Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

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

Accepted Answer

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 4

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.

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

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 6

Your sister paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year.What is the expected rate of return on this investment?

Accepted Answer

A)  6.77% 
B)  7.13% 
C)  7.50% 
D)  7.88% 
E)  8.27%

Question 7

Suppose you are buying your first home for $145,000, and you have $15,000 for your down payment.You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month.What will your monthly payments be?

Accepted Answer

A)  $741.57 
B)  $780.60 
C)  $821.69 
D)  $862.77 
E)  $905.91

Question 8

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

Accepted Answer

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 9

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

Accepted Answer

A) True 
 B)False

Question 10

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

Accepted Answer

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 11

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?

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Which of the following statements is CORRECT?

Accepted Answer

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 14

Your Aunt Elsa has $500,000 invested at 6.5%, and she plans to retire.She wants to withdraw $40,000 at the beginning of each year, starting immediately.What is the maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)

Accepted Answer

A)  18 
B)  19 
C)  20 
D)  21 
E)  22

Question 15

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?

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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.

Accepted Answer

A) True 
 B)False

Question 19

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?

Accepted Answer

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 20

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

Accepted Answer

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

Exam 4: Time Value of Money

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

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

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

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.

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

Your sister paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year.What is the expected rate of return on this investment?

Suppose you are buying your first home for $145,000, and you have $15,000 for your down payment.You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month.What will your monthly payments be?

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

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

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

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?

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

Which of the following statements is CORRECT?

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?

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

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

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.

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?

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