Deck 4: Time Value of Money 1: Analyzing Single Cash Flows

Question 1

To solve for time-value equations, you need to know:

A) the starting cash flow.
B) the interest rate.
C) the future cash flow.
D) all of the above.

Answer 1

all of the above.

Question 2

With regard to money deposited in a bank, future values are

A) smaller than present values.
B) larger than present values.
C) equal to present values.
D) are completely independent of present values.

Answer 2

larger than present values.

Question 3

Which of the following is NOT true when developing a time line?

A) Cash inflows are designated with a positive number.
B) Cash outflows are designated with a positive number.
C) The cost is known as the interest rate.
D) The time line shows the magnitude of cash flows at different points in time.

Answer 3

Cash outflows are designated with a positive number.

Question 4

How are present values affected by changes in interest rates?

A) The lower the interest rate, the larger the present value will be.
B) The higher the interest rate, the larger the present value will be.
C) Present values are not affected by changes in interest rates.
D) One would need to know the future value in order to determine the impact.

Question 5

Moving cash flows from one point in time to another requires us to use

A) only present value equations.
B) only future value equations.
C) both present value and future value equations.
D) the Rule of 72.

Question 6

The Rule of 72 is a simple mathematical approximation for

A) the present value required to double an investment.
B) the future value required to double an investment.
C) the payments required to double an investment.
D) the number of years required to double an investment.

Question 7

We call the process of earning interest on both the original deposit and on the earlier interest payments

A) discounting.
B) multiplying.
C) compounding.
D) computing.

Question 8

When calculating the number of years needed to grow an investment to a specific amount of money

A) the lower the interest rate, the shorter the time period needed to achieve the growth.
B) the higher the interest rate, the shorter the time period needed to achieve the growth.
C) the interest rate has nothing to do with the length of the time period needed to achieve the growth.
D) the Rule of 72 is the only way to calculate the time period needed to achieve the growth.

Question 9

Which of these statements is true of discounting?

A) It is the reverse of compounding.
B) It significantly decreases the value of a future amount to the present.
C) It is the process of figuring out how much an amount that you expect to receive in the future is worth today.
D) All of the above.

Question 10

What is the future value of $700 deposited for one year earning 4 percent interest rate annually?

A) $28
B) $700
C) $728
D) $1,428

Question 11

The longer money can earn interest,

A) the greater the interest earned on the original deposit exceeds the interest-on-interest.
B) the greater the compounding effect.
C) the greater the present value must be to reach a financial goal.
D) the greater the risk to the investor of not reaching a financial goal.

Question 12

When computing the rate of return from selling an investment, the number of years between the present and future cash flows is an important factor in determining

A) the annual rate earned.
B) the annual payments required.
C) whether the present value or the future value is a cash inflow.
D) whether the present value or the future value is a cash outflow.

Question 13

The process of figuring out how much an amount that you expect to receive in the future is worth today is called

A) discounting.
B) multiplying.
C) compounding.
D) computing.

Question 14

How do you calculate the future value of a single period?

A) Add the interest earned to today's cash flow.
B) Add the interest earned to next year's cash flow.
C) Multiply the interest eared with today's cash flow.
D) Multiply the interest eared with next year's cash flow.

Question 15

What information would you need to know to solve a rate of return problem?

A) the present value cash flow.
B) the number of years of the investment.
C) the future value cash flow.
D) all of the above.

Question 16

Which of the following statements about the Rule of 72 is not true?

A) It is a mathematical approximation for the number of years required to double an investment.
B) It illustrates the power of a discounted rate.
C) It can be used to approximate the interest rate needed to double an investment for a specified amount of time.
D) None of the above.

Question 17

The interest rate, i, which we use to calculate present value, is often referred to as the

A) discount rate.
B) multiplier.
C) compound rate.
D) dividend.

Question 18

People borrow money because they expect

A) their purchases to give them the satisfaction in the future that compensates them for the interest payments charged on the loan.
B) the time value of money to apply only if they are saving money.
C) interest rates to rise.
D) that consumers don't need to calculate the impact of interest on their purchases.

Question 19

How are future values affected by changes in interest rates?

A) The lower the interest rate, the larger the future value will be.
B) The higher the interest rate, the larger the future value will be.
C) Future values are not affected by changes in interest rates.
D) One would need to know the present value in order to determine the impact.

Question 20

A dollar paid (or received) in the future is

A) worth more than a dollar paid (or received) today.
B) worth as much as a dollar paid (or received) today.
C) not worth as much as a dollar paid (or received) today.
D) not comparable to a dollar paid (or received) today.

Question 21

A deposit of $1,000 earns the following interest rates?
8 percent in the first year,
7 percent in the second year, and
8 percent in the third year.
What would be the third year future value?

A) $1,082.15
B) $1,230.00
C) $1,248.05
D) $3,030.00

Question 22

What is the future value of $2,000 deposited for one year earning 6 percent interest rate annually?

A) $120
B) $2.000
C) $2,120
D) $4,120

Question 23

What is the present value of a $200 payment made in three years when the discount rate is 8 percent?

A) $150.00
B) $158.77
C) $251.94
D) $515.42

Question 24

What is the present value of a $250 payment in one year when the discount rate is 6 percent?

A) $245.00
B) $235.85
C) $250.00
D) $265.00

Question 25

A deposit of $500 earns the following interest rates?
5 percent in the first year,
6 percent in the second year, and
8 percent in the third year.
What would be the third year future value?

A) $527.14
B) $595.00
C) $601.02
D) $1595.00

Question 26

Determine the interest rate earned on a $1,500 deposit when $1,680 is paid back in one year.

A) 0.89 percent
B) 1.12 percent
C) 12.00 percent
D) 89.00 percent

Question 27

Approximately what interest rate is needed to double an investment over six years?

A) 6 percent
B) 12 percent
C) 17 percent
D) 100 percent

Question 28

How much would be in your savings account in 7 years after depositing $100 today if the bank pays 5 percent interest per year?

A) $135.00
B) $140.71
C) $735.00
D) $814.20

Question 29

What is the future value of $1,000 deposited for one year earning 5 percent interest rate annually?

A) $1,000
B) $1,005
C) $1,050
D) $2,050

Question 30

A deposit of $700 earns interest rates of 10 percent in the first year and 7 percent in the second year. What would be the second year future value?

A) $771.07
B) $819.00
C) $823.90
D) $1519.00

Question 31

Approximately what interest rate is needed to double an investment over four years?

A) 4 percent
B) 18 percent
C) 25 percent
D) 100 percent

Question 32

Approximately how many years does it take to double a $500 investment when interest rates are 4 percent per year?

A) 0.06 year
B) 6 years
C) 6.94 years
D) 18 years

Question 33

Approximately how many years does it take to double a $600 investment when interest rates are 6 percent per year?

A) 0.08 year
B) 8 years
C) 8.33 years
D) 12 years

Question 34

How much would be in your savings account in 10 years after depositing $50 today if the bank pays 7 percent interest per year?

A) $35.00
B) $98.36
C) $535.00
D) $690.82

Question 35

What is the present value of a $500 payment in one year when the discount rate is 5 percent?

A) $475.00
B) $476.19
C) $500.00
D) $525.00

Question 36

Approximately what interest rate is needed to double an investment over eight years?

A) 8 percent
B) 9 percent
C) 12 percent
D) 100 percent

Question 37

Approximately how many years does it take to double a $300 investment when interest rates are 8 percent per year?

A) 0.11 years
B) 4.17 years
C) 9 years
D) 11 years

Question 38

What is the present value of a $500 payment made in four years when the discount rate is 8 percent?

A) $365.35
B) $367.51
C) $460.00
D) $680.24

Question 39

A deposit of $300 earns interest rates of 7 percent in the first year and 10 percent in the second year. What would be the second year future value?

A) $351.00
B) $353.10
C) $602.17
D) $651.00

Question 40

What is the present value of a $750 payment made in three years when the discount rate is 5 percent?

A) $646.96
B) $647.88
C) $712.50
D) $868.22

Question 41

How many years will it take $200 to grow to $250 with an annual interest rate of 4 percent?

A) 1.24 years
B) 5.69 years
C) 6.25 years
D) 18.00 years

Question 42

Consider a $200 deposit earning 8 percent interest per year for three years. How much total interest is earned on interest (excluding interest earned on the original deposit)?

A) $3.94
B) $24.00
C) $48.00
D) $51.94

Question 43

How many years will it take $1 million to grow to $3 million with an annual interest rate of 7 percent?

A) 10.29 years
B) 14.52 years
C) 16.24 years
D) 33.33 years

Question 44

What is the value in year 15 of a $600 cash flow made in year 3 when the interest rates are 4 percent?

A) $374.76
B) $888.00
C) $960.62
D) $1,080.57

Question 45

How long will it take $3,000 to reach $5,000 when it grows at 7 percent per year?

A) 7.00 years
B) 7.55 years
C) 9.52 years
D) 10.29 years

Question 46

What is the value in year 5 of a $600 cash flow made in year 10 when interest rates are 5 percent?

A) $368.35
B) $450.00
C) $470.12
D) $570.00

Question 47

Consider a $500 deposit earning 5 percent interest per year for five years. How much total interest is earned on the original deposit (excluding interest earned on interest)?

A) $13.14
B) $25.00
C) $125.00
D) $138.14

Question 48

What annual rate of return is earned on a $200 investment when it grows to $850 in 10 years?

A) 3.25 percent
B) 4.25 percent
C) 13.47 percent
D) 15.57 percent

Question 49

Determine the interest rate earned on a $500 deposit when $650 is paid back in one year.

A) 0.77 percent
B) 1.30 percent
C) 30.0 percent
D) 77.0 percent

Question 50

How many years will it take $100 to grow to $1,000 with an annual interest rate of 8 percent?

A) 9.00 years
B) 10.00 years
C) 29.92 years
D) 33.35 years

Question 51

Consider a $2,000 deposit earning 6 percent interest per year for five years. How much total interest is earned on the original deposit (excluding interest earned on interest)?

A) $60.00
B) $76.45
C) $600.00
D) $676.45

Question 52

What is the value in year 6 of a $900 cash flow made in year 4 when the interest rates are 8 percent?

A) $1,044.00
B) $1,049.76
C) $1,332.00
D) $1,428.19

Question 53

What annual rate of return is earned on a $10,000 investment when it grows to $15,000 in 10 years?

A) 1.50 percent
B) 3.97 percent
C) 4.14 percent
D) 5.00 percent

Question 54

Consider a $1,000 deposit earning 7 percent interest per year for four years. How much total interest is earned on the original deposit (excluding interest earned on interest)?

A) $28.00
B) $30.00
C) $280.00
D) $310.00

Question 55

What is the value in year 7 of a $700 cash flow made in year 3 when the interest rates are 10 percent?

A) $478.11
B) $980.00
C) $1,024.87
D) $1,364.10

Question 56

What annual rate of return is earned on a $900 investment when it grows to $2,500 in 15 years?

A) 1.78 percent
B) 2.78 percent
C) 6.58 percent
D) 7.05 percent

Question 57

What is the value in year 3 of a $250 cash flow made in year 15 when interest rates are 12 percent?

A) $45.67
B) $64.17
C) $177.95
D) $220.00

Question 58

What is the value in year 3 of a $500 cash flow made in year 5 when interest rates are 6 percent?

A) $374
B) $420
C) $440
D) $445

Question 59

What annual rate of return is earned on a $5,000 investment when it grows to $7,000 in six years?

A) 1.40 percent
B) 5.45 percent
C) 5.77 percent
D) 40.00 percent

Question 60

Determine the interest rate earned on a $450 deposit when $475 is paid back in one year.

A) 0.89 percent
B) 1.13 percent
C) 5.56 percent
D) 13.0 percent

Question 61

What annual rate of return is implied on a $1,000 loan taken next year when $1,500 must be repaid in year 5?

A) 8.45 percent
B) 10.00 percent
C) 10.67 percent
D) 12.50 percent

Question 62

At age 20 you invest $1,000 that earns 7 percent each year. At age 30 you invest $1,000 that earns 10 percent per year. In which case would you have more money at age 60?

A) At age 20 invest $1,000 at 7 percent.
B) At age 30 invest $1,000 at 10 percent.
C) Both yield the same amount at age 60.
D) There is not enough information to determine which case earns the most money at age 60.

Question 63

Five years ago, Jane invested $5,000 and locked in an 8 percent annual interest rate for 25 years (end 20 years from now). James can make a 20-year investment today and lock in a 10 percent interest rate. How much money should he invest now in order to have the same amount of money in 20 years as Jane?

A) $3,160.43
B) $3,464.11
C) $5,089.91
D) $7,346.64

Question 64

You invested $5,000 in the stock market one year ago. Today, the investment is valued at $4,500. What return did you earn? What return would you need to get next year to break even overall?

A) −111.11 percent, +90 percent, respectively
B) −90 percent, +111.11 percent, respectively
C) −10 percent, +11.11 percent, respectively
D) −11.11 percent, +10 percent, respectively

Question 65

What is the present value of a $7,000 payment made in six years when the discount rate is 4 percent?

A) $5,290.42
B) $5,532.20
C) $5,802.82
D) $6,103.73

Question 66

A deposit of $500 earns 5 percent the first year, 6 percent the second year, and 7 percent the third year. What would be the third year future value?

A) $595.46
B) $615.62
C) $634.91
D) $671.02

Question 67

How long will it take $4,000 to reach $4,500 when it grows at 8 percent per year?

A) 1.12 years
B) 1.48 years
C) 1.53 years
D) 9.00 years

Question 68

At age 25 you invest $2,000 that earns 6 percent each year. At age 35 you invest $2,000 that earns 9 percent per year. In which case would you have more money at age 60?

A) At age 25 invest $2,000 at 6 percent.
B) At age 35 invest $2,000 at 9 percent.
C) Both yield the same amount at age 60.
D) There is not enough information to determine which case earns the most money at age 60.

Question 69

You invested $1,000 in the stock market one year ago. Today, the investment is valued at $750. What return did you earn? What return would you need to get next year to break even overall?

A) −112.5 percent, +75 percent, respectively
B) −75 percent, +112.5 percent, respectively
C) −33.33 percent, +25 percent, respectively
D) −25 percent, +33.33 percent, respectively

Question 70

What is the future value of $600 invested for four years earning an 11 percent interest rate annually?

A) $792.90
B) $803.61
C) $899.23
D) $910.84

Question 71

What annual rate of return is earned on a $2,000 investment made in year 3 when it grows to $3,000 by the end of year 6?

A) 6.99 percent
B) 14.47 percent
C) 24.00 percent
D) 50.00 percent

Question 72

Compute the present value of $3,000 paid in four years using the following discount rates: 3 percent in year 1, 4 percent in year 2, 5 percent in year 3, and 6 percent in year 4.

A) $1,998.73
B) $2,109.14
C) $2,491.28
D) $2,516.26

Question 73

Ten years ago, Jane invested $1,000 and locked in a 7 percent annual interest rate for 30 years (end 20 years from now). James can made a 20-year investment today and lock in a 6 percent interest rate. How much money should he invest now in order to have the same amount of money in 20 years as Jane?

A) $673.75
B) $1,206.59
C) $1,967.15
D) $2,373.54

Question 74

What annual rate of return is earned on a $4,000 investment made in year 2 when it grows to $8,000 by the end of year 8?

A) 9.00 percent
B) 12.00 percent
C) 12.25 percent
D) 50.00 percent

Question 75

What is the present value of a $600 payment in one year when the discount rate is 8 percent?

A) $498.61
B) $525.87
C) $555.56
D) $575.09

Question 76

What is the future value of $2,500 deposited for one year earning a 14 percent interest rate annually?

A) $2,550
B) $2,850
C) $2,950
D) $3,150

Question 77

You invested $5,000 in the stock market one year ago. Today, the investment is valued at $5,500. What return did you earn? What return would you suffer next year for your investment to be valued at the original $5,000?

A) 10 percent, −9.09 percent, respectively
B) −10 percent, +9.09 percent, respectively
C) 110 percent, −10 percent, respectively
D) 110 percent, −9.09 percent, respectively

Question 78

You invested $1,000 in the stock market one year ago. Today, the investment is valued at $1,250. What return did you earn? What return would you suffer next year for your investment to be valued at the original $1,000?

A) +25 percent, −20 percent, respectively
B) −25 percent, +20 percent, respectively
C) 125 percent, −25 percent, respectively
D) 125 percent, −20 percent, respectively

Question 79

What annual rate of return is implied on a $700 loan taken next year when $800 must be repaid in year 3?

A) 4.55 percent
B) 4.76 percent
C) 6.90 percent
D) 7.14 percent

Question 80

How long will it take $100 to reach $500 when it grows at 10 percent per year?

A) 7.20 years
B) 16.89 years
C) 17.46 years
D) 40.00 years