Deck 4: Time Value of Money

Question 1

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.

Answer 1

the number of years required to double an investment.

Question 2

One Year Future Value 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

Answer 2

$728

Question 3

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.

Answer 3

discounting.

Question 4

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 5

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 6

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

Question 7

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 8

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 9

Multi-Year Future Value 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 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

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 18

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 19

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 20

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 21

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

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

Question 22

Interest-on-Interest 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 23

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 24

Rule of 72 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 25

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 26

Interest-on-Interest 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 27

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 28

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 29

Rule of 72 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 30

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 31

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

Question 32

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 33

Compounding with Different Interest Rates 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)$1,248.05
D)$,3030.00

Question 34

Rule of 72 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 35

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

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

Question 36

Rates over One Year 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 37

Rates over One Year 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 38

Rule of 72 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 39

Interest-on-Interest 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 40

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 41

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 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 42

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 43

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 44

Interest-on-Interest 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 45

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 46

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

Question 47

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 48

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 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 Rates 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 51

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 52

Solving for Rates 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 53

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 54

Solving for Rates 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 55

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 56

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 57

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 58

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 59

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 60

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 61

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 percent, -20 percent, respectively
B)-25 percent, +20 percent, respectively
C)125 percent, -25 percent, respectively
D)125 percent, -20 percent, respectively

Question 62

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

Question 63

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

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

Question 64

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

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

Question 65

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

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

Question 66

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 67

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

Question 68

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 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 69

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 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 70

Which is more valuable,receiving $775 today or receiving $885 in 2.5 years if interest rates are 7.25 percent?

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 71

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

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

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

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 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 74

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 75

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 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 76

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 8?

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

Question 77

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

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

Question 78

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 79

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 6?

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

Question 80

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