Deck 3: Understanding and Appreciating the Time Value of Money

Question 1

As a future graduation present, you uncle has just placed $6,000 in a bank account that will earn an annual rate of return of 6%. How much will be in that account when you graduate in four years?

A) $7,731.55
B) $6,752.56
C) $6,247.70
D) $7,790.63
E) $7,574.86

Answer 1

$7,574.86

Question 2

You have just remembered that four years ago you placed $1,000 in a bank account. If the bank was paying an annual rate of return of 8% during that time, how much should you have in your forgotten account?

A) $1,253.03
B) $1,360.49
C) $1,321.92
D) $1,301.92

Answer 2

$1,360.49

Question 3

The ________ Principle states that a dollar today is worth more than a dollar in the future.

A) Future value of money
B) Discounted value of money
C) Adjusted value of money
D) Time value of money
E) Annuity value of money

Answer 3

Time value of money

Question 4

By allowing the interest that you earn on an investment to stay in the investment and to earn interest on the interest you have already earned is called what?

A) the power of of present value
B) the power of compound interest
C) the power of simple interest
D) the power of time
E) the power of future value

Question 5

You have been saving for five years toward the purchase of a new mountain bike. You placed $600 in a bank account and have earned an annual rate of return of 12%. How much do you now have in your bank account?

A) $1,057.41
B) $1,293.71
C) $978.70
D) $1,138.70

Question 6

The current value in today's dollars of a future sum of money is called

A) future value.
B) adjusted value.
C) compounded value.
D) present value.
E) discounted value.

Question 7

Your great-uncle placed $500 a year in a bank account for your "college fund" for each of the last 18 years. How much is now in your college account (at the end of the eighteenth year) if your account earned an annual rate of return of 6%?

A) $15,452.83
B) $15,175.17
C) $16,427.17
D) $15,413.80
E) $15,546.18

Question 8

Suppose that you placed $500 in a bank account at the end of each year for the next 10 years. How much would be in that account at the end of the tenth year if the deposits earned an annual rate of return of 8% each year?

A) $8,079.46
B) $5400.00
C) $7,243.28
D) $6,355.04
E) $7,774.51

Question 9

Which financial planning concepts should be helpful to a couple planning for how much money to start saving for their retirement?

A) reinvesting
B) compound interest
C) future values
D) present values
E) all of the above

Question 10

John Madrid put $1,000 into a mutual fund yielding an 18% Annual Rate of Return. Using the Rule of 72 calculate approximately how long will it take to double in value.

A) three years, four months
B) three years, seven months
C) four years
D) four years, four months
E) five years

Question 11

Suppose that you want to create a "college fund" for your newborn child and place $300 in a bank account at the end of each of the next 20 years. If that account earns an annual rate of return of 7%, how much will be in that account at the end of the twentieth year?

A) $13,420.00
B) $12,977.53
C) $13,178.20
D) $11,828.32
E) $12,298.65

Question 12

This helpful investment rule-of-thumb tells you approximately how many years it takes for a sum of money to double in size.

A) rule of compound interest
B) rule of 72
C) rule of 100
D) rule of future value
E) rule of annuity doubling

Question 13

You have just placed $500 in a bank account that earns an annual rate of return of 6%. How much will you have in that bank account after 6 years?

A) $652.48
B) $709.26
C) $787.66
D) $758.66
E) $801.68

Question 14

The dollar value of an investment at some future point in time is also known as

A) future value.
B) present value.
C) compounded annuity.
D) the time value of money.
E) calculated value.

Question 15

An investment earning twelve percent interest per year should double in value in approximately four years.

Question 16

A one-time investment of $200 at a 10% Annual Rate of Return yields $242 in two years. The $242 is known as the

A) present value.
B) compound value.
C) principal plus interest.
D) future value.
E) annuity value

Question 17

Suppose that you invested $100 in a bank account that earned an annual rate of return of 10%. How much would you have in that bank account at the end of 10 years?

A) $259.37
B) $238.55
C) $293.74
D) $214.46
E) $279.23

Question 18

The present value of a financial asset is what you should be willing to pay today for that financial asset.

Question 19

Your money grows faster as the compounding period becomes longer.

Question 20

By the Rule of 72, what annual interest rate would be required to turn $100 into $200 in approximately six years?

A) 4%
B) 8%
C) 12%
D) 16%

Question 21

Suppose that you want to create a "retirement party fund" for yourself and place $50 in a bank account for each of the next 20 years. If that account earns an annual rate of return of 7%, how much will be in your retirement party fund at the end of the twentieth year?

A) $1,529.70
B) $2,679.22
C) $1,032.57
D) $2,049.77

Question 22

If your bank pays you interest in the form of an annual rate of return of 10% over each of the next five years, how much will your balance be if you make annual deposits of $400?

A) $2,248.37
B) $2,644.20
C) $2,516.31
D) $2,442.04

Question 23

Time value of Money calculations can be made much easier through the use of a financial calculator.

Question 24

The earlier you begin saving for your retirement, the easier it will be to reach your financial goals for retirement.

Question 25

Generally speaking, saving a little money on a regular basis when you are young can result in a large final payoff.

Question 26

A dollar received in the future is worth more than a dollar received today.

Question 27

What are some practical uses of present and future values?

Question 28

You invest $1,000 at age 20 at an annual rate of return of 12%. By the time you are 62 you will have amassed approximately ________.

A) $47,040
B) $67,214
C) $116,723
D) $504,000

Question 29

If you set your calculator to the "end" mode your calculator will assume cash flows occur at the end of each time period.

Question 30

Using the Rule of 72, if it will take approximately 12 years for your money to double, at what annually compounded interest rate is it invested?

A) 6%
B) 8%
C) 9%
D) 12%

Question 31

Your great-aunt wants to help with your college graduation party. She has just placed $5,000 dollars in a bank account that will earn an annual rate of return of 6%. If you graduate in four years, how much will be in your party account?

A) $7,120.89
B) $6,142.96
C) $5,960.47
D) $6,312.38

Question 32

Two of the most important factors in reaching your financial goals are the return on your investments and the length of time you have until you need your money.

Question 33

You currently have $11,167 in your savings account. What interest rate do you need to earn in order to have $20,000 in the account in 10 years?

A) 6%
B) 8%
C) 10%
D) There is not enough information to solve this question.

Question 34

Why is the time value of money an important concept in financial planning?

Question 35

The I/Y key on a financial calculator stores the information for the interest rate or the discount rate per period.

Question 36

Describe the effects and benefits of compound interest.

Question 37

Suppose that you place $450 in a bank account each year for the next 20 years. How much would be in your bank account at the end of the twentieth year if the deposits earned an annual rate of return of 6% each year?

A) $9,540.00
B) $10,876.31
C) $14,729.44
D) $16,553.52

Question 38

A compound interest table is useful in solving a time value of money problem. Name the variables involved.

Question 39

Using the Rule of 72, approximately how long will it take to double your money if you invest it at 8% compounded annually?

A) 6 months
B) 9 months
C) 6 years
D) 9 years
E) It depends on the amount of the initial investment.

Question 40

Your daughter has been saving $500 a year for each of the last 10 years for her "sweet sixteen" party. How much is now in her party account (at the end of the tenth year) if she earned an annual rate of return of 6%?

A) $6,590.40
B) $7,680.04
C) $5,300.00
D) $8,714.84

Question 41

Arnold learned something very valuable as a teenager from his dad. He was told to invest $1,000 at 12% interest at age 20 and leave it alone until age 65. Arnold's dad knew that one strategy that wealthy people use is to exercise self-discipline to never touch this long-term plan. Arnold is very happy he applied his dad's advice.
If he sticks to this plan, Arnold's savings will have grown to approximately ________ by age 62.

A) $116,723
B) $163,987
C) $9,646
D) $1,125,945

Question 42

One day as you were going through some old memorabilia, you discovered an old savings account in which you placed $100 twenty years ago. When you checked out the account, it currently had a balance of $320.71. What annual rate of interest did you earn?

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

Question 43

Most people achieve comfortable retirements by postponing saving until after age 50, when they are able to save a large amount on a regular basis.

Question 44

It is not realistic for a 20-year-old person to ever accumulate one million dollars by the time they reach 65 years of age.

Question 45

Suppose that you had deposited $100 in a bank account for each of the last 5 years. What annual interest rate is attached to this account if there is now (at the end of the fifth year) $758.92 in the account?

A) 10%
B) 16%
C) 19%
D) 21%
E) 23%

Question 46

Describe the two factors that affect how much we need to save to achieve financial goals.

Question 47

Who will end up with the largest amount of money invested at an annual rate of return of 9% over the next 42 years?

A) Jim saves $1,200 per year for the first 14 years and then stops putting any new money into the account for the remaining 28 years.
B) Jeremy saves nothing for the first 14 years and saves $1,200 per year for the next 14 years and then puts no more money into the account during the last 14 years.
C) Jerry saves nothing for the first 14 years and then saves $1,200 per year for the remaining 28 years.
D) Joey saves nothing for the first 14 years and then saves $1,500 per year for 14 years then stops putting any new money into the account for the remaining 14 years.
E) John saves nothing for the first 10 years and saves $1,500 per year for the remaining 32 years.

Question 48

Your money will grow or compound ________ as the number of compounding periods per year becomes ________.

A) faster; smaller
B) faster; larger
C) slower; larger
D) slower; compounded
E) none of the above are correct

Question 49

Arnold learned something very valuable as a teenager from his dad. He was told to invest $1,000 at 12% interest at age 20 and leave it alone until age 65. Arnold's dad knew that one strategy that wealthy people use is to exercise self-discipline to never touch this long-term plan. Arnold is very happy he applied his dad's advice.
If Arnold were to leave his money in the account until he was 68, by approximately what amount would the balance increase between his 62nd and 68th years?

A) $113,667
B) $1,096,471
C) $160,457
D) $1,973

Question 50

The present value interest factor is the inverse of the corresponding future value interest factor.

Question 51

What is the annual interest rate earned on a deposit that grew from $250 to $502.84 over the last 5 years?

A) 15%
B) 13%
C) 11%
D) 9%

Question 52

What is the annual interest rate earned on a deposit that grew from $60 to $111.06 over the last 8 years?

A) 14%
B) 12%
C) 8%
D) 6%

Question 53

It is really pretty easy to create a valuable personal financial plan without understanding the time value of money principle.

Question 54

Charlie is starting to save for his retirement now at age 20. If inflation averages 4% annually until his retirement age and he earns an annual rate of return of 4% on his investments during this period, then he should be able to enjoy a very comfortable retirement when he is retired.

Question 55

Is it possible to create a retirement estate of $585,000 instead of $310,000 without requiring much more to be invested every month?

A) probably not with inflation working against you
B) depends upon the interest rate or return you earn on the investment as well as the number of years until retirement.
C) absolutely not
D) there is not enough information available to answer this question

Question 56

Small changes in the interest rate can have a dramatic impact on future values.

Question 57

Arnold learned something very valuable as a teenager from his dad. He was told to invest $1,000 at 12% interest at age 20 and leave it alone until age 65. Arnold's dad knew that one strategy that wealthy people use is to exercise self-discipline to never touch this long-term plan. Arnold is very happy he applied his dad's advice.
Approximately how long will it take Arnold's savings to grow into $2,000?

A) 60 months.
B) 5 years.
C) 8.5 years.
D) 6 years.

Question 58

Arnold learned something very valuable as a teenager from his dad. He was told to invest $1,000 at 12% interest at age 20 and leave it alone until age 65. Arnold's dad knew that one strategy that wealthy people use is to exercise self-discipline to never touch this long-term plan. Arnold is very happy he applied his dad's advice.
Suppose the investment rate of return were 18%. At this rate, when would Arnold reach the $1,000,000 mark?

A) at age 42
B) at age 54
C) at age 62
D) at age 68

Question 59

Why should you care about the power of compounding and the time value of money?

A) It is critical to obtaining your future financial goals.
B) The sooner you start saving for retirement, the less you have to save each year.
C) You may outlive your Social Security and employer's retirement plan.
D) It is possible to build a large estate for yourself, spouse, and children.
E) all of the above

Question 60

Arnold learned something very valuable as a teenager from his dad. He was told to invest $1,000 at 12% interest at age 20 and leave it alone until age 65. Arnold's dad knew that one strategy that wealthy people use is to exercise self-discipline to never touch this long-term plan. Arnold is very happy he applied his dad's advice.
If his savings account had earned a more conservative 9% annual rate of return, Arnold's savings would be approximately ________ less by age 68.

A) $4,132
B) $62,585
C) $167,805
D) $1,871,663

Question 61

What is the present value of an annual payment of $1,500 discounted back 15 years at an annual rate of return of 3%?

A) $10,663.87
B) $12,334.56
C) $13,449.87
D) $17,906.90

Question 62

Present value lets us compare dollar values from different time periods.

Question 63

List at least five common examples of annuities.

Question 64

What is the future value of a series of $500 annual payments received at the end of each of the next 5 years' worth if they are invested at an annual rate of return of 6%?

A) $1,223.44
B) $2,176.65
C) $2,818.50
D) $3,309.76

Question 65

What is the present value of $500 received at the end of each of the next 5 years worth to you today at the appropriate discount rate of 6%?

A) $1,105
B) $1,850
C) $2,106
D) $2,778

Question 66

The discount rate is the interest rate used to bring ________ back to ________.

A) current dollars; present dollars
B) future dollars; present dollars
C) current interest rate; present present interest rate
D) future interest rate; present interest rate

Question 67

What is the present value of a $1,000 payment at the end of each of the next 10 years discounted back to the present at 5%?

A) $5,098
B) $7,722
C) $8,775
D) $9,112

Question 68

Someone has offered you the opportunity to purchase an IOU. The IOU will pay back a total of $500 in three years. How much would you be willing to pay for that IOU today if you want to earn an annual rate of return of 16%?

A) $320.33
B) $422.63
C) $292.63
D) $380.45

Question 69

What is the maximum that you would be willing to loan your brother for a $100 IOU if he promises to pay you back at the end of the year? You want to earn an annual rate of return of 12%.

A) $82.00
B) $89.29
C) $92.73
D) $88.00

Question 70

The future value of a current investment earning a positive rate of return is always greater than the present value of the investment.

Question 71

A compound annuity involves depositing or investing an equal sum of money at the end of each time period for a certain number of time periods and allowing it to grow.

Question 72

A series of equal dollar payments at the end of each period for "x" number of time periods is

A) an annuity.
B) a complex annuity.
C) an annuity due.
D) a deferred annuity.
E) an equal installment annuity.

Question 73

What is the price you would be willing to pay today for an IOU for $500 due in one year if you want to earn at least 16%?

A) $480.00
B) $431.03
C) $450.00
D) $395.33
E) $418.23

Question 74

An annuity is a series of unequal dollar payments coming at the end of each time period for a specified number of time periods.

Question 75

At the end of each year for ten years you deposit $750 in an account that earns an annual rate of return of 12%. What is the present value of these deposits?

A) $4,329.39
B) $5,241.48
C) $3,161.55
D) $4,237.67
E) $4,482.63

Question 76

What is the future value of a stream of $800 annual payments worth to the investor at the end of 10 years if these payments are invested at an annual rate of return of 8.5%?

A) $11,868.08
B) $12,195.22
C) $13,334.90
D) $13,667.88

Question 77

What is the present value today of $150 that will be received in four years from now if the discount rate is 12%?

A) $76.03
B) $95.33
C) $116.90
D) $105.60
E) $83.39

Question 78

What is the present value of an IOU for $1,000 due to be paid in two years, if the discount rate is 8%?

A) $857.34
B) $766.40
C) $885.00
D) $683.26
E) $810.77

Question 79

A compound annuity uses the principles of

A) reinvesting and present value.
B) compound interest and future value.
C) reinvesting and compound interest.
D) compound interest and present value.
E) amortization and reinvesting.

Question 80

Which one of the following is the "enemy" of compound interest and makes it very difficult to reach your financial goals?

A) inflation
B) annuity factor
C) simple interest
D) compound frequency
E) none of the above