
E)Terry will be earning simple interest.

Answer 2

Terry could have the same future value and invest less than $2,000 initially if he could earn more than 6.5 percent interest.

Question 3

Jenny needs to borrow $16,000 for 3 years.The loan will be repaid in one lump sum at the end of the loan term.Which one of the following interest rates is best for Jenny?

A)8 percent simple interest
B)8 percent interest, compounded annually
C)8.5 percent simple interest
D)8.5 percent interest, compounded annually
E)9 percent interest, compounded annually

Answer 3

8 percent simple interest

Question 4

Todd will be receiving a $10,000 bonus one year from now.The process of determining how much that bonus is worth today is called:

A)aggregating.
B)discounting.
C)simplifying.
D)compounding.
E)extrapolating.

Question 5

Lester had $6,270 in his savings account at the beginning of this year.This amount includes both the $6,000 he originally invested at the beginning of last year plus the $270 he earned in interest last year.This year,Lester earned a total of $282.15 in interest even though the interest rate on the account remained constant.This $282.15 is best described as:

A)simple interest.
B)interest on interest.
C)discounted interest.
D)complex interest.
E)compound interest.

Question 6

Martha is investing $5 today at 6 percent interest so she can have $10 later.The $10 is referred to as the:

A)true value.
B)future value.
C)present value.
D)discounted value.
E)complex value.

Question 7

Computing the present value of a future cash flow to determine what that cash flow is worth today is called:

A)compounding.
B)factoring.
C)time valuation.
D)simple cash flow valuation.
E)discounted cash flow valuation.

Question 8

Which of the following will increase the future value of a lump sum investment?
I.Decreasing the interest rate
II.Increasing the interest rate
III.Increasing the time period
IV.Decreasing the amount of the lump sum investment

A)I and III only
B)I and IV only
C)II and III only
D)II and IV only
E)II, III, and IV only

Question 9

Sue needs to invest $3,626 today in order for her savings account to be worth $5,000 six years from now.Which one of the following terms refers to the $3,626?

A)Present value
B)Compound value
C)Future value
D)Complex value
E)Factor value

Question 10

Which one of the following will increase the present value of a lump sum future amount? Assume the interest rate is a positive value and all interest is reinvested.

A)Increase in the time period
B)Increase in the interest rate
C)Decrease in the future value
D)Decrease in the interest rate
E)None of these

Question 11

Sam wants to invest $5,000 for 5 years.Which one of the following rates will provide him with the largest future value?

A)5 percent simple interest
B)5 percent interest, compounded annually
C)6 percent interest, compounded annually
D)7 percent simple interest
E)7 percent interest, compounded annually

Question 12

Sara is investing $1,000 today.Which one of the following will increase the future value of that amount?

A)Shortening the investment time period.
B)Paying interest only on the principal amount.
C)Paying simple interest rather than compound interest.
D)Paying interest only at the end of the investment period rather than throughout the investment period.
E)Increasing the interest rate.

Question 13

By definition,a bank that pays simple interest on a savings account will pay interest:

A)only at the beginning of the investment period.
B)on interest.
C)only on the principal amount originally invested.
D)on both the principal amount and the reinvested interest.
E)only if all previous interest payments are reinvested.

Question 14

Which of the following will decrease the future value of a lump sum investment made today assuming that all interest is reinvested? Assume the interest rate is a positive value.
I.Increase in the interest rate
II.Decrease in the lump sum amount
III.Increase in the investment time period
IV.Decrease in the investment time period

A)I and III only
B)I and IV only
C)I, II, and III only
D)II and III only
E)II and IV only

Question 15

Jamie earned $180 in interest on her savings account last year.She has decided to leave the $180 in her account so that she can earn interest on the $180 this year.The interest Jamie earns this year on this $180 is referred to as:

A)simple interest.
B)complex interest.
C)accrued interest.
D)interest on interest.
E)discounted interest.

Question 16

Tom earned $120 in interest on his savings account last year.Tom has decided to leave the $120 in his account so that he can earn interest on the $120 this year.This process of earning interest on prior interest earnings is called:

A)discounting.
B)compounding.
C)duplicating.
D)multiplying.
E)indexing.

Question 17

Given an interest rate of zero percent,the future value of a lump sum invested today will always:

A)remain constant, regardless of the investment time period.
B)decrease if the investment time period is shortened.
C)decrease if the investment time period is lengthened.
D)be equal to $0.
E)be infinite in value.

Question 18

Jeff deposits $3,000 into an account which pays 2.5 percent interest,compounded annually.At the same time,Kurt deposits $3,000 into an account paying 5 percent interest,compounded annually.At the end of three years:

A)Both Jeff and Kurt will have accounts of equal value.
B)Kurt will have twice the money saved that Jeff does.
C)Kurt will earn exactly twice the amount of interest that Jeff earns.
D)Kurt will have a larger account value than Jeff will.
E)Jeff will have more money saved than Kurt.

Question 19

Which one of the following is the correct formula for the future value of $500 invested today at 7 percent interest for 8 years?

A)FV = $500/[(1 + 0.08) × 7]
B)FV = $500/[(1 + 0.07) × 8]
C)FV = $500/(0.07 × 8)
D)FV = $500 (1 + 0.07)⁸
E)FV = $500 (1 + 0.08)⁷

Question 20

Lisa has $1,000 in cash today.Which one of the following investment options is most apt to double her money?

A)6 percent interest for 3 years
B)12 percent interest for 5 years
C)7 percent interest for 9 years
D)8 percent interest for 9 years
E)6 percent interest for 10 years

Question 21

You just won $50,000 and deposited your winnings into an account that pays 5.5 percent interest,compounded annually.How long will you have to wait until your winnings are worth $100,000?

A)11.24 years
B)12.00 years
C)12.29 years
D)12.67 years
E)12.95 years

Question 22

When you were born,your parents opened an investment account in your name and deposited $500 into the account.The account has earned an average annual rate of return of 4.8 percent.Today,the account is valued at $36,911.22.How old are you?

A)74.47 years
B)76.67 years
C)81.08 years
D)87.33 years
E)91.75 years

Question 23

Precision Engineering invested $110,000 at 6.5 percent interest,compounded annually for 4 years.How much interest on interest did the company earn over this period of time?

A)$2,481.25
B)$2,911.30
C)$3,014.14
D)$3,250.00
E)$3,333.33

Question 24

Which one of the following is the correct formula for computing the present value of $600 to be received in 6 years? The discount rate is 7 percent.

A)PV = $600 (1 + 6)⁷
B)PV = $600 (1 + 0.07)⁶
C)PV = $600 × (0.07 × 6)
D)PV = $600/(1 + 0.07)⁶
E)PV = $600/(1 + 6)^0.07

Question 25

Twelve years ago,you deposited $3,400 into an account.Seven years ago,you added an additional $1,000 to this account.You earned 8 percent,compounded annually,for the first 5 years and 5.5 percent,compounded annually,for the last 7 years.How much money do you have in your account today?

A)$5,666.67
B)$6,717.29
C)$7,411.90
D)$8,708.15
E)$8,721.97

Question 26

Your grandparents just gave you a gift of $15,000.You are investing this money for 12 years at 6 percent simple interest.How much money will you have at the end of the 12 years?

A)$15,900
B)$16,000
C)$17,375
D)$25,800
E)$26,938

Question 27

Centre Bank pays 2.5 percent interest,compounded annually,on its savings accounts.Country Bank pays 2.5 percent simple interest on its savings accounts.You want to deposit sufficient funds today so that you will have $1,500 in your account 2 years from today.The amount you must deposit today:

A)is the same regardless of which bank you choose because they both pay compound interest.
B)is the same regardless of which bank you choose because they both pay simple interest.
C)is the same regardless of which bank you choose because the time period is the same for both banks.
D)will be greater if you invest with Centre Bank.
E)will be greater if you invest with Country Bank.

Question 28

Which one of the following is a correct statement,all else held constant?

A)The present value is inversely related to the future value.
B)The future value is inversely related to the period of time.
C)The period of time is directly related to the interest rate.
D)The present value is directly related to the interest rate.
E)The future value is directly related to the interest rate.

Question 29

Angela has just received an insurance settlement of $35,000.She wants to save this money until her daughter goes to college.If she can earn an average of 5.5 percent,compounded annually,how much will she have saved when her daughter enters college 10 years from now?

A)$48,000.00
B)$50,929.02
C)$51,374.89
D)$59,875.06
E)$59,785.06

Question 30

The relationship between the present value and the time period is best described as:

A)direct.
B)inverse.
C)unrelated.
D)ambiguous.
E)parallel.

Question 31

Jim just deposited $13,000 into his account at Traditions Bank.The bank will pay 1.3 percent interest,compounded annually,on this account.How much interest on interest will he earn over the next 15 years?

A)$238.16
B)$244.20
C)$360.70
D)$606.15
E)$623.70

Question 32

Your parents spent $6,200 to buy 500 shares of stock in a new company 13 years ago.The stock has appreciated 9 percent per year on average.What is the current value of those 500 shares?

A)$18,824.17
B)$19,007.99
C)$19,580.92
D)$20,515.08
E)$22,449.92

Question 33

Ben invested $5,000 twenty years ago with an insurance company that has paid him 5 percent simple interest on his funds.Charles invested $5,000 twenty years ago in a fund that has paid him 5 percent interest,compounded annually.How much more interest has Charles earned than Ben over the past 20 years?

A)$0
B)$2,109.16
C)$3,266.49
D)$7,109.16
E)$8,266.49

Question 34

Travis invests $10,000 today into a retirement account.He expects to earn 8 percent,compounded annually,on his money for the next 26 years.After that,he wants to be more conservative,so only expects to earn 5 percent,compounded annually.How much money will he have in his account when he retires 38 years from now,assuming this is the only deposit he makes into the account?

A)$129,411.20
B)$132,827.88
C)$134,616.56
D)$141,919.67
E)$142,003.12

Question 35

Today,you deposit $2,400 in a bank account that pays 4 percent simple interest.How much interest will you earn over the next 5 years?

A)$96.00
B)$101.15
C)$480.00
D)$492.16
E)$519.97

Question 36

Eric has $4,800 that he wants to invest for 4 years.He can invest this amount at his credit union and earn 4 percent simple interest.Or,he can open an account at Compass Bank and earn 3.65 percent interest,compounded annually.If he decides to invest at Copmpass Bank for 3 years,he will:

A)earn $15.02 more than if he had invested with his credit union.
B)earn $27.89 less than if he had invested with his credit union.
C)earn the same amount as if he had invested with the credit union.
D)have a total balance of $4,992 in his account after one year.
E)have a total balance of $4,876 in his account after one year.

Question 37

Today,Courtney wants to invest less than $5,000 with the goal of receiving $5,000 back some time in the future.Which one of the following statements is correct?

A)The period of time she has to wait until she reaches her goal is unaffected by the compounding of interest.
B)The lower the rate of interest she earns, the shorter the time she will have to wait to reach her goal.
C)She will have to wait longer if she earns 6 percent compound interest instead of 6 percent simple interest.
D)The length of time she has to wait to reach her goal is directly related to the interest rate she earns.
E)The period of time she has to wait decreases as the amount she invests today increases.

Question 38

What is the future value of $4,900 invested for 8 years at 7 percent compounded annually?

A)$8,397.74
B)$8,419.11
C)$8,511.15
D)$8,513.06
E)$8,520.22

Question 39

The present value of a lump sum future amount:

A)increases as the interest rate decreases.
B)decreases as the time period decreases.
C)is inversely related to the future value.
D)is directly related to the interest rate.
E)is directly related to the time period.

Question 40

You want to invest an amount of money today and receive back twice that amount in the future.You expect to earn 6 percent interest.Approximately how long must you wait for your investment to double in value?

A)6 years
B)7 years
C)8 years
D)12 years
E)14 years

Question 41

Skyline Industries will need $1.8 million 5 years from now to replace some equipment.Currently,the firm has some extra cash and would like to establish a savings account for this purpose.The account pays 5.25 percent interest,compounded annually.How much money must the company deposit today to fully fund the equipment purchase?

A)$1,279,947.20
B)$1,298,407.21
C)$1,350,868.47
D)$1,393,676.52
E)$1,412,308.18

Question 42

Sixty years ago,your grandparents opened two savings accounts and deposited $200 in each account.The first account was with City Bank at 3 percent,compounded annually.The second account was with Country Bank at 3.5 percent,compounded annually.Which one of the following statements is true concerning these accounts?

A)The City Bank account is currently worth $1,201.54.
B)The City Bank account has earned $211.19 more in interest than the Country Bank account.
C)The Country Bank account is currently worth $1,526.08.
D)The Country Bank account has paid $367.48 more in interest than the City Bank account.
E)The Country Bank account has paid $397.30 more in interest than the City Bank account.

Question 43

You want to have $25,000 for a down payment on a house 6 years from now.If you can earn 6.5 percent,compounded annually,on your savings,how much do you need to deposit today to reach your goal?

A)$17,133.35
B)$17,420.73
C)$17,880.69
D)$18,211.17
E)$18,886.40

Question 44

Your coin collection contains ten 1939 silver dollars.If your great grandparents purchased them for their face value when they were new,how much will your collection be worth when you retire in 2050,assuming they appreciate at a 5.1 percent annual rate?

A)$2,243.63
B)$2,329.29
C)$2,348.98
D)$2,499.78
E)$2,644.29

Question 45

Your friend claims that he invested $5,000 seven years ago and that this investment is worth $38,700 today.For this to be true,what annual rate of return did he have to earn? Assume the interest compounds annually.

A)28.87 percent
B)31.39 percent
C)33.96 percent
D)36.01 percent
E)37.87 percent

Question 46

Ten years from now,you will be inheriting $100,000.What is this inheritance worth to you today if you can earn 5.5 percent interest,compounded annually?

A)$58,543.06
B)$63,215.46
C)$72,419.05
D)$72,798.47
E)$74,003.15

Question 47

At 10 percent interest,how long does it take to quadruple your money?

A)14.33 years
B)14.55 years
C)15.11 years
D)15.36 years
E)15.56 years

Question 48

You have been told that you need $25,600 today in order to have $100,000 when you retire 35 years from now.What rate of interest was used in the present value computation? Assume interest is compounded annually.

A)3.97 percent
B)4.15 percent
C)4.29 percent
D)4.53 percent
E)4.58 percent

Question 49

You want to have $45,000 in cash to buy a car 4 years from today.You expect to earn 4.5 percent,compounded annually,on your savings.How much do you need to deposit today if this is the only money you save for this purpose?

A)$33,618.92
B)$34,511.68
C)$35,726.04
D)$37,735.26
E)$38,156.19

Question 50

Today,Stacy is investing $26,000 at 6.0 percent,compounded annually,for 4 years.How much additional income could he earn if he had invested this amount at 7 percent,compounded annually?

A)$1,043.11
B)$1,256.30
C)$1,401.16
D)$1,442.79
E)$1,484.08

Question 51

Isaac only has $690 today but needs $800 to buy a new laptop.How long will he have to wait to buy the laptop if he earns 5.4 percent compounded annually on his savings?

A)2.29 years
B)2.48 years
C)2.51 years
D)2.77 years
E)2.81 years

Question 52

You have $1,100 today and want to triple your money in 5 years.What interest rate must you earn if the interest is compounded annually?

A)18.08 percent
B)19.90 percent
C)22.15 percent
D)24.57 percent
E)27.21 percent

Question 53

You're trying to save to buy a new $210,000 Ferrari.You have $38,000 today that can be invested at your bank.The bank pays 4.1 percent annual interest on its accounts.How long will it be before you have enough to buy the car?

A)39.13 years
B)39.29 years
C)40.67 years
D)41.08 years
E)42.54 years

Question 54

Planters Bank pays 5 percent simple interest on its savings account balances,whereas Centura Bank pays 5 percent compounded annually.If you made a $12,000 deposit in each bank,how much more money would you earn from your Centura Bank account at the end of 20 years?

A)$7,155.84
B)$7,839.57
C)$7,960.47
D)$8,400.09
E)$8,784.14

Question 55

You have $1,500 today in your savings account.How long must you wait for your savings to be worth $4,000 if you are earning 1.1 percent interest,compounded annually?

A)76.68 years
B)79.69 years
C)72.13 years
D)80.57 years
E)89.66 years

Question 56

How long will it take to double your savings if you earn 7.2 percent interest,compounded annually?

A)8.89 years
B)9.02 years
C)9.34 years
D)9.97 years
E)11 years

Question 57

You and your sister are planning a large anniversary party 3 years from today for your parents' 50^th wedding anniversary.You have estimated that you will need $4,500 for this party.You can earn 2.5 percent compounded annually on your savings.How much would you and your sister have to deposit today in one lump sum to pay for the entire party?

A)$4,076.55
B)$4,178.70
C)$4,308.16
D)$4,334.90
E)$4,368.81

Question 58

You have just made your first $5,000 contribution to your individual retirement account.Assuming you earn a 5 percent rate of return and make no additional contributions,what will your account be worth when you retire in 35 years? What if you wait for 5 years before contributing?

A)$26,335.37; $23,011.60
B)$27,311.20; $29,803.04
C)$27,311.20; $22,614.08
D)$27,580.08; 21,609.71
E)$31,241.90; $32,614.08

Question 59

Assume the total cost of a college education will be $285,000 when your child enters college in 22 years.You presently have $35,000 to invest.What annual rate of interest must you earn on your investment to cover the cost of your child's college education?

A)8.65 percent
B)9.40 percent
C)10.00 percent
D)10.60 percent
E)11.00 percent

Question 60

Suppose that in 2010,a $10 silver certificate from 1898 sold for $11,200.For this to have been true,what would the annual increase in the value of the certificate have been?

A)6.47 percent
B)6.81 percent
C)7.23 percent
D)7.49 percent
E)7.97 percent

Question 61

You have $5,000 you want to invest for the next 45 years.You are offered an investment plan that will pay you 6 percent per year for the next 15 years and 10 percent per year for the last 30 years.How much will you have at the end of the 45 years? How much will you have if the investment plan pays you 10 percent per year for the first 15 years and 6 percent per year for the next 30 years?

A)$201,516.38; $201,516.38
B)$209,092.54; $201,516.38
C)$209,092.54; $119,959.94
D)$209,092.54; $209,092.52
E)$221,408.97; $119,949.94

Question 62

You want to have $2.5 million saved on the day you retire.Explain how you can minimize the amount of cash you must invest in order to achieve this goal.

Question 63

Draw a graph that illustrates the relationship between interest rates and the present value of $1,000 to be received in one year.

Question 64

You are scheduled to receive $7,500 in three years.When you receive it,you will invest it for eight more years at 7.5 percent per year.How much will you have in eleven years?

A)$13,376.08
B)$14,428.09
C)$15,110.24
D)$16,113.33
E)$16,617.07

Question 65

Explain the Rule of 72.

Question 66

Explain the time value of money principle and also identify the underlying assumption of that principle.

Question 67

Identify the relationship (direct or inverse)between each of the following pairs of variables as they relate to the time value of money:
(Assume all else constant)
Present value and future value _________
Present value and interest rate _________
Present value and time _________
Time and interest rate _________
Time and future value _________
Interest rate and future value _________

Question 68

You expect to receive $20,000 at graduation one year from now.You plan on investing it at 6 percent until you have $100,000.How long will you wait from now?

A)27.47 years
B)27.51 years
C)27.55 years
D)28.54 years
E)28.62 years