Deck 28: Time Value of Money

Question 1

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.

Answer 1

False

Question 2

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.)

Answer 2

False
Work out the numbers with a calculator:

Question 3

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.)

Answer 3

True
Work out the numbers with a calculator:

Question 4

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

Question 5

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

Question 6

Your bank offers a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. If you invest $2,000 in the CD, how much will you have when it matures?

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

Question 7

How much would Roderick have after 6 years if he has $500 now and leaves it invested at 5.5% with annual compounding?

A) $591.09
B) $622.20
C) $654.95
D) $689.42
E) $723.89

Question 8

Cochrane Associate's net sales last year were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?

A) $845.03
B) $889.51
C) $936.33
D) $983.14
E) $1,032.30

Question 9

Cyberhost Corporation's sales were $225 million last year. 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 10

Ellen now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding?

A) $205.83
B) $216.67
C) $228.07
D) $240.08
E) $252.08

Question 11

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

Question 12

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 13

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

Question 14

JG Asset Services is recommending that you invest $1,500 in 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 15

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

Question 16

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

Question 17

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

Question 18

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 19

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

Question 20

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 21

Your bank offers a savings account that pays 3.5% interest, compounded annually. How much will $500 invested today be worth at the end of 25 years?

A) $1,122.54
B) $1,181.62
C) $1,240.70
D) $1,302.74
E) $1,367.88

Question 22

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

Question 23

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 24

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

Question 25

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

Question 26

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

Question 27

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 28

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 29

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 30

Suppose a State of North Carolina bond will pay $1,000 ten years from now. If the going interest rate on these 10-year bonds is 5.5%, how much is the bond worth today?

A) $585.43
B) $614.70
C) $645.44
D) $677.71
E) $711.59

Question 31

Suppose a State of New Mexico 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 32

Suppose a Google.com bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year bonds is 4.25%, how much is the bond worth today?

A) $2,819.52
B) $2,967.92
C) $3,116.31
D) $3,272.13
E) $3,435.74

Question 33

The going rate of interest on a 5-year treasury bond is 4.25%. You have one that will pay $2,500 five years from now. How much is the bond worth today?

A) $1,928.78
B) $2,030.30
C) $2,131.81
D) $2,238.40
E) $2,350.32

Question 34

You expect to receive $5,000 in 25 years. How much is it worth today if the discount rate is 5.5%?

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

Question 35

Your bank offers a savings account that pays 3.5% interest, compounded annually. If you invest $1,000 in the account, then how much will it 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 36

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 37

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

Question 38

How much would $1, growing at 3.5% per year, be worth after 75 years?

A) $12.54
B) $13.20
C) $13.86
D) $14.55
E) $15.28

Question 39

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

Question 40

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 discount rate decreases.
B) 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.
C) the discount rate increases.
D) the riskiness of the investment's cash flows decreases.
E) 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.

Question 41

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 42

Which of the following statements is CORRECT?

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

Question 43

Your bank account pays a 5% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

A) the periodic rate of interest is 5% and the effective rate of interest is also 5%.
B) the periodic rate of interest is 1.25% and the effective rate of interest is 2.5%.
C) the periodic rate of interest is 5% and the effective rate of interest is greater than 5%.
D) the periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%.
E) the periodic rate of interest is 2.5% and the effective rate of interest is 5%.

Question 44

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

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

Question 45

What's the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?

A) $3,089
B) $3,251
C) $3,422
D) $3,602
E) $3,782

Question 46

What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?

A) $1,537.69
B) $1,618.62
C) $1,699.55
D) $1,784.53
E) $1,873.76

Question 47

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

Question 48

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?

A) $1,819
B) $1,915
C) $2,016
D) $2,117
E) $2,223

Question 49

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 50

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

Question 51

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

Question 52

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 53

Of the following investments, which 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 54

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

A) 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.
B) the present value of a 5-year, $250 annuity due will be lower than the pv of a similar ordinary annuity.
C) a 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.
D) a bank loan's nominal interest rate will always be equal to or less than its effective annual rate.
E) if an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%.

Question 55

At the end of 10 years, which of the following investments would have the highest future 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 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).
E) investment e pays $250 at the end of every year for the next 10 years (a total of 10 payments).

Question 56

Which of the following statements is CORRECT?

A) an investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.
B) the present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity due.
C) if a loan has a nominal annual rate of 7%, then the effective rate will never be less than 7%.
D) if a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.
E) the proportion of the payment that goes toward interest on a fully amortized loan increases over time.

Question 57

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 58

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

A) 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.
B) the present value of a 5-year, $250 annuity due will be lower than the pv of a similar ordinary annuity.
C) a 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.
D) a bank loan's nominal interest rate will always be equal to or greater than its effective annual rate.
E) if an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than 10%.

Question 59

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

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

Question 60

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 61

Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is invested to earn a guaranteed 5% rate of return. If inflation averages 2% per year, how much can she withdraw (to the nearest dollar) at the beginning of each year and keep the withdrawals constant in real terms, i.e., growing at the same rate as inflation and thus enabling her to maintain a constant standard of living?

A) $65,632
B) $72,925
C) $81,027
D) $89,130
E) $98,043

Question 62

You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9 more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be to enable you to reach your $50,000 target?

A) $3,008
B) $3,342
C) $3,676
D) $4,044
E) $4,448

Question 63

Suppose People's bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year. What is the effective annual rate on the loan?

A) 8.46%
B) 8.90%
C) 9.37%
D) 9.86%
E) 10.38%

Question 64

Suppose United Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan?

A) 8.24%
B) 8.45%
C) 8.66%
D) 8.88%
E) 9.10%

Question 65

Scott and Linda have been saving to pay for their daughter Casie's college education. Casie just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years?if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11).??So far, Scott and Linda have accumulated $15,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Casie's anticipated college costs?

A) $1,965.21
B) $2,068.64
C) $2,177.51
D) $2,292.12
E) $2,412.76

Question 66

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

Question 67

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

Question 68

Pacific Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay?

A) 3.72%
B) 4.13%
C) 4.59%
D) 5.05%
E) 5.56%

Question 69

You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?

A) $15,234.08
B) $16,035.88
C) $16,837.67
D) $17,679.55
E) $18,563.53

Question 70

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 71

Southwestern Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Woodburn Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Woodburn versus the rate charged by Southwestern?

A) 0.52%
B) 0.44%
C) 0.36%
D) 0.30%
E) 0.24%

Question 72

Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. An offer to lend you the $50,000 also comes from Community Bank, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?

A) 1.56%
B) 1.30%
C) 1.09%
D) 0.91%
E) 0.72%

Question 73

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

Question 74

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate?

A) 15.27%
B) 16.08%
C) 16.88%
D) 17.72%
E) 18.61%

Question 75

You are considering two equally risky annuities, each of which pays $25,000 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) 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.
B) a rational investor would be willing to pay more for due than for ord, so their market prices should differ.
C) 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.
D) the present value of ord exceeds the present value of due, and the future value of ord also exceeds the future value of due.
E) the present value of ord exceeds the present value of due, while the future value of due exceeds the future value of ord.

Question 76

American Express and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card's EFF%?

A) 18.58%
B) 19.56%
C) 20.54%
D) 21.57%
E) 22.65%

Question 77

You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

A) 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.
B) 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.
C) 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.
D) the present value of ord exceeds the present value of due, and the future value of ord also exceeds the future value of due.
E) 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 78

What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly?

A) $969
B) $1,020
C) $1,074
D) $1,131
E) $1,187

Question 79

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

Question 80

What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%?

A) $16,806
B) $17,690
C) $18,621
D) $19,601
E) $20,633