Deck 5: The Time Value of Money

Question 1

The future value increases as either the interest rate or the number of periods per year increases, other things held constant.

Answer 1

True

Question 2

Due to compounding effects, the growth in the future value of an investment over time is linear.

Answer 2

False

Question 3

The time value of money accounts for the fact that people place different value on that money over time.

Answer 3

True

Question 4

The higher the rate of interest, the more likely you will forgo current consumption.

Question 5

Compound interest increases as the number of years decreases.

Question 6

The time value of money concept recognizes that people require additional compensation for deferring consumption.

Question 7

The process of converting the initial amount into future value is called discounting.

Question 8

The future value technique uses discounting to find the future value of each cash flow at the end of a project's life.

Question 9

Some of the cash flows shown on a time line can be equal in size, but none can be unequal.

Question 10

Compounding increases the growth of the total interest earned.

Question 11

The higher the rate of interest, the more likely you will elect to invest your funds and forgo current consumption. Same question as the previous question?

Question 12

The growth in the future value of an investment over time is not linear, but exponential.

Question 13

The value of a dollar invested at a positive interest rate grows over time but at a slower rate further into the future.

Question 14

The further in the future you receive a dollar, the more value you place on the dollar today.

Question 15

Starting to invest early for retirement reduces the benefits of compound interest.

Question 16

Compounding is the process by which interest earned on an investment is reinvested so that in future periods, there is interest on interest as well as the original principal.

Question 17

The value of a dollar invested at a positive interest rate grows over time.

Question 18

The value of a dollar invested at a positive interest rate grows at an increasing rate over time.

Question 19

The time value of money is based on the principle that people have a positive time preference for consumption.

Question 20

Compound interest consists of both simple interest and interest on interest.

Question 21

If the discount rate increases, then the present value of a potential investment would fall.

Question 22

The present value is simply the current value of a future cash flow that has been discounted at the relevant discount rate.

Question 23

The future value factor for 10 years at 15% with annual compounding is calculated as (1 + 0.15)¹⁰.

Question 24

The lower the discount rate, the lower the present value of a future cash flow.

Question 25

The process of calculating the present value of a future cash flow is called compounding.

Question 26

If the discount rate falls, then the present value of a potential investment would also fall.

Question 27

The more frequently the interest payments are compounded, the larger the future value of $1 for a given time period.

Question 28

The present value technique uses discounting to find the present value of each cash flow at the beginning of a project.

Question 29

To calculate the present value of a future amount, we divide the future value by the future value factor.

Question 30

William invested $5,000 in an account earning 10 percent for one year. If he had left his investment in that account for another two years, he would expect the total interest earned over the three years to be higher by exactly $1,000.

Question 31

The present value of $3,000 to be received in two years at a discount rate of 10 percent is $3,630.

Question 32

The farther in the future a dollar will be received, the less it is worth today.

Question 33

The higher the interest rate on an investment, the more money that is accumulated for any time period.

Question 34

If Bank A pays interest on a monthly basis and Bank B pays the same interest rate, but on a quarterly basis, then investing $1,000 in Bank B will result in a higher future value compared to investing the same amount in Bank A.

Question 35

The future value of an investment of $5,000 earning an interest rate of 10 percent compounded annually equals $6,000 at the end of one year.

Question 36

The higher the discount rate, the lower the present value of a future cash flow.

Question 37

Suppose Randy plans to invest $1,000. He can earn an annual rate of 5% on Security A, while Security B has an effective annual rate of 10%. After 11 years, the compounded value of Security B should be somewhat less than double the compounded value of Security A.

Question 38

The future value in three years of $5,000 invested today at a discount rate of 10 percent is $6,655.

Question 39

The present value factor increases as the number of period decreases.

Question 40

You need $5000 in five years. If you could choose a discount rate of 8 percent or 10 percent, you should always choose the higher rate because you would need a higher starting amount.

Question 41

Which of the following equations is used to compute the future value using continuous compounding?

A) FV_∞ = PV × e ^{i × n}
B) FV_∞ = PV ÷ e ^{i × n}
C) FV_∞ = eⁱ ÷ PV
D) FV_∞ = eⁱ × PV

Question 42

Which of the following statements about the time value of money concept is true ?

A) A dollar received today is worth more than a dollar to be received in the future because future dollars are not affected by inflation.
B) A dollar received today is worth less than a dollar to be received in the future because future dollars are not affected by inflation.
C) A dollar received today is worth more than a dollar to be received in the future because funds received today can be invested to earn a return.
D) A dollar to be received in the future is worth more than a dollar received today because it would have less risk associated with it.

Question 43

The Rule of 72 allows one to calculate the approximate amount of time required to double an investment.

Question 44

Future value measures:

A) what one or more cash flows are worth at the end of a specified period.
B) what one or more cash flows that is to be received in the future will be worth today.
C) the value of an investment after subtracting interest earned on it for one or more periods.
D) the value of an investment in today's terms.

Question 45

You are considering two investments (ORD and DUE) that each pay $5000 each year for the next 10 years. Investment ORD makes each payment at the end of the year, and Investment DUE makes payments at the beginning of each year. Which of the following statements is correct?

A) The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.
B) The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.
C) The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
D) The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.

Question 46

Future value focuses on the valuation of cash flows received over time, while present value focuses only on the valuation of cash flows received at a point in time.

Question 47

The time value of money refers to the concept of:

A) what the value of the stream of future cash flows is today.
B) why a dollar received tomorrow is worth more than a dollar received today.
C) what the time required to double an amount of money.
D) why people prefer to consume things at some time in the future rather than today.

Question 48

The compound annual growth rate (CAGR) is the average annual growth rate over a given number of years.

Question 49

Which of the following investments will have the highest future value?

A) $1,300 invested at an annual interest rate of 10% for 5 years
B) $1,000 invested at an quarterly interest rate of 2.25% for 10 years
C) $1,300 invested at an quarterly interest rate of 2.25% for 5 years
D) $1,000 invested at an annual interest rate of 10% for 10 years

Question 50

The Rule of 72 allows one to calculate the return earned on an investment over six years.

Question 51

Which of the following statements is correct, assuming positive interest rates and holding other things constant?

A) Banks A and B offer the same annual rate of interest, but A pays interest quarterly and B pays semiannually. A deposit in Bank B will have a higher value in five years.
B) Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays monthly. A deposit in Bank B will have a higher value in five years.
C) Banks A and B offer the same nominal annual rate of interest, but A pays interest daily and B pays semiannually. A deposit in Bank B will have a higher value in five years.
D) Banks A and B offer the same nominal annual rate of interest, but A pays interest weekly and B pays quarterly. A deposit in Bank B will have a higher value in five years.

Question 52

The present value factor 1 / (1 + i)ⁿ is the reciprocal of the future value factor (1 + i)ⁿ.

Question 53

The process of converting an amount given at the present time into a future value is called:

A) annualizing.
B) discounting.
C) compounding.
D) capital budgeting.

Question 54

Your bank account pays a 6% annual rate of interest. The interest is compounded quarterly. This implies that the periodic rate of interest is 1.5% and the annual rate of interest is greater than 6%.

Question 55

Compound growth occurs when the initial value of a number increases or decreases each period by the factor (1 + growth rate).

Question 56

Which of the following statements about the time value of money concept is true?

A) It means a dollar received today is worth less than a dollar received tomorrow.
B) It assumes that inflation rate remains constant for the foreseeable future.
C) It refers to the fact that higher cash flows in earlier years are less desirable.
D) It assumes that people prefer to consume things at some time in the future rather than today.

Question 57

Jane has $5,000 invested in a bank that pays 4% compounded annually. It will take her approximately 28 years for her funds to triple.

Question 58

Which of the following is true of the future value of an investment?

A) The higher the interest rate, the higher the future value of an investment.
B) The lower the interest rate, the higher the future value of an investment.
C) The lower the number of compounding periods, the higher the future value of an investment.
D) The lower the present value of an investment, the higher the future value of an investment.

Question 59

Which of the following statements is correct?

A) A time line is not meaningful unless all cash flows occur annually.
B) Time lines are useful for visualizing complex problems prior to doing actual calculations.
C) Time lines cannot be constructed in situations when the cash flows occur at yearly and quarterly frequencies
D) Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods.

Question 60

Which of the following statements about the time value of money is true?

A) The value of a dollar invested at a positive interest rate decreases over time.
B) The further in the future you receive a dollar, the less it is worth today.
C) A dollar in hand today is worth less than a dollar to be received in the future.
D) The higher the rate of interest, the more likely an investor will elect to consume at present and forgo invest his funds.

Question 61

Kevin Robertson would like to buy a condo in Florida in six years. He is looking to invest $75,000 today in a stock that is expected to earn a return of 18.3 percent annually. How much will he have at the end of six years? (Round to the nearest dollar.)

A) $205,575
B) $157,350
C) $184,681
D) $273,620

Question 62

You are interested in investing $15,000, a gift from your grandparents, for the next four years in a mutual fund that will earn an annual return of 8 percent. What will your investment be worth at the end of four years? (Round to the nearest dollar.)

A) $18,816
B) $20,407
C) $20,221
D) $18,089

Question 63

Carlos Lopes is looking to invest for the next three years. He is looking to invest $7,500 today in a bank CD that will earn interest at 5.75 percent annually. How much will he have at the end of three years? (Round to the nearest dollar.)

A) $8,870
B) $8,575
C) $8,681
D) $8,990

Question 64

What is the future value of $1,500 after 5 years if the annual return is 6%, compounded semiannually?

A) $1,819
B) $1,915
C) $2,016
D) $2,117

Question 65

What's the future value of $1,500 after 5 years if the annual return is 6%, compounded quarterly?

A) $1,819
B) $2,020
C) $2,016
D) $2,117

Question 66

Jack Palomo has deposited $2,500 today in an account paying 6 percent interest annually. What would be the simple interest earned on this investment in five years? If the account pays compound interest, what will be the interest on interest in five years?

A) $750; $95.56
B) $150; $845.56
C) $150; $95.56
D) $95.56; $845.56

Question 67

Which of the following statements is true?

A) The longer the time period that funds are invested, the greater the future value.
B) The lower the discount rate that funds are invested at, the greater the future value.
C) The shorter the time period that funds are invested, the greater the future value.
D) The higher the interest rate, the slower the value of an investment will grow.

Question 68

Lori Willis plans to invest for retirement, which she hopes will be in 20 years. She is planning to invest $25,000 today in U.S. Treasury bonds that will earn interest at 6.25 percent annually. How much will she have at the end of 20 years? (Round to the nearest dollar.)

A) $68,870
B) $50,625
C) $84,046
D) $75,000

Question 69

Your mother is trying to choose one of the following bank CDs to deposit $10,000. Which will have the highest future value if she plans to invest for three years?

A) 3.50% compounded daily
B) 3.25% compounded monthly
C) 3.40% compounded quarterly
D) 3.75% compounded annually

Question 70

Juan Vinson is planning to buy a house in five years. He is looking to invest $25,000 today in an index mutual fund that will provide him a return of 12 percent annually. How much will he have at the end of five years? (Round to the nearest dollar.)

A) $45,000
B) $28,000
C) $44,059
D) $28,530

Question 71

Richard McLean wants to invest $3,000 in an account paying annual interest of 5.25 percent compounded quarterly. What is the interest on interest after four years?

A) $695.98
B) $65.98
C) $630.00
D) $157.50

Question 72

Lorene Buckley wants to invest $3,500 today in a money market fund that pays an annual rate of 5 percent paid quarterly. She plans to fund a scholarship with the proceeds at her alma mater, Towson University. How much will Lorene have at the end of seven years? (Round to the nearest dollar.)

A) $5,091
B) $3,849
C) $4,956
D) $5,075

Question 73

Dat Nguyen is depositing $17,500 in an account paying an annual interest rate of 8.25 percent compounded monthly. What is the interest on interest after six years?

A) $8,662.50
B) $10,925.44
C) $2,497.63
D) $1,092.48

Question 74

Your aunt is looking to invest a certain amount today. Which of the following choices will give the maximum interest?

A) Three-year CD at 6.5% annual rate
B) Three-year CD at 6.75% annual rate
C) Three-year CD at 6.25% annual rate
D) Three-year CD at 7% annual rate

Question 75

Your brother has asked you to help him to choose an investment. He has $6,000 to invest today for a period of two years. You identify a bank CD that pays an annual interest rate of 4.25 percent with the interest being paid quarterly. What will be the value of the investment in two years?

A) $6,550
B) $6,529
C) $6,107
D) $6,216

Question 76

Dynoxo Textiles has a cash inflow of $1 million, which it needs for a long-term investment, at the end of one year. It plans to deposit the money in a bank CD that pays daily interest at an annual rate of 4.50 percent. What will be the value of the investment at the end of the year? (Round to the nearest dollar.)

A) $1,020,475
B) $1,000,103
C) $1,037,500
D) $1,046,025

Question 77

Joseph Ray just received an inheritance of $50,000 from his great aunt. He plans to invest the funds for retirement. If Joseph can earn 6% per year with quarterly compounding for 30 years, how much will he have accumulated? (Round off to the nearest dollar.)

A) $298,466
B) $271,550
C) $284,622
D) $269,113

Question 78

Camille Noah is investing $5,000 in an account that pays an annually compounded rate of 6.75 percent for three years. What is the interest on interest if interest is compounded?

A) $1,012.50
B) $1,082.38
C) $82.38
D) $69.88

Question 79

Joseph Ray just received an inheritance of $35,775 from his great aunt. He plans to invest the funds for retirement. If Joseph can earn 4.75% per year with quarterly compounding for 32 years, how much will he have accumulated? (Round off to the nearest dollar.)

A) $237,416
B) $71,550
C) $184,622
D) $162,113

Question 80

Paul Springer plans to save for a down payment for a house in 10 years. He will be able to invest $12,000 today in a money market account that will pay him an annual interest rate of 5.50 percent on a monthly basis. How much will he have at the end of 10 years?

A) $12,640
B) $20,773
C) $24,859
D) $23,080