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12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

19. 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%.

20. 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%.

21. 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.

22. 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.