# FIN 534 Week 4 Quiz 3 (All Correct)

Question 1

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?

Answer

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.

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.

The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.

The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.

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.

2 points

Question 2

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?

Answer

The periodic interest rate is greater than 3%.

The periodic rate is less than 3%.

The present value would be greater if the lump sum were discounted back for more periods.

The present value of the $1,000 would be larger if interest were compounded monthly rather than semiannually.

The PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year, $333.33 ordinary annuity.

2 points

Question 3

Which of the following statements is CORRECT?

Answer

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

Time lines are useful for visualizing complex problems prior to doing actual calculations.

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

Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods.

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

2 points

Question 4

Which of the following statements is CORRECT?

Answer

The present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity due.

If a loan has a nominal annual rate of 8%, then the effective rate will never be less than 8%.

If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.

The proportion of the payment that goes toward interest on a fully amortized loan increases over time.

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

2 points

Question 5

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.

Answer

Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).

Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).

Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).

Investment D pays $2,500 at the end of 10 years (just one payment).

Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).

2 points

Question 6

Which of the following statements is CORRECT?

Answer

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.

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.

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.

If you solve for I and get a negative number, then you must have made a mistake.

If CF0

is positive and all the other CFs are negative, then you can still solve for I.

2 points

Question 7

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.

Answer

Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments).

Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).

Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).

Investment D pays $2,500 at the end of 10 years (just one payment).

Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).

2 points

Question 8

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?

Answer

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.

The discount rate decreases.

The riskiness of the investment’s cash flows increases.

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.

The discount rate increases.

2 points

Question 9

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

Answer

The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years.

Because the outstanding balance declines over time, the monthly payments will also decline over time.

Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.

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.

The outstanding balance declines at a faster rate in the later years of the loan’s life.

2 points

Question 10

Which of the following statements is CORRECT?

Answer

The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.

If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.

If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.

The proportion of the payment that goes toward interest on a fully amortized loan increases over time.

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

2 points

Question 11

Which of the following statements is CORRECT?

Answer

The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.

If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.

The cash flows for an annuity due must all occur at the ends of the periods.

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.

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.

2 points

Question 12

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

Answer

The periodic rate of interest is 2% and the effective rate of interest is 4%.

The periodic rate of interest is 8% and the effective rate of interest is greater than 8%.

The periodic rate of interest is 4% and the effective rate of interest is less than 8%.

The periodic rate of interest is 2% and the effective rate of interest is greater than 8%.

The periodic rate of interest is 8% and the effective rate of interest is also 8%.

2 points

Question 13

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

Answer

Bank 1; 6.1% with annual compounding.

Bank 2; 6.0% with monthly compounding.

Bank 3; 6.0% with annual compounding.

Bank 4; 6.0% with quarterly compounding.

Bank 5; 6.0% with daily (365-day) compounding.

2 points

Question 14

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

Answer

The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years.

Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant.

Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.

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.

The outstanding balance declines at a slower rate in the later years of the loan’s life.

2 points

Question 15

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

Answer

The monthly payments will decline over time.

A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment.

The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity.

The amount representing interest in the first payment would be…