Deck 3: The Time Value of Money Part 1

Question 1

Which of the following investments has a larger future value? A $100 investment earning 10% per year for 5 years or a $100 investment earning 5% per year for 10 years?

A) An investment of $100 invested at 10% per year for 5 years because it has a future value of $161.05.
B) An investment of $100 invested at 10% per year for 5 years because it has a future value of $162.89.
C) An investment of $100 invested at 5% per year for 10 years because it has a future value of $161.05.
D) An investment of $100 invested at 5% per year for 10 years because it has a future value of $162.89.

Answer 1

D

Question 2

An investment of $100 today is worth $116.64 at the end of two years if it earns an annual interest rate of 8%. How much interest is earned in the first year and how much in the second year of this investment?

A) The interest earned in year one is $8.32 and the interest earned in year two is $8.32.
B) The interest earned in year one is $8.00 and the interest earned in year two is $8.64.
C) The interest earned in year one is $8.64 and the interest earned in year two is $8.00.
D) There is not enough information to solve this problem.

Answer 2

B

Question 3

________ is simply the interest earned in subsequent periods on the interest earned in prior periods.

A) Quoted interest
B) Anticipated interest
C) Simple interest
D) Compound interest

Answer 3

D

Question 4

A home improvement firm has quoted a price of $9,800 to fix up John's backyard. Five years ago, John put $7,500 into a home improvement account that has earned an average of 5.25% per year. Does John have enough money in his account to pay for the backyard fix-up?

A) Yes; John now has exactly $9,800 in his home improvement account.
B) No; John has only $9,687 in his home improvement account.
C) Yes; John now has $10,519 in his home improvement account.
D) There is not enough information to answer this question.

Question 5

The financial aid office at your university has offered to pay your full annual tuition cost of $22,000 this year, as long as you maintain a grade point average of 3.00. If tuition costs rise at a rate of 6% per year while you are in college, but the financial aid office continues to pay exactly $22,000 per year for your tuition, how much out-of-pocket tuition costs will you have your senior year? NOTE: Think carefully about this problem when figuring the number of years from the start of your freshman year to the start of your senior year, assuming normal progress toward graduation in four years. Further, be aware that while tuition costs are rising your tuition is covered up to only $22,000. You must pay any excess tuition costs.

A) $0
B) $3,351
C) $4,202
D) $5,774

Question 6

Which of the following will result in a future value greater than $100?

A) PV = $50, r = an annual interest rate of 10%, and n = 8 years.
B) PV = $75, r = an annual interest rate of 12%, and n = 3 years.
C) PV = $90, r = an annual interest rate of 14%, and n = 1 year.
D) All of the future values are greater than $100.

Question 7

A two-year investment of $200 is made today at an annual interest rate of 6%. Which of the following statements is true?

A) The interest earned in year two is $12.00 and year one is $12.72.
B) The interest earned in year one is $12.00 and year two is $12.72.
C) The FV is $224.00.
D) The future value would be greater if the interest rate were lower.

Question 8

Which of the following investments has a larger future value: Investment A--a $1,000 investment earning 5% per year for 6 years, or Investment B--a $500 investment earning 10% per year for 6 years, with a bonus of an extra $500 added at the end of the sixth year?

A) Investment B, with a future value of $1,386.
B) Investment A, with a future value of $1,386.
C) Investment A, with a future value of $1,340.
D) The investments have equal value.

Question 9

A two-year investment of $200 is made today at an annual interest rate of 6%. Which of the following statements is true?

A) The future value would be greater if the interest rate was higher.
B) The present value would be greater if the interest rate was higher.
C) The future value would be greater if the interest rate was lower.
D) The future value does not change as the interest rate changes.

Question 10

A two-year investment of $200 is made today at an annual interest rate of 6%. Which of the following statements is true?

A) The PV is $178.00.
B) The FV is $224.00.
C) The FV is $224.72.
D) This question is irrelevant because there are no two-year investments that earn an average of 6% per year.

Question 11

Jasmine and her spouse have saved $4,500 for a 12-day cruise vacation in Europe. The couple needs $5,000 for a "nice" cabin or $6,000 for a "luxury" cabin. If cabin prices are expected to remain constant for the next three years and Jasmine expects to earn 6% per year on her investments, will the couple's savings be enough to afford the "nice" cabin in three years? Can they afford the luxury cabin? Why or why not?

A) Yes, they can afford the "nice" cabin or the luxury cabin because their $4,500 investment will increase to $6,360 by the end of year three.
B) Yes, they can afford the "nice" cabin or the luxury cabin because their $4,500 investment will increase to $5,360 by the end of year three.
C) Yes, they can afford the "nice" cabin but NOT the luxury cabin because their $4,500 investment will only increase to $5,360 by the end of year three.
D) No, they cannot afford the "nice" cabin or the luxury cabin because their $4,500 investment will only increase to $4,950 by the end of year three.

Question 12

The one-time payment of money at a future date is often called a ________.

A) lump-sum payment
B) present value
C) principal amount
D) perpetuity payment

Question 13

The current price on a 60-inch flat panel LCD HD television is $2,300. Big screen HD television prices have dropped at an average rate of 9% per year in recent years. If you expect this trend to continue, how much will this style of television cost in three years?

A) $2,979
B) $2,300
C) $1,958
D) $1,733

Question 14

Your aunt places $13,000 into an account earning an interest rate of 7% per year. After 5 years the account will be valued at $18,233.17. Which of the following statements is correct?

A) The present value is $13,000, the time period is 7 years, the present value is $18,233.17, and the interest rate is 5%.
B) The future value is $13,000, the time period is 5 years, the principal is $18,233.17, and the interest rate is 7%.
C) The principal is $13,000, the time period is 5 years, the future value is $18,233.17, and the interest rate is 7%.
D) The principal is $13,000, the time period is 7 years, the future value is $18,233.17, and the interest rate is 5%.

Question 15

If you invest $1,800 today, how much money will you have in 5 years?

A) $1,800
B) This question cannot be answered because it is missing an annual rate of return.
C) $2,287
D) This question cannot be answered because it is missing the type of investment made.

Question 16

In two years Rocky plans to enroll at Whatsamatta U., a prestigious university in Frostbite Falls, MN. If the current tuition is $23,500 per year and is expected to increase at a rate of 6% per year, how much will Rocky pay in tuition his first year of school? (His first tuition payment is exactly two years from today.) In his fourth year? (His last tuition payment is exactly 5 years from today) (Rounded to the nearest dollar.)

A) $23,500 and $29,668
B) $26,405 and $29,668
C) $23,500 and $31,448
D) $26,405 and $31,448

Question 17

Which of the following is the correct formula for calculating the future value?

Question 18

You wish to make a sizeable down payment on a house and you currently have $18,325 invested at an annual rate of 4.75%. How much money will be in the account in 2.5 years if it continues to earn at its present rate?

A) $18,325
B) $19,464
C) $20,579
D) $20,605

Question 19

A $100 deposit today that earns an annual interest rate of 10% is worth how much at the end of two years? Assume all interest received at the end of the first year is reinvested the second year.

A) $100
B) $120
C) $121
D) $122

Question 20

Steve would like to buy a new car but must complete a two-year commitment to the Peace Corp before he will drive the new car. The current price of the car Steve wants to buy is $22,000, and the dealer expects the price of a similar new car to be $24,000 in two years. If Steve can earn an annual interest rate of 3% on his money, should he buy the car now or wait for two years? Why? Note: Storage costs if Steve purchases the car are $0. Please limit your considerations to the factors offered in the answer choices.

A) Buy now because if Steve invests the $22,000 today it will only increase in value to $23,340, and this is less than the cost of his desired new car in two years.
B) Steve is indifferent because his $22,000 investment will be worth exactly $24,000 after two years.
C) Buy in two years because at $24,000 the car will cost less than the $24,385 Steve will have after investing the money for two years.
D) Buy in two years because $24,000 is a real deal for the car Steve wants.

Question 21

Consider a two-year investment: Given a constant and positive interest rate, the interest earned in the second year will be greater than the interest earned in the first year (assuming annual compounding).

Question 22

An investment promises a payoff of $195 two and one-half years from today. At a discount rate of 7.5% per year, what is the present value of this investment?

A) $162.03
B) $162.75
C) $169.47
D) There is not enough information to answer this question.

Question 23

Which of the following actions will INCREASE the present value of an investment?

A) Decrease the interest rate.
B) Decrease the future value.
C) Increase the amount of time.
D) All of the above will increase the present value.

Question 24

Your parents plan to spend $20,000 on a car for you upon graduation from college. If you will graduate in three years and your parents can earn 4.125% annually on their investment, how much money must they set aside today for your car?

A) $20,000
B) $17,704
C) $17,716
D) $16,387

Question 25

The TVM equation can be algebraically manipulated to solve for any of the variables EXCEPT for the time period n.

Question 26

Sam wishes to invest $8,000 into an account earning 6% compounded annually. If he invests the money today, how much will be in the account in 6 years? If he waits three years before investing his $8,000 and invests that money for three years, will he earn one-half of the interest earned in the first scenario since he had the same amount invested at the same rate but for only one-half of the time? Explain how you arrived at your answer.

Question 27

Consider the TVM equation: A decrease in the interest rate will decrease the future value, other things remaining equal.

Question 28

$5,000 invested at an annual rate of 6% for 3 years has a smaller future value than $5,000 invested at an annual rate of 3% for 6 years.

Question 29

Consider the TVM equation: The future value is always greater than the present value, even if the interest rate is negative.

Question 30

In five years your oldest child will be in 8^th grade, at which point you and your family plan to vacation in Europe. You estimate that you will need $20,000 for the trip. How much do you need to set aside today if you can place your money in an investment vehicle earning an average of 4.50% per year?

A) $14,961
B) $15,073
C) $16,049
D) $16,058

Question 31

$100 invested at a rate of 5% for 10 years has the same future value as $100 invested at 10% compounded annually for 5 years.

Question 32

Your university is running a special offer on tuition. This year's tuition cost is $18,000. Next year's tuition cost is scheduled to be $19,080. The university offers to discount next year's tuition at a rate of 6% if you agree to pay both years' tuition in full today. How much is the total tuition bill today if you take the offer?

A) $18,000
B) $34,981
C) $37,080
D) $36,000

Question 33

Consider the TVM equation: A decrease in the time period will increase the future value, other things remaining equal.

Question 34

Consider the TVM equation: An increase in the present value will decrease the future value, other things remaining equal.

Question 35

You have purchased a Treasury bond that will pay $10,000 to your newborn child in 15 years. If this bond is discounted at a rate of 3.875% per year, what is today's price (present value) for this bond?

A) $8,417
B) $8,500
C) $5,654
D) $10,000

Question 36

Which of the following formulas is correct for finding the present value of an investment?

Question 37

You intend to buy a vacation home in seven years and plan to have saved $50,000 for a down payment. How much money would you have to place today into an investment that earns 8% per year to have enough for your desired down payment?

A) $29,175
B) $29,100
C) $37,065
D) $25,000

Question 38

A furniture store has a sofa on sale for $399.00, with the payment due one year from today. The store is willing to discount the price at an annual rate of 5% if you pay today. What is the amount if you pay today?

A) $380.
B) $399
C) $419
D) $394

Question 39

Which of the following actions will DECREASE the present value of an investment?

A) Decrease the interest rate.
B) Decrease the future value.
C) Decrease the amount of time.
D) All of the above will decrease the present value.

Question 40

If your bank offers a 5% annual rate of return compounded annually, then at the end of one year your $1.00 deposit would grow by $0.05 to $1.05. However, in the second year, your deposit would increase by $0.0525 to a total ending value of $1.1025. Explain why the second year earns more interest on the investment than the first year.

Question 41

Given an interest rate of 0%, the present value of $1,500 to be received 5 years in the future is less than $1,500.

Question 42

Your parts supplier gives you one-quarter of a year to pay for parts ordered today, or offers you a discount if you pay cash at purchase. You have just purchased $73,500 worth of parts from your supplier and the discount is at an annual rate of 8%. How much will you pay for the parts if you pay today?

A) $73,500
B) $72,099
C) $68,056
D) $72,046

Question 43

You grandparents leave on their dream vacation to Antarctica in two years.The cruise vacation will cost them $25,000. If they have already saved $23,500 and are investing it at a rate of 2.75% per year, will they have saved enough money for their trip?

A) No, because they forgot to factor in long underwear expenses.
B) Yes, to have enough money they would have already needed to save $23,375.
C) Yes, to have enough money they would have already needed to save $23,680.
D) No, to have enough money they would have already needed to save $23,680.

Question 44

When solving for a present value, the interest rate is commonly referred to as the compound rate, but when solving for the future value, the interest rate is called the discount rate.

Question 45

In the equation r = (FV/PV)^1/n - 1, the r is sometimes referred to as the ________.

A) interest rate
B) discount rate
C) growth rate
D) All of the above

Question 46

Compare and contrast the discount rate with the compound (or growth) rate.

Question 47

Consider the TVM equation: Present values and interest rates are inversely related.

Question 48

The Present Value Interest Factor (PVIF) is the reciprocal of the Future Value Interest Factor (FVIF).

Question 49

The school district needs to pass a bond levy for funding to remodel existing schools and to build new schools. Expenditures for the new and remodeled buildings will begin 18 months after passage of the bond. If the school district receives all funding immediately after the passage of the bond and can invest the funds at a rate of 3.75% per year, how large must the bond be for the district to have $45,000,000 at the start of construction?

A) $45,000,000
B) $47,554,834
C) $42,556,397
D) $42,582,422

Question 50

Write the equation for present value. How are prices and interest rates related? Refer to your equation when answering the first part of this question. Give an example of a real-world situation in which knowing the relationship between prices and interest rates would be valuable.

Question 51

The question "How much will I have in my account at a specific point in the future, given a specific interest rate?" is best answered by which form of the TVM equation?

Question 52

Your firm has sold a fleet of 100 cars to a local firm at a discounted price of $20,000 each (a total of $2,000,000) due in six months. You are willing to discount the purchase price at an annual rate of 4% if the firm pays cash today. What is the least amount of money you will accept if the firm pays your company today?

A) $2,039,608
B) $1,961,161
C) $1,960,495
D) This problem cannot be answered because we have an annual interest rate but only one-half year in time.

Question 53

Harold's parents have offered him a $10,000 high school graduation gift with an option for another $20,000 upon graduation from college in four years. His friends tell him this is a $30,000 gift from his parents, but Harold already knows something about the time value of money. If the expected inflation rate over the next four years is expected to be 4% per year, what does Harold think the gift is worth in today's dollars? How should he explain his thinking to his friends?

Question 54

John has always planned to save enough money to pay cash for his first new car. If John increases the rate he earns on his savings, then he will have to save more money today to buy his car at the same date in the future.

Question 55

Your manufacturing firm has just secured a sale to the federal government with payment of $450,000 due in nine months. You have asked your bank for cash today with the stipulation that you will give the proceeds from the government contract to the bank in nine months. The bank has agreed to your request if you allow them to discount the cash flows at an annual rate of 8%. How much will the bank pay you today under this agreement?

A) $424,761
B) $423,889
C) $476,739
D) $450,000

Question 56

Consider the TVM equation: The greater the interest rate, other things remaining equal, the greater the present value.

Question 57

Consider the TVM equation: Present value and time period are inversely related.

Question 58

$1,000 received 5 years from today discounted at an annual rate of 10% has a smaller present value than $1,000 received 10 years from today discounted at an annual rate of 5%.

Question 59

Your trust fund will pay you $100,000 in six years when you turn 25. A shady financial institution has encouraged you to sign away the rights to your trust fund in exchange for cash today. Would you prefer that the financial institution use a discount rate of 8% or 10% to determine the value of your lump sum payment? Why?

A) Use 8% because the lump sum payment of $62,741 is greater than the 10% discounted value of $55,839.
B) Use 10% because the lump sum payment of $62,741 is greater than the 10% discounted value of $55,839.
C) Use 8% because the lump sum payment of $63,017 is greater than the 10% discounted value of $56,447.
D) Use 10% because the lump sum payment of $63,017 is greater than the 10% discounted value of $56,447.

Question 60

To determine the present value of a future amount, one should ________ the future cash flows.

A) annuitize
B) compound
C) discount
D) multiply

Question 61

Four years ago, Robert's annual salary was $52,500. Today, he earns $73,800. What has been the average annual rate of growth of Robert's salary?

A) $5,325 per year
B) 10.38%
C) 41.52%
D) 8.89%

Question 62

Your grandfather likes to tell the story about how he started with 50 head of cattle on his ranch and grew the ranch to 1,000 head of cattle. He said "My plan was simple: grow the number of head of cattle at a rate of 10% per year." Your grandfather reached his goal before he retired. How long did it take him?

A) 18.63 years
B) 31.43 years
C) 25.22 years
D) 47.65 years

Question 63

Madison is taking over as Chief Marketing Officer at MidWest Graphics. She has pledged to increase sales from their current level of $12,000,000 at a rate of 10% per year until the firm hits sales of $20,000,000 per year. How long will it take Madison to hit the target goal at this rate of increase?

A) 7.67 years
B) 1.53 years
C) 5.36 years
D) At that rate, Madison will never reach the target sales level in her lifetime.

Question 64

You have just won the university lottery. If you graduate, you will receive a refund equal to the amount of tuition you paid in your first four years of school. However, you need money now and a firm that specializes in buying expected future cash flows has offered to discount the lottery winnings at a rate of 8% and pay you cash today in exchange for your future lottery winnings. Since you have studied finance, you insist that they discount the cash flows at 12% instead of 8% because there is some risk as to the certainty of your graduating. If the firm agrees to your demand, then this means they will increase the present value of what they will pay you today.

Question 65

Current annual dividends for Simpson's Frozen Foods Inc., are $1.35 per share. Four years ago, dividends per share were exactly $1.00. What has been the rate of growth for Simpsons dividends per share?

Question 66

Even if you are given a present value, a single future value, and a time period, solving for the rate of return, r, is still a trial-and-error process.

Question 67

The question "At what rate is my money growing over time?" is best answered by which form of the TVM equation?

Question 68

The question "What is the current value of an amount of cash that will be received at a specific time in the future?" is best answered by which form of the TVM equation?

Question 69

Simpson Construction had sales seven years ago of $2,150,000. This year their sales hit $4,600,000. What has been Simpson's average annual rate of growth of sales?

A) 30.56%
B) 11.48%
C) $350,000 per year
D) None of the above

Question 70

Even if you are given a present value, a future value, and an interest rate, solving for the time period "n" is still a trial-and-error process.

Question 71

Dividend growth rate is important to many investors. You are considering investing in a firm after looking at the firm's dividends over a seven-year period. At the end of the year 2002, the firm paid a dividend of $1.15. At year-end 2009, it paid a dividend of $1.84. What was the average annual growth rate of dividends for this firm?

A) 7.25%
B) 9.86%
C) 6.94%
D) There is not enough information to answer this question.

Question 72

Upon taking his first job out of college, your Dad earned an annual salary of $38,000 and set a goal to earn $100,000 per year. If his salary increased at an average annual rate of 12%, how long did it take to reach his goal?

A) At that rate of growth, your Dad still has not earned $100,000 in a single year.
B) 2.63 years
C) 26.31 years
D) 8.54 years

Question 73

You have saved $1,200 for a used motorcycle that has a current price of $1,500. If your money is sitting in an account earning 2.50% per year, how long will it take for this account to grow to $1,500? Note: The motorcycle's price may have changed by the time your account reaches a value of $1,500.

A) 9.04 months
B) 9.04 years
C) 4.25 years
D) 4.25 months

Question 74

The question "How long will I have to wait to reach a certain future value?" is best answered by which form of the TVM equation?

Question 75

At your birth, your grandparents put $5,000 into a college fund for you. Now you want to use the fund to pay your first year of college costs of $23,000. To have enough money in your college fund for your stated purpose, what annual rate of return would have to have been earned on the account over an 18-year period?

Question 76

You gave your little sister two rabbits for Easter three years ago and now she has 84 of the cute little bunnies. What is the average annual rate of increase in the number of rabbits your sister owns? Note: Your parents are not very pleased with you right now.

A) 247.60%
B) 14.00%
C) 410.00%
D) The TVM equations are designed for currency amounts and cannot be used for non-financial calculations such as this one.

Question 77

You currently have $2,500 invested at an annual rate of 8%. How long will it take for this investment to grow to a value of $3,500?

A) 4.37 years
B) 5.00 years
C) 5.60 years
D) 8.03 years

Question 78

The Millville School District had 3,071 students enrolled five years ago. Today, the district enrollment is 2,418 students. What has been the annual rate of change of student enrollment in the Millville School District over this time period?

A) -5.40%
B) -4.25%
C) -4.67%
D) 4.25%

Question 79

Consider the TVM equation: the variable "r" may be defined as the discount rate or the growth rate depending upon how the equation is being used.

Question 80

Other things remaining equal, the price today and the growth rate are inversely related.