Deck 4: Time Value of Money

Question 1

A "growing annuity" is a cash flow stream that grows at a constant rate for a specified number of periods.

Answer 1

True

Question 2

If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate.

Answer 2

True

Question 3

Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.

Answer 3

True

Question 4

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date.

Question 5

Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.

Question 6

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.

Question 7

Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

Question 8

Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.

Question 9

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

Question 10

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

Question 11

A "growing annuity" is any cash flow stream that grows over time.

Question 12

Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Question 13

Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts.

Question 14

Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.

Question 15

If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.

Question 16

Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.

Question 17

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

Question 18

A time line is meaningful even if all cash flows do not occur annually.

Question 19

A time line is not meaningful unless all cash flows occur annually.

Question 20

If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series.

Question 21

Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

A) The periodic rate of interest is 2% and the effective rate of interest is 4%.
B) The periodic rate of interest is 8% and the effective rate of interest is greater than 8%.
C) The periodic rate of interest is 4% and the effective rate of interest is less than 8%.
D) The periodic rate of interest is 2% and the effective rate of interest is greater than 8%.
E) The periodic rate of interest is 8% and the effective rate of interest is also 8%.

Question 22

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal.

Question 23

You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would increase the calculated value of the investment?

A) If expected inflation remains constant but the market risk premium (rM − rRF) declines, the required return of Stock LB will decline but the required return of Stock HB will increase.
B) If both expected inflation and the market risk premium (rM − rRF) increase, the required return on Stock HB will increase by more than that on Stock LB.
C) If both expected inflation and the market risk premium (rM − rRF) increase, the required returns of both stocks will increase by the same amount.
D) Since the market is in equilibrium, the required returns of the two stocks should be the same.

Question 24

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan).

Question 25

The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant.

Question 26

Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Question 27

When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage declines in the loan's later years.

Question 28

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

Question 29

A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?

A) The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
B) If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
C) The cash flows for an annuity due must all occur at the beginning of the periods.
D) The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month.

Question 30

Which of the following statements is CORRECT?

A) Portfolio P has a standard deviation of 25% and a beta of 1.0.
B) Based on the information we are given, and assuming those are the views of the marginal investor, it is apparent that the two stocks are in equilibrium.
C) Portfolio P has more market risk than Stock A but less market risk than B.
D) Stock A should have a higher expected return than Stock B as viewed by the marginal investor.

Question 31

You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?

A) The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.
B) The discount rate increases.
C) The riskiness of the investment's cash flows decreases.
D) The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.
E) The discount rate decreases.

Question 32

When a loan is amortized, a relatively low percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage increases in the loan's later years.

Question 33

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan).

Question 34

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

Question 35

Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

A) The periodic rate of interest is 1.5% and the effective rate of interest is 3%.
B) The periodic rate of interest is 6% and the effective rate of interest is greater than 6%.
C) The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.
D) The periodic rate of interest is 3% and the effective rate of interest is 6%.
E) The periodic rate of interest is 6% and the effective rate of interest is also 6%.

Question 36

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

Question 37

All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases.

Question 38

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

Question 39

All other things held constant, the present value of a given annual annuity increases as the number of periods per year increases.

Question 40

Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal. This is true regardless of the original life of the loan or the interest rate on the loan.

Question 41

Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures?

A) $1,781.53
B) $1,870.61
C) $1,964.14
D) $2,062.34
E) $2,165.46

Question 42

Which of the following statements is CORRECT?

A) If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0.
B) If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost.
C) To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the FV of the negative CFs. It is impossible to find the value of I without a computer or financial calculator.
D) If you solve for I and get a negative number, then you must have made a mistake.
E) If CF0 is positive and all the other CFs are negative, then you can still solve for I.

Question 43

You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?

A) Bank 1; 6.1% with annual compounding.
B) Bank 2; 6.0% with monthly compounding.
C) Bank 3; 6.0% with annual compounding.
D) Bank 4; 6.0% with quarterly compounding.
E) Bank 5; 6.0% with daily (365-day) compounding.

Question 44

Which of the following investments would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.

A) Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments).
B) Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
C) Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
D) Investment D pays $2,500 at the end of 10 years (just one payment).
E) Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).

Question 45

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

A) The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.
B) A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.
C) A bank loan's nominal interest rate will always be equal to or greater than its effective annual rate.
D) If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than 10%.
E) Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit.

Question 46

Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.

Question 47

You are considering two equally risky annuities, each of which pays
$5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

A) The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.
B) If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.
C) If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.
D) The proportion of the payment that goes toward interest on a fully amortized loan increases over time.

Question 48

You are considering two equally risky annuities, each of which pays
$5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. 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.
E) If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.

Question 49

Which of the following bank accounts has the lowest effective annual return?

A) An account that pays 8% nominal interest with monthly compounding.
B) An account that pays 8% nominal interest with annual compounding.
C) An account that pays 7% nominal interest with daily (365-day) compounding.
D) An account that pays 7% nominal interest with monthly compounding.
E) An account that pays 8% nominal interest with daily (365-day) compounding.

Question 50

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

A) The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.
B) A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.
C) A bank loan's nominal interest rate will always be equal to or less than its effective annual rate.
D) If an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%.
E) Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit.

Question 51

Which of the following statements regarding a 15-year (180-month)
$125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

A) The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years.
B) Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant.
C) Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.
D) The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year.
E) The outstanding balance declines at a slower rate in the later years of the loan's life.

Question 52

Which of the following statements is CORRECT?

A) The present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity due.
B) If a loan has a nominal annual rate of 8%, then the effective rate will never be less than 8%.
C) If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.
D) The proportion of the payment that goes toward interest on a fully amortized loan increases over time.
E) An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.

Question 53

A $150,000 loan is to be amortized over 7 years, with annual end-of- year payments. Which of these statements is CORRECT?

A) The annual payments would be larger if the interest rate were lower.
B) If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan.
C) The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were lower.
D) The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher.
E) The proportion of interest versus principal repayment would be the same for each of the 7 payments.

Question 54

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?

A) The monthly payments will increase over time.
B) A larger proportion of the first monthly payment will be interest, and a smaller proportion will be principal, than for the last monthly payment.
C) The total dollar amount of interest being paid off each month gets larger as the loan approaches maturity.
D) The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%.
E) Exactly 10% of the first monthly payment represents interest.

Question 55

Which of the following statements is CORRECT?

A) If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0.
B) If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost.
C) To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the PV of the negative CFs. This is, essentially, a trial-and-error procedure that is easy with a computer or financial calculator but quite difficult otherwise.
D) If you solve for I and get a negative number, then you must have made a mistake.
E) If CF0 is positive and all the other CFs are negative, then you cannot solve for I.

Question 56

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?

A) The monthly payments will decline over time.
B) A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment.
C) The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity.
D) The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%.
E) Exactly 10% of the first monthly payment represents interest.

Question 57

Last year Rocco Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?

A) $271.74
B) $286.05
C) $301.10
D) $316.16
E) $331.96

Question 58

Which of the following statements is CORRECT?

A) Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
B) Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
C) Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
D) Investment D pays $2,500 at the end of 10 years (just one payment).

Question 59

Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. How much will you have when the CD matures?

A) $3,754.27
B) $3,941.99
C) $4,139.09
D) $4,346.04
E) $4,563.34

Question 60

A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT?

A) The periodic interest rate is greater than 3%.
B) The periodic rate is less than 3%.
C) The present value would be greater if the lump sum were discounted back for more periods.
D) The present value of the $1,000 would be smaller if interest were compounded monthly rather than semiannually.
E) The PV of the $1,000 lump sum has a higher present value than the PV of a 3-year, $333.33 ordinary annuity.

Question 61

How much would $5,000 due in 25 years be worth today if the discount rate were 5.5%?

A) $1,067.95
B) $1,124.16
C) $1,183.33
D) $1,245.61
E) $1,311.17

Question 62

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?

A) $16,576
B) $17,449
C) $18,367
D) $19,334
E) $20,352

Question 63

You want to quit your job and return to school for an MBA degree 3 years from now, and you plan to save $7,000 per year, beginning immediately. You will make 3 deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today?

A) $20,993
B) $22,098
C) $23,261
D) $24,424
E) $25,645

Question 64

Suppose a State of California bond will pay $1,000 eight years from now. If the going interest rate on these 8-year bonds is 5.5%, how much is the bond worth today?

A) $651.60
B) $684.18
C) $718.39
D) $754.31
E) $792.02

Question 65

You want to buy a new sports car 3 years from now, and you plan to save
$4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?

A) $11,973
B) $12,603
C) $13,267
D) $13,930
E) $14,626

Question 66

How much would $20,000 due in 50 years be worth today if the discount rate were 7.5%?

A) $438.03
B) $461.08
C) $485.35
D) $510.89
E) $537.78

Question 67

You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

A) 5.14
B) 5.71
C) 6.35
D) 7.05
E) 7.84

Question 68

Ten years ago, Spielberg Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in earnings per share (EPS) over the 10-year period?

A) 15.17%
B) 15.97%
C) 16.77%
D) 17.61%
E) 18.49%

Question 69

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

A) $4,750
B) $5,000
C) $5,250
D) $5,513
E) $5,788

Question 70

Chuck has $2,500 invested in a bank that pays 4% annually. How long will it take for his funds to double?

A) 14.39
B) 15.15
C) 15.95
D) 16.79
E) 17.67

Question 71

What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?

A) $11,262.88
B) $11,826.02
C) $12,417.32
D) $13,038.19
E) $13,690.10

Question 72

Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

A) 4.37%
B) 4.86%
C) 5.40%
D) 6.00%
E) 6.60%

Question 73

Five years ago, Greenery Inc. earned $1.50 per share. Its earnings this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period?

A) 15.54%
B) 16.36%
C) 17.18%
D) 18.04%
E) 18.94%

Question 74

You want to buy a new ski boat 2 years from now, and you plan to save
$8,200 per year, beginning one year from today. You will deposit your savings in an account that pays 6.2% interest. How much will you have just after you make the 2nd deposit, 2 years from now?

A) $15,260
B) $16,063
C) $16,908
D) $17,754
E) $18,642

Question 75

Last year Ellis Inc's earnings per share were $3.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Ellis' EPS to triple?

A) 9.29
B) 10.33
C) 11.47
D) 12.75
E) 14.02

Question 76

Wendy has $5,000 invested in a bank that pays 3.8% annually. How long will it take for her funds to triple?

A) 23.99
B) 25.26
C) 26.58
D) 27.98
E) 29.46

Question 77

How much would $100, growing at 5% per year, be worth after 75 years?

A) $3,689.11
B) $3,883.27
C) $4,077.43
D) $4,281.30
E) $4,495.37

Question 78

Suppose the U.S. Treasury offers to sell you a bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000. What interest rate would you earn if you bought this bond at the offer price?

A) 3.82%
B) 4.25%
C) 4.72%
D) 5.24%
E) 5.77%

Question 79

You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of
25 years?

A) $2,245.08
B) $2,363.24
C) $2,481.41
D) $2,605.48
E) $2,735.75

Question 80

You plan to invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $30,000?

A) 12.37
B) 13.74
C) 15.27
D) 16.97
E) 18.85