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

Question 1

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.

Answer 1

remain constant, regardless of the investment time period.

Question 2

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.

Answer 2

only on the principal amount originally invested.

Question 3

Which one of the following is the correct formula for the current value of $600 invested today at 5 percent interest for 6 years?

A)PV = $600/ [(1 + .06) ×5]
B)PV = $600/ [(1 +.05) ×6]
C)PV = $600/ (.06×5)
D)PV = $600/ (1 + .05) ⁶
E)PV = $600/ (1 + .06) ⁵

Answer 3

PV = $600/ (1 + .05) ⁶

Question 4

Tomas earned $89 in interest on his savings account last year and has decided to leave the $86 in his account this coming year so it will earn interest.This process of earning interest on prior interest earnings is called:

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

Question 5

Katlyn needs to invest $5,318 today in order for her savings account to be worth $8,000 six years from now.Which one of the following terms refers to the $5,318?

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

Question 6

Lucas expects to receive a sales bonus of $7,500 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 7

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 8

Rob wants to invest $15,000 for 7 years.Which one of the following rates will provide him with the largest future value?

A)3 percent simple interest
B)3 percent interest, compounded annually
C)2 percent interest, compounded annually
D)4 percent simple interest
E)4 percent interest, compounded annually

Question 9

Jenny needs to borrow $5,500 for four 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)6.5 percent simple interest
B)6.5 percent interest, compounded annually
C)6.6 percent simple interest
D)6.75 percent interest, compounded annually
E)6.80 percent interest, compounded annually

Question 10

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 11

Jessica 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)She will earn the same amount of interest each year.
B)She could have the same future value and invest less than $2,000 initially if she could earn more than 6.5 percent interest.
C)She will earn an increasing amount of interest each and every year even if she should decide to withdraw the interest annually rather than reinvesting the interest.
D)Her interest for Year 2 will be equal to $2,000×.065 ×2.
E)She will be earning simple interest.

Question 12

Jamie earned $14 in interest on her savings account last year.She has decided to leave the $14 in her account so that she can earn interest on the $14 this year.The interest earned on last year’s interest earnings is called:

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

Question 13

The future value of a lump sum investment will increase if you:  

A)decrease the interest rate.
B)decrease the number of compounding periods.
C)increase the time period.
D)decrease the time period.
E)decrease the lump sum amount.

Question 14

Kendall is investing $3,333 today at 3 percent annual interest for three years.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 15

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.

Question 16

Marcos is investing $5 today at 7 percent interest so he can have $35 later.This $35 is referred to as the:

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

Question 17

All else held constant,the future value of a lump sum investment will decrease if the:  

A)amount of the lump sum investment increases.
B)time period is increased.
C)interest is left in the investment.
D)interest rate increases.
E)interest is changed to simple interest from compound interest.

Question 18

Which one of the following will increase the present value of a lump sum future amount to be received in 15 years?

A)An increase in the time period
B)An increase in the interest rate
C)A decrease in the future value
D)A decrease in the interest rate
E)Changing to compound interest from simple interest

Question 19

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 20

Stacey deposits $5,000 into an account that pays 2 percent interest,compounded annually.At the same time,Kurt deposits $5,000 into an account paying 3.5 percent interest,compounded annually.At the end of three years:

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

Question 21

Today,Charity wants to invest less than $3,000 with the goal of receiving $3,000 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 increases.

Question 22

What is the future value of $5,700 invested for 18 years at 9 percent compounded annually?

A)$26,397.74
B)$26,887.59
C)$28,511.15
D)$27,513.06
E)$27,520.22

Question 23

You just won $30,000 and deposited your winnings into an account that pays 3.9 percent interest,compounded annually.How long will you have to wait until your winnings are worth $75,000?

A)21.24 years
B)25.00 years
C)22.29 years
D)22.67 years
E)23.95 years

Question 24

Ben invested $7,500 twenty years ago with an insurance company that has paid him 6 percent simple interest on his funds.Charles invested $7,500 twenty years ago in a fund that has paid him 6 percent interest,compounded annually.How much more interest has Charles earned than Ben over the past 20 years?

A)$0
B)$6,827.04
C)$7,553.52
D)$7,109.16
E)$8,266.49

Question 25

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 26

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 27

Travis invests $5,500 today into a retirement account.He expects to earn 9.2 percent,compounded annually,on his money for the next 13 years.After that,he wants to be more conservative,so only expects to earn 6 percent,compounded annually.How much money will he have in his account when he retires 25 years from now,assuming this is the only deposit he makes into the account?

A)$29,411.20
B)$34,747.80
C)$34,616.56
D)$41,919.67
E)$42,003.12

Question 28

South Central Bank pays 2.5 percent interest,compounded annually,on its savings accounts.Northern 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 the same rate of 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 South Central Bank.
E)will be greater if you invest with Northern Bank.

Question 29

Kevin just deposited $13,000 into his savings account at Traditions Bank.The bank will pay .87 percent interest,compounded annually,on this account.How much interest on interest will he earn over the next 5 years?

A)$8.67
B)$9.93
C)$8.92
D)$9.49
E)$9.73

Question 30

When you were born,your parents opened an investment account in your name and deposited $1,500 into the account.The account has earned an average annual rate of return of 5.3percent.Today,the account is valued at $42,856.How old are you?

A)71.47 years
B)70.67 years
C)61.08 years
D)67.33 years
E)64.91 years

Question 31

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 + .06) ⁷
B)PV = $600 (1 + .07) ⁶
C)PV = $600 × (.07 ×6)
D)PV = $600/(1 + .07) ⁶
E)PV = $600/(1 + 6)⁰⁷

Question 32

Today,you deposit $2,500 in a bank account that pays 3.6 percent simple interest.How much interest will you earn over the next 5 years?

A)$90.00
B)$120.00
C)$450.00
D)$483.59
E)$492.27

Question 33

Precision Engineering invested $125,000 at 6 percent interest,compounded annually for 3 years.How much interest on interest did the company earn over this period of time?

A)$1,284
B)$1,377
C)$1,317
D)$1,369
E)$2,679

Question 34

Eleven years ago,you deposited $3,200 into an account.Seven years ago,you added an additional $1,000 to this account.You earned 9.2 percent,compounded annually,for the first 4 years and 5.5 percent,compounded annually,for the last 7 years.How much money do you have in your account today?

A)$8,666.67
B)$7,717.29
C)$7,411.90
D)$8,708.15
E)$8,073.91

Question 35

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 36

Angela has just received an insurance settlement of $22,500.She wants to save this money until her daughter goes to college.If she can earn an average of 4.7 percent,compounded annually,how much will she have saved when her daughter enters college 6 years from now?

A)$30,106.14
B)$30,929.02
C)$31,374.89
D)$29,875.06
E)$29,638.94

Question 37

Lew has $3,600 that he wants to invest for 5 years.He can invest this amount at his credit union and earn 2.2 percent simple interest.Or,he can open an account at Compass Bank and earn 2.15 percent interest,compounded annually.If he decides to invest at Compass Bank for 5 years,he will:

A)earn $6 more than if he had invested with his credit union.
B)earn $8 more 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 $3,680 in his account after one year.
E)have a total balance of $4,012 in his account after 5 years.

Question 38

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

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

Question 39

Your parents spent $7,800 to buy 200 shares of stock in a new company 12 years ago.The stock has appreciated 14.6 percent per year on average.What is the current value of those 200 shares?

A)$36,408.70
B)$40,023.03
C)$39,580.92
D)$40,515.08
E)$37,449.92

Question 40

Your grandparents just gave you a gift of $6,500.You are investing this money for 6 years at 4 percent simple interest.How much money will you have at the end of the 6 years?

A)$6,760
B)$7,280
C)$7,800
D)$8,060
E)$6,938

Question 41

You want to have $35,000 in cash to buy a car 3 years from today.You expect to earn 3.6 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)$32,618.92
B)$34,511.68
C)$33,726.04
D)$31,476.67
E)$30,156.19

Question 42

Suppose that in 2015,a $10 silver certificate from 1898 sold for $11,700.For this to have been true,what would the annual increase in the value of the certificate have been?

A)6.22 percent
B)6.01 percent
C)7.23 percent
D)6.49 percent
E)7.07 percent

Question 43

Assume the total cost of a college education will be $325,000 when your child enters college in 16 years.You presently have $40,000 to invest and do not plan to invest anything further.What annual rate of interest must you earn on your investment to cover the entire cost of your child's college education?

A)12.65 percent
B)10.40 percent
C)13.99 percent
D)14.62 percent
E)11.08 percent

Question 44

Stephen claims that he invested $6,000 six years ago and that this investment is worth $28,700 today.For this to be true,what annual rate of return did he have to earn? Assume the interest compounded annually.

A)28.87 percent
B)31.39 percent
C)29.80 percent
D)26.01 percent
E)27.87 percent

Question 45

You have been told that you need $32,000 today for each $100,000 you want when you retire 28 years from now.What rate of interest was used in the present value computation? Assume interest is compounded annually.

A)4.15 percent
B)4.37 percent
C)4.29 percent
D)4.53 percent
E)4.58 percent

Question 46

Eight years from now,you will be inheriting $100,000.What is this inheritance worth to you today if you can earn 7.25 percent interest,compounded annually?

A)$57,124.39
B)$63,215.46
C)$58,419.05
D)$61,798.47
E)$53,003.15

Question 47

Isaac only has $1,090 today but needs $1,979 to buy a new computer.How long will he have to wait to buy the computer if he earns 5.4 percent compounded annually on his savings? Assume the price of the computer remains constant.

A)11.83 years
B)11.48 years
C)12.51 years
D)12.77 years
E)11.34 years

Question 48

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 $6,500 for this party.You can earn 2.6 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)$6,076.55
B)$6,018.26
C)$6,308.16
D)$5,934.90
E)$5,868.81

Question 49

You want to have $40,000 for a down payment on a house 4 years from now.If you can earn 5.6 percent,compounded annually on your savings,how much do you need to deposit today to reach your goal?

A)$32,166.54
B)$34,420.73
C)$27,880.69
D)$28,211.17
E)$30,886.40

Question 50

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 51

How long will it take to double your savings if you earn 6.4 percent interest,compounded annually?

A)11.89 years
B)12.02 years
C)11.39 years
D)11.17 years
E)10.58 years

Question 52

Starlite Industries will need $2.2 million 4.5 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 3.6 percent interest,compounded annually.How much money must the company deposit today to fully fund the equipment purchase?

A)$1,679,947.20
B)$1,798,407.21
C)$1,350,868.47
D)$1,876,306.49
E)$1,412,308.18

Question 53

Sixty years ago,your grandparents opened two savings accounts and deposited $250 in each account.The first account was with City Bank at 3.6 percent,compounded annually.The second account was with Country Bank at 3.65 percent,compounded annually.Which one of the following statements is true concerning these accounts? (Do not round intermediate calculations.)

A)The City Bank account is currently worth $2,076.42.
B)The City Bank account has paid $48.19 more in interest than the Country Bank account.
C)The Country Bank account is currently worth $2,170.32.
D)The Country Bank account has paid $72.24 more in interest than the City Bank account.
E)The Country Bank account has paid $61.30 more in interest than the City Bank account.

Question 54

Today,Stacy is investing $18,000 at 6.72 percent,compounded annually,for 5 years.How much additional income could she earn if she had invested this amount at 7.15 percent,compounded annually?

A)$43.11
B)$506.06
C)$401.16
D)$442.79
E)$484.08

Question 55

Your coin collection contains ten 1949 silver dollars.If your grandparents purchased the coins for their face value when they were new,how much will your collection be worth when you retire in 2065,assuming the coins appreciate at an annual rate of 5.1 percent?

A)$3,440.63
B)$2,329.29
C)$3,348.98
D)$3,205.64
E)$2,644.29

Question 56

You're trying to save to buy a new car valued at $48,690.You have $38,000 today that can be invested at your bank.The bank pays 3.7 percent annual interest on its accounts.How long will it be before you have enough to buy the car for cash? Assume the price of the car remains constant.

A)5.13 years
B)9.29 years
C)4.67 years
D)7.08 years
E)6.82 years

Question 57

You have $500 today and want to triple your money in 6 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)20.09 percent
E)21.21 percent

Question 58

Western Bank pays 5 percent simple interest on its savings account balances,whereas Eastern Bank pays 5 percent compounded annually.If you deposited $6,000in each bank,how much more money would you earn from the Eastern Bank account at the end of 3 years?

A)$55.84
B)$45.75
C)$60.47
D)$40.09
E)$50.14

Question 59

You have just made your first $5,000 contribution to your retirement account.Assuming you earn a rate of return of 5 percent 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 60

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

A)14.33 years
B)11.53 years
C)9.67 years
D)10.36 years
E)10.56 years

Question 61

You are scheduled to receive $7,500 in two years.When you receive it,you will invest it at 4.5 percent per year.How much will your investment be worth ten years from now?

A)$10,665.75
B)$11,428.09
C)$9,110.24
D)$10,113.33
E)$11,617.07

Question 62

You expect to receive $5,000 at graduation one year from now.Your plan is to invest this money at 6.5 percent,compounded annually,until you have $50,000.At that time,you plan to travel around the world.How long from now will it be until you can begin your travels?

A)36.57 years
B)31.08 years
C)34.55 years
D)32.08 years
E)37.57years

Question 63

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?

A)$201,516.38
B)$209,092.540
C)$209,092.54
D)-$209,092.54
E)$221,408.97