Deck 9: The Time Value of Money

Question 1

A home buyer signed a 20-year, 8% mortgage for $72,500. How much should the annual loan payments be? (Assume annual compounding.)

A) $5,560
B) $7,384
C) $8,074
D) $13,900

Answer 1

B

Question 2

Dr. J. wants to buy an IBM personal computer which will cost $2,788 four years from today. He would like to set aside an equal amount at the end of each year in order to accumulate the amount needed. He can earn a 7% annual return. How much should he set aside?

A) $697.00
B) $627.94
C) $823.15
D) $531.81

Answer 2

B

Question 3

In determining the compound sum of a single amount, one measures:

A) the future value of periodic payments at a given interest rate.
B) the present value of an amount discounted at a given interest rate.
C) the future value of an amount allowed to grow at a given interest rate.
D) the present value of periodic payments at a given interest rate.

Answer 3

C

Question 4

If you were to put $1,000 in the bank at 6% interest each year for the next 10 years, which table would you use to find the ending balance in your account?

A) Present value of $1
B) Future value of $1
C) Present value of an annuity of $1
D) Compound sum of an annuity of $1

Question 5

As the time period until receipt increases, the present value of an amount at a fixed interest rate:

A) decreases.
B) remains the same.
C) increases.
D) not enough information to tell.

Question 6

Ambrin Corp. expects to receive $2,000 per year for 10 years and $3,500 per year for the next 10 years. What is the present value of this 20 year cash flow? Use an 11% discount rate.

A) $19,038
B) $27,872
C) $32,391
D) $15,927

Question 7

Under what conditions must a distinction be made between money to be received today and money to be received in the future?

A) A period of recession
B) When idle money can earn a positive return
C) When there is no risk of nonpayment in the future
D) When current interest rates are different from expected future rates

Question 8

Mr. Blochirt is creating a university investment fund for his daughter. He will put in $850 per year at the end of each year for the next 15 years and expects to earn an 8% annual rate of return. How much money will his daughter have when she starts university?

A) $11,250
B) $12,263
C) $24,003
D) $23,079

Question 9

The FV_IFA for the future value of an annuity is 4.641 at 10% for 4 years. If we wish to accumulate $8,000 by the end of 4 years, how much should the annual payments be?

A) $2,500
B) $2,000
C) $1,724
D) $2,200

Question 10

As the interest rate increases, the present value of an amount to be received at the end of a fixed period:

A) increases.
B) decreases.
C) remains the same.
D) not enough information to tell.

Question 11

John Doeber borrowed $125,000 to buy a house. His loan cost was 11% and he promised to repay the loan over 15 years (amortization). How much are the monthly payments with semiannual compounding?

A) $1,146
B) $1,380
C) $1,421
D) $1,402

Question 12

Mr. Fish wants to build a house in 10 years. He estimates that the total cost will be $170,000. If he can put aside $10,000 at the end of each year, what rate of return must he earn in order to have the amount needed?

A) Between 11% and 12%
B) Between 8% and 9%
C) 17%
D) 14%

Question 13

The concept of time value of money is not important to financial decision making because:

A) it emphasizes earning a return on invested capital.
B) it recognizes that earning a return makes $1 worth more today than $1 received in the future.
C) it can be applied to future cash flows in order to compare different streams of income.
D) it emphasizes the historic interest paid.

Question 14

After 20 years, 100 shares of stock originally purchased for $1,000 was sold for $5,000. What was the annual yield on the investment? Choose the closest answer.

A) 19.00%
B) 5.00%
C) 12.70%
D) 8.38%

Question 15

Babe Ruth Jr. has agreed to play for the Toronto Blue Jays for $9 million per year for the next 10 years. What table would you use to calculate the value of this contract in today's dollars?

A) Present value of an annuity.
B) Present value of a single amount.
C) Future value of an annuity.
D) Future value of an annuity due.

Question 16

You are to receive $12,000 at the end of 5 years. The available yield on investments is 6%. Which table would you use to determine the value of that sum today?

A) Present value of an annuity of $1
B) Future value of an annuity
C) Present value of $1
D) Compound sum of $1

Question 17

A retirement plan guarantees to pay to you or your estate a fixed amount for 20 years. At the time of retirement you will have $73,425 to your credit in the plan. The plan anticipates earning 9% interest. How much will your annual benefits be?

A) $1,435
B) $3,671
C) $6,608
D) $8,043

Question 18

An annuity may be defined as:

A) a payment at a fixed interest rate.
B) a series of payments of unequal amount.
C) a series of yearly payments.
D) a series of consecutive payments or receipts of equal amounts.

Question 19

A dollar today is worth more than a dollar to be received in the future because:

A) risk of nonpayment in the future.
B) the dollar can be invested today and earn interest.
C) inflation will reduce purchasing power of a future dollar.
D) a dollar today is not worth more than a dollar to be received in the future.

Question 20

Mr. Nailor invests $5,000 in a certificate of deposit at his local bank. He receives annual interest of 8% for 7 years. How much interest will his investment earn during this time period?

A) $2,915
B) $3,569
C) $6,254
D) $8,570

Question 21

Carol Thomas will pay out $6,000 at the end of the year 2, $8,000 at the end of year 3, and receive $10,000 at the end of year 4. With an interest rate of 13%, how much money does she need to have on hand today to meet her obligations?

A) $4,110
B) $10,243
C) $14,000
D) $4,000

Question 22

The future value of a $1,000 investment today at 8% annual interest compounded semiannually for 5 years is:

A) $1,469
B) $1,480
C) $1,520
D) $1,555

Question 23

As the discount rate becomes higher and higher, the present value of inflows approaches:

A) zero.
B) minus infinity.
C) plus infinity.
D) need more information.

Question 24

Mr. Darden is selling his house for $165,000. He bought it for $55,000 nine years ago. What is the annual return on his investment?

A) 13%
B) 22%
C) 33%
D) 16%

Question 25

If we wish to accumulate $8,000 by the end of 4 years, how much should the annual payments be if we receive an interest rate of 10% on our investments? The first payment is made at the end of each year.

A) $1,379.24
B) $1,567.06
C) $1,723.77
D) $2,000.00

Question 26

To find the yield on investments that require the payment of a single amount initially, and which then return a single amount sometime in the future, the correct table to use is:

A) the future value of $1.
B) the compound sum of $1.
C) present value of an annuity of $1.
D) present value of an annuity due of $1.

Question 27

Sharon Smith will receive $1,000,000 in 50 years. The discount rate is 14%. As an alternative she can receive $2,000 today. Which should she choose?

A) The $1,000,000 in 50 years.
B) The $2,000 today.
C) She should be indifferent.
D) It depends on the inflation rate.

Question 28

As the interest rate decreases, the present value of an amount to be received at the end of a fixed period:

A) increases.
B) decreases.
C) remains the same.
D) not enough information to tell.

Question 29

Janice Hardin sets aside $5,000 each year for 10 years. She then withdraws the funds on an equal annual basis for the next 10 years. The two tables she should use in the correct order are:

A) present value of an annuity of $1; future value of an annuity of $1.
B) future value of an annuity of $1; present value of an annuity of $1.
C) future value of an annuity of $1; present value of $1.
D) future value of an annuity of $1; future value of $1.

Question 30

Mike Carlson will receive $10,000 a year from the end of the third year to the end of the 12^th year (10 payments). The discount rate is 10%. The present value today of this deferred annuity is:

A) $61,446
B) $55,860
C) $46,165
D) $50,782

Question 31

The shorter the length of time between a present value and its corresponding future value:

A) the lower the present value, relative to the future value.
B) the higher the present value, relative to the future value.
C) the higher the interest rate used in the present-valuation.
D) the lower the discount rate used.

Question 32

A 20-year mortgage with monthly payments has a principal outstanding of $125,000. Interest is at 8% compounded semi-annually. What are the monthly payments?

A) $833.33
B) $1,035.24
C) $1,045.55
D) $1,354.16

Question 33

You will deposit $2,000 today. It will grow for 6 years at 10% interest compounded semiannually. You will then withdraw the funds annually over the next 4 years. The annual interest rate is 8%. Your annual withdrawal will be:

A) $2,340
B) $4,332
C) $797
D) $1,084

Question 34

Lou Lewis borrows $10,000 to be repaid over 10 years with equal annual payments at 9 percent. Repayment of principal in the first year is:

A) $1,558.20.
B) $1,000.00.
C) $900.00.
D) $658.20.

Question 35

Increasing the number of periods will increase all of the following except:

A) the present value of an annuity.
B) the present value of $1.
C) the future value of $1.
D) the future value of an annuity.

Question 36

Pedro Gonzalez will invest $5,000 at the beginning of each year for the next 9 years. The current yield is 8%. What is the future value?

A) $45,000
B) $62,438
C) $67,433
D) $60,105

Question 37

The higher the discount rate used in determining the future value of a $1 annuity:

A) the greater the future value at the end of a period.
B) the smaller the future value at the end of a period.
C) the greater the present value at the beginning of a period.
D) none of the other answers are correct: the interest has no effect on the future value of an annuity.

Question 38

Football player Walter Johnson signs a contract calling for payments of $2,500,000 per year, to begin 10 years from now. To find the present value of this contract, which table or tables should you use?

A) The future value of $1
B) The future value of an annuity of $1 and the future value of $1
C) The present value of an annuity of $1 and the present value of $1
D) The present value of an annuity of $1

Question 39

If you were to put $5,000 in the bank at 4% interest each year for the next 8 years, which table would you use to find the ending balance in your account?

A) Present value of $1
B) Future value of $1
C) Present value of an annuity of $1
D) Future value of an annuity of $1

Question 40

Joe Nautilus has $120,000 and wants to retire. What return must his money earn so he may receive annual benefits of $20,000 for the next 14 years?

A) 12%
B) Between 12% and 13%
C) 14%
D) Greater than 15%

Question 41

You have decided to purchase a new home valued at $300,000. You have a 20% down payment the bank has offered to finance a mortgage at a rate of 3.25% over 30 years. What would be your biweekly payments?

A) 602
B) $1,204
C) $482
D) $241

Question 42

You can lease a vehicle today for 36 months. The dealer will guarantee a residual value of $10,000. If the cash price of the car is $38,000, and the financing is priced at 8.75%, what would be your monthly payment?

A) $1,204
B) $602
C) $960
D) $782

Question 43

Morgan

A) $22,122.59
B) $34,052.02
C) $54,000.00
D) $15,134.23
D) expects to receive $200 per month for 10 years and $250 per month for the next 10 years. What is the present value of this 20-year cash flow? Use a 10% discount rate, assuming monthly compounding.

Question 44

If an individual's cost of capital were 10%, he or she would prefer to receive $107 at the end of one year rather than $100 right now.

Question 45

A retirement plan guarantees to pay to you or your estate a fixed amount for 20 years. At the time of retirement you will have $250,000 to your credit in the plan. The plan anticipates earning 9% interest compounded monthly. How much will your monthly benefits be, paid at the end of each month?

A) $2,249.31
B) $1,024.59
C) $1,555.69
D) $1,894.24

Question 46

Canadian Coal Corporation (CCC) produced 420,000 metric tonnes of coal in 20X5. If CCC's coal production in 20X0 was 30,000 metric tonnes, what was CCC's average annual increase in production over the six years between 20X0 and 20X5?

A) 36.5%
B) 14.0%
C) 65.0%
D) 55.0%

Question 47

You will deposit $10,000 today. It will grow for 10 years at 10% interest compounded monthly. You will then withdraw the funds quarterly over the next 4 years. The annual interest rate over those 4 years is 8%. Your annual withdrawal will be:

A) $1691.90.
B) $1993.74.
C) $1789.37.
D) $660.87.

Question 48

After 10 years, 1,000 shares of stock originally purchased for $10/share was sold for $50/share. What was the annual yield on the investment? Choose the closest answer assuming annual compounding.

A) 500.00%
B) 5.00%
C) 12.70%
D) 17.46%

Question 49

Mr. Sheridan is selling his house for $280,000. He bought it for $55,000 15 years ago. What is the annual return on his investment, assuming monthly compounding?

A) 13.20%
B) 10.90%
C) 3.39%
D) 5.09%

Question 50

Dr. Russell wants to buy an expensive car which will cost $74,000 four years from today. He would like to set aside an equal amount at the end of each month in order to accumulate the amount needed. He can earn a 7% annual return. How much should he set aside?

A) $1,340.36
B) $1,541.67
C) $2,236.23
D) $1,109.44

Question 51

You can purchase a strip bond at $888 that has a term to maturity of 7 years. What would be the Yield-to-Maturity on this bond?

A) 5.71%
B) 3.25%
C) 1.71%
D) 2.89%

Question 52

Debby Robinson borrows $10,000 to be repaid over 10 years with equal annual payments at 9%. Repayment of principal in the second year is:

A) $1,558.20.
B) $1,000.00.
C) $717.44.
D) $658.20.

Question 53

As the time period until receipt decreases, the present value of an amount at a fixed interest rate:

A) decreases.
B) remains the same.
C) increases.
D) not enough information to tell.

Question 54

Laura Diane is creating a university investment fund for her son Leland. She will put in $71.00 per month at the end of each month for the next 15 years and expects to earn an 8% annual rate of return, compounded monthly. How much money will Leland have when he starts university?

A) $28,052.38
B) $12,780.00
C) $13,393.98
D) $24,568.71

Question 55

The longer the length of time between a present value and its corresponding future value,:

A) the lower the present value, relative to the future value.
B) the higher the present value, relative to the future value.
C) the higher the interest rate used in the present-valuation.
D) there is no difference.

Question 56

The time value of money is not a useful concept in determining the value of a bond or in capital investment decisions.

Question 57

Cheryl Gold signed a 20-year, 6% mortgage for $250,000. How much should the biweekly loan payments be? (Assume compounding biweekly.)

A) $576.92
B) $826.08
C) $509.62
D) $958.62

Question 58

What is the maximum price you would pay for an investment that guarantees a payment of $1,000 a month beginning immediately lasts for 15 years and yields 12%?

A) $84,155
B) $100,000
C) $62,832
D) $83,262

Question 59

An amount of money to be received in the future is worth less today than the stated amount.

Question 60

Ruth H. wants to build a house in 12 years. She estimates that the total cost will be $350,000. If she can put aside $20,000 at the end of each year, what rate of return must she earn in order to have the amount needed, assuming annual compounding?

A) Between 11% and 12%
B) Between 8% and 9%
C) 17%
D) 6.63%

Question 61

The future value of an annuity assumes that the payments are received at the end of the year and that the last payment does not compound.

Question 62

In determining the PV_IF for the present value of $1, one could use the reciprocal of the FV_IF for the future value of $1 at the same rate and time period.

Question 63

The formula FV = PV (1 + n)ⁱ will determine the present value of $1.

Question 64

If a single amount were put on deposit at a given interest rate and allowed to grow, its future value could be determined by reference to the future value of $1 table.

Question 65

Inflation is the most important reason that a dollar today is worth more than a dollar in the future.

Question 66

To determine the current worth of 4 annual payments of $1,000 at 4%, one would refer to a table for the present value of $1.

Question 67

In determining the future value of an annuity, the final payment is not compounded at all.

Question 68

The amount of annual payments necessary to accumulate a desired total can be found by reference to the present value of an annuity table.

Question 69

As the interest rate increases, the PV_IF for the present value of $1 increases.

Question 70

An annuity is a series of consecutive payments of equal amount.

Question 71

The amount of annual payments necessary to repay a mortgage loan can be found by reference to the present value of an annuity table.

Question 72

The interest factor for the future value of an annuity is simply the sum of the interest factors for the future value using the same number of periods.

Question 73

The interest factor for a future value (FV_IF) is equal to (1 + i)ⁿ.

Question 74

In paying off a mortgage loan, the amount of the periodic payment that goes toward the reduction of principal increases over the life of the mortgage.

Question 75

In evaluating capital investment projects, current outlays must be judged against the current value of future benefits.

Question 76

The interest factor for the present value of a single sum is equal to (1 + i)/i.

Question 77

The annualized return on an investment can be determined by reference to a table for the present value of $1.

Question 78

The future value is the same concept as the way money grows in a bank account.

Question 79

The time value of money concept is fundamental to the analysis of cash inflow and outflow decisions covering periods of over one year.

Question 80

The interest factor for the present value of a single amount is the inverse of the future value interest factor.