BUS 380 Ch. 5

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

FALSE

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

TRUE

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.

TRUE

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

TRUE

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

TRUE

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

TRUE

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. 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).

A

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. e. An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.

A

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. A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ. 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 ORD exceeds the present value of DUE, while the future value of DUE 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.

A

Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. d. Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods. e. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts.

B

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%.

B

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.

B

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.

B

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.

B

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 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. b. The discount rate decreases. c. The riskiness of the investment's cash flows increases.

B

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.

B

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 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 lower if the interest rate were lower. d. The last payment would have a higher proportion of interest than the first payment. e. The proportion of interest versus principal repayment would be the same for each of the 7 payments.

C

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.

C

Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities. e. Time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity.

C

Which of the following 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. e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.

C

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%.

C

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.

D

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.

D

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).

D

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.

D

Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods. e. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts.

D

Which of the following 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 ends of the periods. d. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month. e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.

D

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.

D

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%.

D

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 larger if interest were compounded monthly rather than semiannually. e. The PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year, $333.33 ordinary annuity.

E

Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities. e. Time lines can be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity.

E

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 the outstanding balance declines over time, the monthly payments will also decline over time. 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 faster rate in the later years of the loan's life

E

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

FALSE

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).

FALSE

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

FALSE

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

FALSE

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.

FALSE

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

FALSE

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

FALSE

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.)

FALSE

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.

FALSE

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.

FALSE

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.

FALSE

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

FALSE

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

FALSE

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.

FALSE

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

TRUE

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

TRUE

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).

TRUE

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

TRUE

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

TRUE

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.

TRUE

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.

TRUE

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

TRUE

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.)

TRUE

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.

TRUE

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.

TRUE