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

Question 1

Compounding with Different Interest Rates 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

Answer 1

$601.02

Question 2

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.

Answer 2

the annual rate earned.

Question 3

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.

Answer 3

the higher the interest rate, the shorter the time period needed to achieve the growth.

Question 4

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 5

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 6

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 7

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

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

Question 8

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.

Question 9

What is the future value of $2000 deposited for one year earning 6% interest rate annually?

A) $120
B) $2000
C) $2120
D) $4120

Question 10

Multi-Year Future Value How much would be in your savings account in 10 years after depositing $50 today if the bank pays 7% interest per year?

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

Question 11

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 12

One Year Future Value What is the future value of $700 deposited for one year earning 4% interest rate annually?

A) $28
B) $700
C) $728
D) $1428

Question 13

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 14

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 15

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 16

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 17

What is the future value of $1000 deposited for one year earning 5% interest rate annually?

A) $1000
B) $1005
C) $1050
D) $2050

Question 18

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

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

Question 19

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 20

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 21

Compounding with Different Interest Rates A deposit of $1000 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) $1082.15
B) $1230.00
C) $1248.05
D) $3030.00

Question 22

Present Value What is the present value of a $500 payment made in 4 years when the discount rate is 8 percent?

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

Question 23

Present Value What is the present value of a $200 payment made in 3 years when the discount rate is 8 percent?

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

Question 24

Rule of 72 Approximately how many years does it take to double a $600 investment when interest rates are 6% per year?

A) .08 years
B) 8 years
C) 8.33 years
D) 12 years

Question 25

Discounting One Year 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 26

Present Value What is the present value of a $750 payment made in 3 years when the discount rate is 5 percent?

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

Question 27

Rule of 72 Approximately how many years does it take to double a $300 investment when interest rates are 8% per year?

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

Question 28

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

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

Question 29

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

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

Question 30

Interest-on-Interest Consider a $500 deposit earning 5 percent interest per year for 5 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 31

Rule of 72 Approximately what interest rate is needed to double an investment over 8 years?

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

Question 32

Rule of 72 Approximately what interest rate is needed to double an investment over 4 years?

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

Question 33

Discounting One Year 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 34

Compounding with Different Interest Rates 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 35

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

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

Question 36

Compounding with Different Interest Rates 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 37

Rule of 72 Approximately how many years does it take to double a $500 investment when interest rates are 4% per year?

A) .06 years
B) 6 years
C) 6.94 years
D) 18 years

Question 38

Rule of 72 Approximately what interest rate is needed to double an investment over 6 years?

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

Question 39

Interest-on-Interest Consider a $1,000 deposit earning 7 percent interest per year for 4 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 40

Interest-on-Interest Consider a $2,000 deposit earning 6 percent interest per year for 5 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 41

Moving Cash Flows 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 42

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

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

Question 43

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

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

Question 44

Interest-on-Interest Consider a $200 deposit earning 8 percent interest per year for 3 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 45

Moving Cash Flows 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 46

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

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

Question 47

Future Value 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 48

Solving for Time 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 49

Future Value 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 50

Solving for Time 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

Question 51

Moving Cash Flows 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 52

Solving for Time 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 53

Solving for Time 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 54

Solving for Time 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 55

Solving for Rates 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%, +75%, respectively
B) -75%, +112.5%, respectively
C) -33.33%, +25%, respectively
D) -25%, +33.33% respectively

Question 56

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

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

Question 57

Solving for Time 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 58

Moving Cash Flows 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 59

Moving Cash Flows 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 60

Moving Cash Flows 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 61

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

A) 8%
B) 12.2%
C) 14.4%
D) 15.8%

Question 62

Solving for Rates 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 eight?

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

Question 63

What is the future value of $600 deposited for 4 years earning an 11% interest rate annually?

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

Question 64

Solving for Rates 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%, -20%, respectively
B) -25%, +20%, respectively
C) 125%, -25%, respectively
D) 125%, -20%, respectively

Question 65

Solving for Rates 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%, +90%, respectively
B) -90%, +111.11%, respectively
C) -10%, +11.11%, respectively
D) -11.11%, +10%, respectively

Question 66

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

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

Question 67

General TVM 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 twenty 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 68

Determine the interest rate earned on a $800 deposit when $808 is paid back in one year.

A) 100%
B) 10%
C) 1%
D) 15%

Question 69

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

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

Question 70

Solving for Rates 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%
B) 10.00%
C) 10.67%
D) 12.50%

Question 71

Solving for Rates 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%
B) 4.76%
C) 6.90%
D) 7.14%

Question 72

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

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

Question 73

Solving for Rates 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 six?

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

Question 74

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

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

Question 75

Solving for Rates 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%, -9.09%, respectively
B) -10%, +9.09%, respectively
C) 110%, -10%, respectively
D) 110%, -9.09%, respectively

Question 76

Compute the present value of $4,000 paid in five years using the following discount rates: 10% in year 1, 2% in year 2, 12% in year 3, and 9% in years 4 and 5.

A) $2,679.15
B) $2,206.81
C) $2,317.03
D) $2,362.19

Question 77

Approximately how many years does it take to double a $475 investment when interest rates are 8% per year?

A) 18 years
B) 12 years
C) 9 years
D) 4.75 years

Question 78

Which is more valuable, receiving $775 today or receiving $885 in two and one-half years if interest rates are 7.25%?

A) Receiving $775 today.
B) Receiving $885 in 2.5 years.
C) They are worth the same amount.
D) Need more information to make a determination.

Question 79

General TVM 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 twenty 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 80

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

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