Question 1

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 2

After receiving a reward for information leading to the arrest of a notorious criminal, you are considering investing it in an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Accepted Answer

A)  $50,753 
B)  $53,424 
C)  $56,236 
D)  $59,195 
E)  $62,311

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

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 5

Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Accepted Answer

A)  $5,493.71 
B)  $5,782.85 
C)  $6,087.21 
D)  $6,407.59 
E)  $6,744.83

Question 6

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 7

A perpetuity pays $85 per year and costs $950. What is the rate of return?

Accepted Answer

A)  8.95% 
B)  9.39% 
C)  9.86% 
D)  10.36% 
E)  10.88%

Question 8

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.)

Accepted Answer

A) True 
 B)False

Question 9

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 10

Because your mother is about to retire, she wants to buy an annuity that will provide her with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost her to buy the annuity today?

Accepted Answer

A)  $825,835 
B)  $869,300 
C)  $915,052 
D)  $963,213 
E)  $1,011,374

Question 11

Which of the following statements is CORRECT?

Accepted Answer

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.

Question 12

You want to purchase a motorcycle 4 years from now, and you plan to save $3,500 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today?

Accepted Answer

A)  $16,112 
B)  $16,918 
C)  $17,763 
D)  $18,652 
E)  $19,584

Question 13

Your cousin will sell you his coffee shop for $250,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be?

Accepted Answer

A)  $4,029.37 
B)  $4,241.44 
C)  $4,464.67 
D)  $4,699.66 
E)  $4,947.01

Question 14

Now that your uncle has decided to retire, he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today?

Accepted Answer

A)  $1,063,968 
B)  $1,119,966 
C)  $1,178,912 
D)  $1,240,960 
E)  $1,303,008

Question 15

Your investment advisor has recommended your invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $30,000?

Accepted Answer

A)  12.37 
B)  13.74 
C)  15.27 
D)  16.97 
E)  18.85

Question 16

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 17

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.

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

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%?

Accepted Answer

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

Question 20

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?

Accepted Answer

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

Exam 4: Time Value of Money

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

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

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?

Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

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

A perpetuity pays $85 per year and costs $950. What is the rate of return?

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

Because your mother is about to retire, she wants to buy an annuity that will provide her with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost her to buy the annuity today?

Which of the following statements is CORRECT?

You want to purchase a motorcycle 4 years from now, and you plan to save $3,500 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today?

Now that your uncle has decided to retire, he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today?

Your investment advisor has recommended your invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $30,000?

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

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.

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

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%?

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?