Deck 27: 1: Sec 271 Mc Present Value Measuring the Time Value of Money

Question 1

Melissa offers you $1,000 today or $1,500 in 5 years.You would prefer to take the $1,500 in 5 years if the interest rate is

A)8 percent.
B)9 percent.
C)10 percent.
D)All of the above are correct.

Answer 1

A

Question 2

Suppose you put $500 into a bank account today.Interest is paid annually and the annual interest rate is 8 percent.The future value of the $500 after 2 years is

A)$428.67.
B)$470.00.
C)$580.00.
D)$583.20.

Answer 2

C

Question 3

Suppose you will receive $500 at some point in the future.If the annual interest rate is 7.5 percent,then the present value of the $500 is

A)$411.26 if the $500 is to be received in 5 years and $338.95 if the $500 is to be received in 10 years.
B)$348.28 if the $500 is to be received in 5 years and $242.60 if the $500 is to be received in 10 years.
C)$291.11 if the $500 is to be received in 5 years and $272.89 if the $500 is to be received in 10 years.
D)$291.11 if the $500 is to be received in 5 years and $236.49 if the $500 is to be received in 10 years.

Answer 3

A

Question 4

Suppose the interest rate is 10 percent.Which of the following payments has the largest present value?

A)You receive $90.91 two years from today.
B)You receive $82.64 one year from today.
C)You receive $75.13 today.
D)All of these payments have the same present value to the nearest cent.

Question 5

Discounting refers directly to

A)finding the present value of a future sum of money.
B)finding the future value of a present sum of money.
C)calculations that ignore the phenomenon of compounding for the sake of ease and simplicity.
D)decreases in interest rates over time,while compounding refers to increases in interest rates over time.

Question 6

Suppose you put $500 into a bank account today.Interest is paid annually and the annual interest rate is 5.5 percent.The future value of the $500 is

A)$637.50 after 5 years and $822.09 after 10 years.
B)$637.50 after 5 years and $775.00 after 10 years.
C)$653.48 after 5 years and $854.07 after 10 years.
D)$688.36 after 5 years and $915.56 after 10 years.

Question 7

One way to characterize the difference between compounding and discounting is to say that

A)compounding involves the assumption that the interest rate is zero,whereas discounting does not involve that assumption.
B)discounting involves the assumption that the interest rate is zero,whereas compounding does not involve that assumption.
C)the process of compounding produces a future value,whereas the process of discounting produces a present value.
D)the process of compounding produces a present value,whereas the process of discounting produces a future value.

Question 8

James offers you $1,000 today or $X in 7 years.If the interest rate is 4.5 percent,then you would prefer to take the $1,000 today if and only if

A)X < 1,045.00.
B)X < 1,188.89.
C)X < 1,266.67.
D)X < 1,360.86.

Question 9

If the interest rate is 4 percent,then you would be equally happy if you received a gift of either $100 today or a gift of

A)$110.00 two years from today.
B)$112.49 three years from today.
C)$116.00 four years from today.
D)$123.67 five years from today.

Question 10

If the interest rate is 7.5 percent,then what is the present value of $4,000 to be received in 6 years?

A)$2,420.68
B)$2,591.85
C)$2,996.33
D)$3,040.63

Question 11

Imagine that someone offers you $X today or $1,500 in 5 years.If the interest rate is 4 percent,then you would prefer to take the $X today if and only if

A)X > 1,055.56.
B)X > 1,120.89.
C)X > 1,232.89.
D)X > 1,338.26.

Question 12

A manufacturing company is thinking about building a new factory.The factory,if built,will yield the company $300 million in 7 years,and it would cost $220 million today to build.The company will decide to build the factory if the interest rate is

A)no less than 4.53 percent.
B)no greater than 4.53 percent.
C)no less than 5.81 percent.
D)no greater than 5.81 percent.

Question 13

Suppose you are deciding whether or not to buy a particular bond for $5,980.17.If you buy the bond and hold it for 5 years,then at that time you will receive a payment of $10,000.You will buy the bond today if the interest rate is

A)no less than 9.48 percent.
B)no greater than 9.48 percent.
C)no less than 10.83 percent.
D)no greater than 10.83 percent.

Question 14

Suppose you put $500 into a bank account today.Interest is paid annually and the annual interest rate is 3 percent.The future value of the $500 after 1 year is

A)$485.44.
B)$496.50.
C)$509.28.
D)$515.00.

Question 15

Compounding refers directly to

A)finding the present value of a future sum of money.
B)finding the future value of a present sum of money.
C)changes in the interest rate over time on a bank account or a similar savings vehicle.
D)interest being earned on previously-earned interest.

Question 16

In which of the following instances is the present value of the future payment the largest?

A)You will receive $1,000 in 5 years and the annual interest rate is 5 percent.
B)You will receive $1,000 in 10 years and the annual interest rate is 3 percent.
C)You will receive $2,000 in 10 years and the annual interest rate is 10 percent.
D)You will receive $2,400 in 15 years and the annual interest rate is 8 percent.

Question 17

Suppose your uncle offers you $100 today or $150 in 10 years.You would prefer to take the $100 today if the interest rate is

A)3 percent.
B)4 percent.
C)5 percent.
D)None of the above is correct.

Question 18

Imagine that someone offers you $100 today or $200 in 10 years.You would prefer to take the $100 today if the interest rate is

A)4 percent.
B)6 percent.
C)8 percent.
D)All of the above are correct.

Question 19

Suppose you put $350 into a bank account today.Interest is paid annually and the annual interest rate is 6 percent.The future value of the $350 after 4 years is

A)$414.09.
B)$434.00.
C)$441.87.
D)$481.24.

Question 20

Suppose you are deciding whether to buy a particular bond.If you buy the bond and hold it for 4 years,then at that time you will receive a payment of $10,000.If the interest rate is 6 percent,you will buy the bond if its price today is no greater than

A)$8,225.06.
B)$7,920.94.
C)$7,672.58.
D)$6,998.98.

Question 21

If you put $250 into an account with a 4 percent interest rate,how many years would you have to wait to have $432.92?

A)10
B)14
C)17
D)20

Question 22

At an annual interest rate of 14 percent,about how many years will it take $100 to double in value?

A)3
B)4
C)5
D)7

Question 23

Which of the following is the correct way to compute the future value of $100 put into an account that earns 4 percent interest for 10 years?

A)$100(1 + .04¹⁰)
B)$100(1 + .04 10)
C)$100 × 10 (1 + .04)
D)$100(1 + .04)¹⁰

Question 24

What is the future value of $500 one year from today if the interest rate is 6 percent?

A)$515
B)$520
C)$530
D)None of the above is correct.

Question 25

What is the future value of $750 one year from today if the interest rate is 2.5 percent?

A)$766.50
B)$768.75
C)$770.23
D)None of the above are correct to the nearest cent.

Question 26

At an annual interest rate of 10 percent,about how many years will it take $100 to triple in value?

A)8
B)10
C)12
D)14

Question 27

You put $150 in the bank two years ago and forgot about it.The bank sends you a notice that you now have $169.34 in your account.What interest rate did you earn?

A)5.50 percent
B)5.65 percent
C)6.25 percent
D)7.05 percent

Question 28

You put $75 in the bank one year ago and forgot about it.The bank sends you a notice that you now have $81 in your account.What interest rate did you earn?

A)5 percent
B)6 percent
C)7 percent
D)8 percent

Question 29

Which of the following is the correct way to compute the future value of $1 put into an account that earns 5 percent interest for 16 years?

A)$1(1 + .05)¹⁶
B)$1(1 + .05 16)
16
C)$1(1 + .05 16)
D)$1(1 + 16/.05)¹⁶

Question 30

Which of the following is the correct way to compute the future value of $X that earns r percent interest for N years?

A)$X(1 + rN)^N
B)$X(1 + r)^N
C)$X(1 + rN)
D)$X(1 + r/N)N

Question 31

Amelia knows that she has about $105 in her bank account.She knows she earned an interest rate of 4 percent,but she doesn't remember how much she opened the account with a year ago.How much did she put in?

A)$98.18
B)$100.96
C)$102.04
D)$103.24

Question 32

Tim put $275 in the bank one year ago and forgot about it.Today,the bank sent Tim a statement indicating that he now has $294.25 in his account.What interest rate did Tim earn?

A)5 percent
B)6 percent
C)7 percent
D)8 percent

Question 33

At an annual interest rate of 10 percent,about how many years will it take $100 to double in value?

A)5
B)7
C)9
D)11

Question 34

If you presently have $50,000 saved and earn 15 percent interest per year,about how many years will it take for your investment to triple?

A)6
B)8
C)10
D)12

Question 35

The future value of a deposit in a savings account will be larger

A)the longer a person waits to withdraw the funds.
B)the higher the interest rate is.
C)the larger the initial deposit is.
D)All of the above are correct.

Question 36

The future value of a deposit in a savings account will be smaller

A)the longer a person waits to withdraw the funds.
B)the lower the interest rate is.
C)the larger the initial deposit is.
D)All of the above are correct.

Question 37

What is the future value of $450 at an interest rate of 9 percent two years from today?

A)$534.65
B)$546.35
C)$565.18
D)$574.13

Question 38

What is the future value of $800 one year from today if the interest rate is 7 percent?

A)$747.66
B)$756.00
C)$856.00
D)None of the above are correct to the nearest cent.

Question 39

What is the future value of $375 at an interest rate of 3 percent one year from today?

A)$371.75
B)$386.25
C)$393.33
D)None of the above are correct to the nearest cent.

Question 40

At an annual interest rate of 20 percent,about how many years will it take $100 to triple in value?

A)5
B)6
C)8
D)9

Question 41

Susan put $375 into an account and one year later had $405.What interest rate was paid on Susan's deposit?

A)5 percent
B)7 percent
C)8 percent
D)10 percent

Question 42

Ellen deposited $500 into an account and two years later she had $561.80 in the account.What interest rate was paid on Ellen's deposit?

A)4.88 percent
B)6.00 percent
C)12.36 percent
D)None of the above is correct.

Question 43

Three people go to the bank to cash in their accounts.Amy had her money in an account for 25 years at 4 percent interest.Bill had his money in an account for 20 years at 5 percent interest.Celia had her money in an account for 5 years at 20 percent interest.If each of them originally deposited $500 in their accounts,which of them gets the most money when they cash in their accounts?

A)Amy
B)Bill
C)Celia
D)They each get the same amount.

Question 44

Clint puts $200 into an account when the interest rate is 8 percent.Later he checks his balance and finds that he has a balance of about $272.10.How many years did Clint wait to check his balance?

A)3 years
B)3.5 years
C)4 years
D)4.5 years

Question 45

Jarrod says that the future value of $250 saved for one year at 6 percent interest is less than the future value of $250 saved for two years at 3 percent interest.Simon says that the present value of a $250 payment to be received in one year when the interest rate is 6 percent is less than the value of a $250 payment to be received in two years when the interest rate is 3 percent.

A)Jarrod and Simon are both correct.
B)Jarrod and Simon are both incorrect.
C)Only Jarrod is correct.
D)Only Simon is correct.

Question 46

When you were 10 years old,your grandparents put $500 into an account for you paying 7 percent interest.Now that you are 18 years old,your grandparents tell you that you can take the money out of the account.What is the balance to the nearest cent?

A)$1,200.00
B)$1,111.77
C)$983.58
D)$859.09

Question 47

Felix deposited $500 into an account two years ago.The first year he earned 3 percent interest and the second year he earned 5 percent interest.How much money does Felix have in his account now?

A)$540.75
B)$540.80
C)$540.85
D)None of the above are correct to the nearest cent.

Question 48

If you put $125 into an account that paid 3.25 percent interest,then how much money would you have in the account after 20 years?

A)$285.83
B)$236.98
C)$202.04
D)$145.65

Question 49

Veronica deposited $1,000 into an account two years ago.The first year she earned 7 percent interest;the second year she earned 5 percent.How much money does Veronica have in her account today?

A)$1,133.31
B)$1,120.00
C)$1,123.50
D)None of the above are correct to the nearest cent.

Question 50

Laura says that the present value of $700 to be received one year from today if the interest rate is 6 percent is less than the present value of $700 to be received two years from today if the interest rate is 3 percent.Cassie says that $700 saved for one year at 6 percent interest has a smaller future value than $700 saved for two years at 3 percent interest.

A)Both Laura and Cassie are correct.
B)Both Laura and Cassie are incorrect.
C)Only Laura is correct.
D)Only Cassie is correct.

Question 51

Hector puts $150 into an account when the interest rate is 4 percent.Later he checks his balance and finds he has about $168.73.How long did Hector wait to check his balance?

A)3 years
B)3.5 years
C)4 years
D)4.5 years

Question 52

Toni deposited $250 into an account and one year later she had $272.50 in the account.What interest rate was paid on Toni's deposit?

A)8 percent
B)9 percent
C)10 percent
D)None of the above is correct.

Question 53

Marcia has four savings accounts.Which account has the largest balance?

A)$100 deposited 1 year ago at an 8 percent interest rate
B)$100 deposited 2 years ago at a 4 percent interest rate
C)$100 deposited 4 years ago at a 2 percent interest rate
D)$100 deposited 8 years ago at a 1 percent interest rate

Question 54

Jorge deposited $1,000 into an account three years ago.The first two years he earned 5 percent interest;the third year he earned 6 percent interest.How much money does Jorge have in his account today?

A)$1,157.90
B)$1,168.65
C)$1,176.00
D)None of the above are correct to the nearest cent.

Question 55

Two years ago Darryl put $3,000 into an account paying 3 percent interest.How much does he have in the account today?

A)$3,180.00
B)$3,182.70
C)$3,183.62
D)None of the above are correct to the nearest cent.

Question 56

Braden says that $400 saved for one year at 4 percent interest has a smaller future value than $400 saved for two years at 2 percent interest.Lefty says that the present value of $400 to be received one year from today if the interest rate is 4 percent exceeds the present value of $400 to be received two years from today if the interest rate is 2 percent.

A)Braden and Lefty are both correct.
B)Braden and Lefty are both incorrect.
C)Only Braden is correct.
D)Only Lefty is correct.

Question 57

Three years ago Dawn put $1,200 into an account paying 2 percent interest.How much is Dawn's account worth today?

A)$1,225.38
B)$1,248.48
C)$1,264.72
D)$1,273.45

Question 58

Bert put $75 into an account and one year later had $100.What interest rate was paid on Bert's deposit?

A)20 percent
B)25 percent
C)28 percent
D)None of the above is correct.

Question 59

Lucretia puts $400 into an account when the interest rate is 10 percent.Later she checks her balance and finds it's worth about $708.62.How many years did she wait to check her balance?

A)5 years
B)6 years
C)7 years
D)8 years

Question 60

If you put $300 into an account paying 2 percent interest,what will be the value of this account in 4 years?

A)$320.69
B)$324.00
C)$324.73
D)$327.81

Question 61

Your accountant tells you that if you can continue to earn the current interest rate on your balance of $800 for the next two years you will have $898.88 in your account.If your accountant is correct,then what is the current interest rate?

A)6 percent
B)7 percent
C)8 percent
D)9 percent

Question 62

Your financial advisor tells you that if you earn the historical rate of return on a certain mutual fund,then in three years your $20,000 will grow to $23,152.50.What rate of interest does your financial advisor expect you to earn?

A)5 percent
B)6 percent
C)7 percent
D)8 percent

Question 63

Al,Ralph,and Stan are all intending to retire.Each currently has $1 million in assets.Al will earn 16% interest and retire in two years.Ralph will earn 8% interest and retire in four years.Stan will earn 4% interest and retire in eight years.Who will have the largest sum when he retires?

A)Al
B)Ralph
C)Stan
D)They all retire with the same amount.

Question 64

Your accountant tells you that if you can continue to earn the current interest rate on your balance of $500 for ten years,you will have about $983.58.If your accountant is correct,what is the current rate of interest?

A)5 percent
B)6 percent
C)7 percent
D)8 percent

Question 65

Your accountant tells you that if you can continue to earn the current interest rate on your balance of $750 for the next three years,you will have $944.78 in your account.If your accountant is correct,then what is the current interest rate?

A)6 percent
B)7 percent
C)8 percent
D)10 percent

Question 66

Sage decides to cash in all his savings to open a recording studio.He has three accounts to cash in.The first earned 9 percent for two years.The second earned 6 percent for three years.And the last earned 3 percent for six years.Supposing he started with $5,000 in each account,from which account will he get the most cash?

A)the two-year account at 9 percent
B)the three-year account at 6 percent
C)the six-year account at 3 percent
D)The accounts are all worth the same.

Question 67

Two years ago Lenny put some money into an account.He earned 6 percent interest on this account and now he has about $1,000.About how much did Lenny deposit into his account two years ago?

A)about $860
B)about $870
C)about $880
D)about $890

Question 68

Which of the following is the correct expression for finding the present value of a $1,000 payment one year from today if the interest rate is 6 percent?

A)$1,000 (1.06)
B)$1,000^(1.06)
C)$1,000/(1.06)
D)None of the above is correct.

Question 69

When he was 18,Hussam put $100 into an account at an interest rate of 8 percent.He now has $158.69 in this account.For how many years did Hussam leave this money in his account?

A)5 years
B)6 years
C)7 years
D)8 years

Question 70

Robert put $15,000 into an account with a fixed interest rate two years ago and now the account balance is $16,917.66.What rate of interest did Robert earn?

A)4.5 percent
B)5.4 percent
C)6.2 percent
D)8.0 percent

Question 71

You are given three options.You may have the balance in an account that has been collecting 5 percent interest for 20 years,the balance in an account that has been collecting 10 percent interest for 10 years,or the balance in an account that has been collecting 20 percent interest for five years.Each account had the same original balance.Which account now has the lowest balance?

A)the first one
B)the second one
C)the third one
D)They all have the same balance.

Question 72

You want to have $100,000 in five years.If the interest rate is 8 percent,about how much do you need to have today?

A)$66,225.25
B)$67,556.42
C)$68,058.32
D)$71,428.57

Question 73

The price of a bond is equal to the sum of the present values of its future payments.Suppose a certain bond pays $50 one year from today and $1,050 two years from today.What is the price of the bond if the interest rate is 5 percent?

A)$1,050.00
B)$1,045.35
C)$1,000.00
D)$945.35

Question 74

Imagine that two years ago you inherited $20,000 and put it into an account paying a fixed 8 percent annual interest rate.How much money do you have in your account now?

A)$22,880.00
B)$23,200.00
C)$23,232.00
D)$23,328.00

Question 75

Daniel has $300 in a bank account.Some years ago he put $213.20 into this account,and it has earned 5 percent interest every year since then.How many years ago did Daniel open his account?

A)4 years
B)5 years
C)6 years
D)7 years

Question 76

Tonya put $250 into an account three years ago.The first year he earned 6 percent interest,the second year 7 percent,and the third year 8 percent.About how about much does Tonya have in her account now?

A)$302.50
B)$306.23
C)$308.67
D)$309.39

Question 77

On May 25,1980 three pals graduated from high school,pooled together $3,000 and put the money into an account promising to pay 8% for the next 30 years.On May 25,2010 they withdrew all the money from the account.To the nearest dollar,how much did they withdraw?

A)$25,962
B)$27,297
C)$30,188
D)None of the above are correct to the nearest dollar.

Question 78

Zoey wants to have about $750,000 when she retires in 10 years.She has $300,000 to deposit now.At which of the following interest rates would Zoey's deposit come closest to $750,000 after 10 years?

A)9.6 percent
B)9.9 percent
C)10.2 percent
D)10.5 percent

Question 79

Four years ago Ollie deposited some money into an account.He earned 5 percent interest on this account and now it has a balance of $303.88.About how much money did Ollie deposit into his account when he opened it?

A)$210
B)$220
C)$240
D)$250

Question 80

Anna deposited $10,000 into an account three years ago.The first year she earned 12 percent interest,the second year she earned 8 percent interest,and the third year she earned 4 percent interest.How much money does she have in her account today?

A)$12,579.84
B)$12,596.80
C)$12,597.12
D)None of the above are correct to the nearest cent.