Deck 5: Introduction to Valuation: The Time Value of Money

Question 1

Your goal is to have $1 million in your retirement savings on the day you retire. To fund this goal, you will make one lump sum deposit today. If you plan to retire ________ rather than ________ and earn a ________ rate of interest, then you can deposit a smaller lump sum today.

A) sooner; later; low
B) sooner; later; high
C) later; sooner; high
D) later; sooner; low
E) today; later; high

Answer 1

later; sooner; high

Question 2

The interest earned on both the initial principal and the interest reinvested from prior periods is called:

A) free interest.
B) dual interest.
C) simple interest.
D) interest on interest.
E) compound interest.

Answer 2

compound interest.

Question 3

Andy deposited $3,000 this morning into an account that pays 5 percent interest, compounded annually. Barb also deposited $3,000 this morning at 5 percent interest, compounded annually. Andy will withdraw his interest earnings and spend it as soon as possible. Barb will reinvest her interest earnings into her account. Given this, which one of the following statements is true?

A) Barb will earn more interest in Year 1 than Andy will.
B) Andy will earn more interest in Year 3 than Barb will.
C) Barb will earn more interest in Year 2 than Andy.
D) After five years, Andy and Barb will both have earned the same amount of interest.
E) Andy will earn compound interest.

Answer 3

Barb will earn more interest in Year 2 than Andy.

Question 4

Which one of the following variables is the exponent in the present value formula?

A) Present value
B) Future value
C) Interest rate
D) Number of time periods
E) There is no exponent in the present value formula.

Question 5

Terry is calculating the present value of a bonus he will receive next year. The process he is using is called:

A) growth analysis.
B) discounting.
C) accumulating.
D) compounding.
E) reducing.

Question 6

Which one of these will increase the present value of a set amount to be received sometime in the future?

A) Increase in the time until the amount is received
B) Increase in the discount rate
C) Decrease in the future value
D) Decrease in the interest rate
E) Decrease in both the future value and the number of time periods

Question 7

Chang Lee is going to receive $20,000 six years from now. Soo Lee is going to receive $20,000 nine years from now. Which one of the following statements is correct if both individuals apply a discount rate of 7 percent?

A) The present values of Chang Lee's and Soo Lee's money are equal.
B) In future dollars, Soo Lee's money is worth more than Chang Lee's money.
C) In today's dollars, Chang Lee's money is worth more than Soo Lee's.
D) Twenty years from now, the value of Chang Lee's money will equal the value of Soo Lee's money.
E) Soo Lee's money is worth more than Chang Lee's money given the 7 percent discount rate.

Question 8

Which one of the following will produce the lowest present value interest factor?

A) 6 percent interest for 5 years
B) 6 percent interest for 8 years
C) 6 percent interest for 10 years
D) 8 percent interest for 5 years
E) 8 percent interest for 10 years

Question 9

The process of determining the present value of future cash flows in order to know their value today is referred to as:

A) compound interest valuation.
B) interest on interest valuation.
C) discounted cash flow valuation.
D) future value interest factoring.
E) complex factoring.

Question 10

Kurt won a lottery and will receive $1,000 a year for the next 50 years. The current value of these winnings is called the:

A) single amount.
B) future value.
C) present value.
D) simple amount.
E) compounded value.

Question 11

This afternoon, you deposited $1,000 into a retirement savings account. The account will compound interest at 6 percent annually. You will not withdraw any principal or interest until you retire in 40 years. Which one of the following statements is correct?

A) The interest you earn in Year 6 will equal the interest you earn in Year 10.
B) The interest amount you earn will double in value every year.
C) The total amount of interest you will earn will equal $1,000 × .06 × 40.
D) The present value of this investment is equal to $1,000.
E) The future value of this amount is equal to $1,000 × (1 + 40).⁰⁶.

Question 12

Nan and Neal are twins. Nan invests $5,000 at 7 percent at age 25. Neal invests $5,000 at 7 percent at age 30. Both investments compound interest annually. Both twins retire at age 60 and neither adds nor withdraws funds prior to retirement. Which statement is correct?

A) Nan will have less money when she retires than Neal.
B) Neal will earn more interest on interest than Nan.
C) Neal will earn more compound interest than Nan.
D) If both Nan and Neal wait to age 70 to retire they will have equal amounts of savings.
E) Nan will have more money than Neal at any age.

Question 13

Your grandmother has promised to give you $10,000 when you graduate from college. If you speed up your graduation by one year and graduate two years from now rather than the expected three years, the present value of this gift will:

A) remain constant.
B) increase.
C) decrease.
D) equal $10,000.
E) be less than $10,000.

Question 14

Sam just opened a savings account paying 3.5 percent interest, compounded annually. After four years, the savings account will be worth $5,000. Assume there are no additional deposits or withdrawals. Given this, Sam:

A) will earn the same amount of interest each year for four years.
B) will earn simple interest on his savings every year for four years.
C) could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest.
D) has an account currently valued at $5,000.
E) could earn more interest on this account if the interest earnings were withdrawn annually.

Question 15

You are investing $100 today in a savings account. Which one of the following terms refers to the total value of this investment one year from now?

A) Future value
B) Present value
C) Principal amount
D) Discounted value
E) Invested principal

Question 16

Christina invested $3,000 five years ago and earns 2 percent annual interest. By leaving her interest earnings in her account, she increases the amount of interest she earns each year. The way she is handling her interest income is referred to as:

A) simplifying.
B) compounding.
C) aggregating.
D) accumulating.
E) discounting.

Question 17

Art invested $100 two years ago at 8 percent interest. The first year, he earned $8 interest on his $100 investment. He reinvested the $8. The second year, he earned $8.64 interest on his $108 investment. The extra $.64 he earned in interest the second year is referred to as:

A) free interest.
B) bonus income.
C) simple interest.
D) interest on interest.
E) present value interest.

Question 18

Renee invested $2,000 six years ago at 4.5 percent interest. She spends all of her interest earnings immediately so she only receives interest on her initial $2,000 investment. Which type of interest is she earning?

A) Free interest
B) Complex interest
C) Simple interest
D) Interest on interest
E) Compound interest

Question 19

Steve just computed the present value of a $10,000 bonus he will receive next year. The interest rate he used in his computation is referred to as the:

A) current yield.
B) effective rate.
C) compound rate.
D) simple rate.
E) discount rate.

Question 20

What is the relationship between the present value and future value interest factors?

A) The present value and future value factors are equal to each other.
B) The present value factor is the exponent of the future value factor.
C) The future value factor is the exponent of the present value factor.
D) The factors are reciprocals of each other.
E) There is no relationship between these two factors.

Question 21

Marti's coin collection contains fifty 1948 silver dollars. Her grandparents purchased them at their face value in 1948. These coins have appreciated by 7.6 percent annually. How much will the collection be worth in 2025?

A) $13,611.18
B) $18,987.56
C) $14,122.01
D) $11,218.27
E) $14,077.16

Question 22

Suppose the first comic book of a classic series was sold in 1954. In 2017, the estimated price for this comic book was $310,000, which is an annual return of 22 percent. For this to be true, what was the original price of the comic book in 1954?

A) $1.00
B) $.97
C) $1.33
D) $1.12
E) $1.20

Question 23

You just invested $49,000 that you received as an insurance settlement. How much more will this account be worth in 40 years if you earn an average return of 7.6 percent rather than just 7.1 percent?

A) $59,818.92
B) $98,509.16
C) $140,423.33
D) $155,986.70
E) $138,342.91

Question 24

You will receive $15,000 in two years when you graduate. You plan to invest this at an annual interest rate of 6.5 percent. How much money will you have 8 years from now?

A) $24,824.94
B) $19,381.16
C) $21,887.13
D) $23,209.19
E) $20,414.73

Question 25

Today, you earn a salary of $31,000. What will be your annual salary ten years from now if you receive annual raises of 2.2 percent?

A) $38,536.36
B) $37,414.06
C) $38,235.24
D) $37,122.08
E) $36,736.00

Question 26

You hope to buy your dream car five years from now. Today, that car costs $62,500. You expect the price to increase by an average of 2.9 percent per year. How much will your dream car cost by the time you are ready to buy it?

A) $73,340.00
B) $68,666.67
C) $72,103.59
D) $66,818.02
E) $69,023.16

Question 27

You own a classic car currently valued at $64,000. If the value increases by 2.5 percent annually, how much will the car be worth 15 years from now?

A) $94,035.00
B) $86,008.17
C) $80,013.38
D) $92,691.08
E) $91,480.18

Question 28

You invested $6,500 at 6 percent simple interest. How much more could you have earned over a 10-year period if the interest had compounded annually?

A) $1,049.22
B) $930.11
C) $1,182.19
D) $1,201.15
E) $1,240.51

Question 29

You have a savings account valued at $1,500 today that earns an annual interest rate of 8.7 percent. How much more would this account be worth if you wait to spend the entire balance in 25 years rather than in 20 years?

A) $6,306.16
B) $4,658.77
C) $3,311.18
D) $6,907.17
E) $4,117.64

Question 30

This morning, DJ's invested $225,000 to help fund future projects. How much additional money will the firm have three years from now if it can earn an annual interest rate of 4 percent rather than 3.5 percent?

A) $3,391.90
B) $3,632.88
C) $3,008.17
D) $4,219.68
E) $3,711.08

Question 31

Today, you have two coins each of which is valued at $100. One coin is expected to appreciate by 5.2 percent annually while the other coin should appreciate by 5.7 percent annually. What will be the difference in the value of the two coins 50 years from now?

A) $337.43
B) $318.04
C) $191.79
D) $128.32
E) $380.15

Question 32

What is the future value of $11,600 invested for 17 years at 7.25 percent compounded annually?

A) $32,483.60
B) $27,890.87
C) $38,991.07
D) $41,009.13
E) $38,125.20

Question 33

Your father invested a lump sum 28 years ago at 4.05 percent annual interest. Today, he gave you the proceeds of that investment, totalling $48,613.24. How much did your father originally invest?

A) $14,929.47
B) $16,500.00
C) $15,994.70
D) $15,500.00
E) $16,099.45

Question 34

Twenty years from now, you want to spend $175,000 for a fancy car. How much must you deposit as a lump sum today to achieve this goal at an annual interest rate of 6.6 percent?

A) $54,208.16
B) $48,740.95
C) $57,911.08
D) $40,019.82
E) $51,446.60

Question 35

Alex invested $2,550 in an account that pays 5 percent simple interest. How much money will he have at the end of four years?

A) $2,650.00
B) $3,100.26
C) $3,060.00
D) $3,250.00
E) $3,099.54

Question 36

You just received a $5,000 gift from your grandmother which you have decided to save and then gift to your grandchildren 50 years from now. How much additional money will you gift if you earn 7.5 percent interest rather than 7 percent interest over the next 50 years?

A) $39,318.09
B) $39,464.79
C) $38,211.16
D) $37,811.99
E) $38,663.60

Question 37

Travis invested $8,000 in an account that pays 4 percent simple interest. How much more could he have earned over a 7-year period if the interest had compounded annually?

A) $291.41
B) $287.45 
C) $302.16
D) $266.67
E) $258.09

Question 38

You are depositing $4,500 today at an annual interest rate of 7.2 percent. How much additional interest will you earn if you leave the money invested for 45 years instead of 40 years?

A) $25,723.08
B) $30,185.14
C) $22,441.56
D) $6,370.69
E) $11,590.93

Question 39

Al invested $3,630 in an account that pays 6 percent simple interest. How much money will he have at the end of five years?

A) $4,910
B) $5,056
C) $4,719
D) $4,678
E) $5,299

Question 40

Phillippe invested $1,000 ten years ago and expected to have $1,800 today He has neither added nor withdrawn any money since his initial investment. All interest was reinvested and compounded annually. As it turns out, he only has $1,680 in his account today. Which one of the following must be true?

A) He earned simple interest rather than compound interest.
B) He earned a lower interest rate than he expected.
C) He did not earn any interest on interest as he expected.
D) He ignored the Rule of 72 which caused his account to decrease in value.
E) The future value interest factor turned out to be higher than he expected.

Question 41

Some time ago, Tracie purchased two acres of land costing $67,900. Today, that land is valued at $64,800. How long has she owned this land if the price of the land has been decreasing by 1.5 percent per year?

A) 3.33 years
B) 2.48 years
C) 3.09 years
D) 2.97 years
E) 2.08 years

Question 42

Towne Station is saving money to build a new loading platform. Three years ago, they set aside $23,000 for this purpose. Today, that account is worth $31,406. What rate of interest is Towne Station earning on this investment?

A) 8.39 percent
B) 9.47 percent
C) 10.94 percent
D) 8.23 percent
E) 9.01 percent

Question 43

At 5 percent interest, how long would it take to triple your money?

A) 26.55 years
B) 25.64 years
C) 24.87 years
D) 22.52 years
E) 20.01 years

Question 44

According to the Rule of 72, you can do which one of the following?

A) Approximately double your money in five years at 7.24 percent interest
B) Double your money in 7.2 years at 8 percent interest
C) Approximately double your money in 11 years at 6.55 percent interest
D) Triple your money in 7.2 years at 7.2 percent interest
E) Approximately triple your money in 7.2 years at 10 percent interest

Question 45

Friendly Companies has an unfunded pension liability of $327 million that must be paid in 16 years. What is the present value of this liability at a discount rate of 6.24 percent?

A) $129,803,162.22
B) $111,438,907.11
C) $124,147,723.50
D) $134,519,484.14
E) $121,511,366.67

Question 46

Ten years ago, Jackson Supply set aside $125,000 in case of a financial emergency. Today, that account has increased in value to $278,592. What rate of interest is the firm earning on this money?

A) 8.80 percent
B) 8.34 percent
C) 7.75 percent
D) 8.01 percent
E) 7.87 percent

Question 47

Sixty years ago, your mother invested $4,500. Today, that investment is worth $430,065.11. What is the average annual rate of return she earned on this investment?

A) 6.67 percent
B) 11.71 percent
C) 7.90 percent
D) 10.40 percent
E) 12.02 percent

Question 48

One year ago, you invested $1,750. Today it is worth $1,815.48. What rate of interest did you earn?

A) 3.59 percent
B) 4.33 percent
C) 3.88 percent
D) 3.74 percent
E) 4.01 percent

Question 49

You would like to give your child $100,000 to start a career 25 years from now. How much money must you set aside today for this purpose if you can earn 7.5 percent on your investments?

A) $15,388.19
B) $16,397.91
C) $16,817.67
D) $15,911.13
E) $17,488.37

Question 50

On your tenth birthday, you received $300 which you invested at 4.5 percent interest, compounded annually. Your investment is now worth $756. How old are you today?

A) Age 20
B) Age 31
C) Age 30
D) Age 23
E) Age 21

Question 51

What is the present value of $45,000 to be received 50 years from today if the discount rate is 8 percent?

A) $959.46
B) $1,147.07
C) $841.41
D) $1,106.18
E) $1,291.06

Question 52

Four years ago, Saul invested $500. Three years ago, Trek invested $600. Today, these two investments are each worth $800. Assume each account continues to earn its respective rate of return. Which one of the following statements is correct concerning these investments?

A) Three years from today, Trek's investment will be worth more than Saul's.
B) One year ago, Saul's investment was worth less than Trek's investment.
C) Trek earns a higher rate of return than Saul.
D) Trek has earned an average annual interest rate of 9.86 percent.
E) Saul has earned an average annual interest rate of 12.64 percent.

Question 53

When you retire 45 years from now, you want to have $1.25 million saved. You think you can earn an average of 7.6 percent on your investments. To meet your goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum five years from today to fund this goal. How much more will you have to deposit if you wait for five years before making the deposit?

A) $17,414.14
B) $21,319.47
C) $19,891.11
D) $20,468.85
E) $13,406.78

Question 54

Twelve years ago, your parents set aside $8,000 to help fund your college education. Today, that fund is valued at $23,902. What rate of interest is being earned on this account?

A) 8.99 percent
B) 9.42 percent
C) 9.67 percent
D) 9.55 percent
E) 9.06 percent

Question 55

You want to have $30,000 saved 5 years from now to buy a house. How much less do you have to deposit today to reach this goal if you can earn 3.5 percent rather than 2.5 percent on your savings? Today's deposit is the only deposit you will make to this savings account.

A) $1,256.43
B) $891.18
C) $1,124.60
D) $945.11
E) $1,219.02

Question 56

Assume the total cost of a college education will be $245,000 when your child enters college in 15 years. You presently have $108,000 to invest for this purpose. What rate of interest must you earn to cover the cost of your child's college education?

A) 5.79 percent
B) 5.50 percent
C) 5.61 percent
D) 6.25 percent
E) 6.81 percent

Question 57

Theo wants to have $40,000 for a down payment on a house five years from now. He can either deposit one lump sum today or he can wait one year and deposit a lump sum. Assume an annual interest rate of 3.5 percent. How much additional money must he deposit if he waits for one year rather than making the deposit today?

A) $1,001.98
B) $986.13
C) $1,178.76
D) $948.03
E) $1,020.18

Question 58

You have just received notification that you have won the $1.25 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100ᵗʰ birthday, 79 years from now. The appropriate discount rate is 6.4 percent. What is the present value of your winnings?

A) $11,288.16
B) $9,300.82
C) $10,309.91
D) $8,333.33
E) $10,500.00

Question 59

Duane and Thad plan on retiring 27 years from today and plan to have the same amount saved at that time. In preparation for this, Duane is depositing $15,000 today at an annual interest rate of 5.2 percent. How will Thad's deposit amount vary from Duane's if Thad also makes a deposit today but earns an annual interest rate of 6.2 percent?

A) $4,118.42 more
B) $4,333.33 less
C) $3,417.09 more
D) $4,274.12 less
E) $3,381.39 less

Question 60

Your older sister deposited $2,500 today at 6.5 percent interest for 15 years. However, you can only earn 6.25 percent interest. How much more money must you deposit today than your sister did if you are to have the same amount saved at the end of the 15 years?

A) $92.19
B) $89.70
C) $88.78
D) $90.21
E) $93.39

Question 61

In 1903, the winner of a competition was paid $50. In 2017, the winner's prize was $235,000. What will the winner's prize be in 2040 if the prize continues increasing at the same rate? (Do not round intermediate calculations. Round your answer to the nearest $500.)

A) $1,080,000
B) $1,176,500
C) $1,250,000
D) $1,294,000
E) $1,188,500

Question 62

Assume the average vehicle selling price in the United States last year was $36,420. The average price five years earlier was $31,208. What was the annual increase in the selling price over this time period?

A) 1.67 percent
B) 3.14 percent
C) 2.56 percent
D) 3.01 percent
E) 2.89 percent

Question 63

You will receive $4,000 at graduation 3 years from now. You plan on investing this money at 5 percent annual interest until you have accumulated $50,000. How many years from today will it be when this occurs?

A) 51.42 years
B) 49.08 years
C) 54.77 years
D) 48.42 years
E) 51.77 years

Question 64

You're trying to save to buy a new $68,000 sports car. Currently, you have saved $36,840 which is invested at 4.9 percent annual interest. How many years will it be before you purchase the car, assuming the price of the car remains constant?

A) 9.67 years
B) 17.18 years
C) 12.81 years
D) 16.91 years
E) 10.84 years